By Christopher Monckton of Brenchley
Well, we sent out our paper On an error in defining temperature feedback to a leading journal for review. The reviewers did not like it at all. “And, gracious! How Lord Lundy cried!”
We are persevering, though, for in our submission nothing the reviewers have said in any way undermines the scientific validity of our result, which I outlined here in a series some months back.
Here, I shall summarize our argument in layman’s terms (for a layman is what I am). If you want a more detailed account of the physics, Anthony has kindly posted a single-sheet scientific summary here:
error-summary (PDF)
After the brief account of our argument that follows, just for fun I shall set out the reviewers’ principal objections, together with our answers. Feel free to comment on whether we or the reviewers are right.
How climatologists forgot the Sun was shining
Climatologists trying to predict global warming forgot the sunshine in their sums. After correction of this startling error of physics, global warming will not be 2 to 4.5 K per CO2 doubling, as climate models imagine. It will be a small, slow, harmless and net-beneficial 1.17 K.
The Climate Model Intercomparison Project (CMIP5: Andrews+ 2012) had predicted that doubling CO2 will warm the world by 1.04 ± 0.1 K (before feedbacks act) and 3.37 ± 1.3 K (after feedbacks have acted). IPCC says 3.0 ± 1.5 K. Some papers (e.g. Murphy 2009) give high-end estimates up to 10 K per CO2 doubling.
Climatologists erred when they borrowed feedback mathematics from control theory without quite understanding it. They used a variant feedback system-gain equation that relied solely on small changes in reference temperature (before feedback) and in equilibrium temperature (after feedback). But the mainstream equation they borrowed from control theory uses entire, absolute temperatures in Kelvin, not just changes in temperature.
Their variant equation is a valid equation, for it constitutes the difference between two instances of the mainstream equation. However, in taking that difference, they effectively subtracted out the term for the 243.3 K emission temperature as it would have been at the Earth’s surface without non-condensing greenhouse gases, driven by the fact that the Sun is shining, as well as the term for the 11.5 K warming from the pre-industrial greenhouse gases.
Because they lost this vital information, their variant equation could not reliably yield the true system-gain factor – the ratio of equilibrium to reference temperature. Instead, they tried to find that factor, the Holy Grail of global warming studies, by hunting for individual feedbacks computer models’ outputs. They were looking for blunt needles in the wrong haystack, when all they needed (if only they had known it) was a pin they already had.
Measurement and observation cannot tell us the magnitudes of individual feedbacks, and cannot help us to distinguish individual feedbacks either from each other from the manmade warmings that triggered them.
Restoring the missing sunshine and pre-industrial greenhouse-gas warming allows anyone to calculate the true system-gain factor. The calculation is direct, swift and accurate. You do not even need to know the magnitude of any individual feedback. All you need are the entire reference temperature (before feedback) and equilibrium temperature (after feedback) in any chosen year.
In 1850, reference temperature – the sum of the 243.3 K warming from the Sun and a further 11.5 K from the pre-industrial non-condensing greenhouse gases – was 254.8 K. The measured equilibrium surface temperature was 287.5 K (HadCRUT4). Therefore, the feedback system-gain factor for that year was 287.5 / 254.8, or 1.13.
Using the variant equation, however, one cannot derive the system-gain factor for 1850 at all.
By 2011, manmade influences had increased reference temperature by 0.68 K to 255.5 K. Measured temperature had risen by 0.75 K, but another 0.27 K that might not yet have come through because of an imagined “radiative imbalance” has to be allowed for, raising equilibrium temperature by 1.02 K to 288.5 K. Therefore, the system-gain factor for 2011 was 288.5 / 255.5, or 1.13.
That 2011 value is just as it was in 1850. It is not difficult to see why. The 254.8 K reference temperature in 1850 that was left out of climatologists’ sums is about 375 times the 0.68 K manmade reference warming from 1850 to 2011. That is why our effect on the system-gain factor is minuscule.
The climate stability evident after correcting climatologists’ striking error of physics should come as no surprise. For more than 800,000 years, according to analyses of air trapped in ancient ice (Jouzel+ 2006), global mean surface temperature has varied by little more than 3 K either side of the average temperature for the period.
Though IPCC (2013) mentions “feedback” 1000 times, feedback can be ignored with very little error. The system-gain factor may be taken as constant at 1.13. The non-linearity in feedbacks that climatologists had imagined makes very little difference.
Using the variant equation, the system-gain factor would be 1.02 / 0.68, i.e, 1.50, and the equilibrium warming from doubled CO2 would thus be 1.50 times the reference warming of 1.04 K in response to doubled CO2: i.e., 1.55 K. Even that value is only half the 3.37 K mid-range estimate in the CMIP5 models.
Using the mainstream equation, though, the true equilibrium warming from doubled CO2 is even smaller. It is 1.13 times the reference warming of 1.04 K: i.e., a harmless 1.17 K. To make sure, ten separate official estimates of manmade radiative forcing were studied. In each case, global warming in response to doubled CO2 was 1.17 K.
A statistical Monte Carlo simulation showed the true range of global warming as 1.08 to 1.25 K.
The control theory underlying the present result was verified on two test rigs, one of them at a government laboratory.
Climatologists had imagined that individual temperature feedbacks would self-cancel, except for water vapor, the largest. The atmosphere can carry 7% more water vapor for each Kelvin of warming. Can, not must. Models had predicted that, if and only if warming were manmade, the tropical upper air would warm at thrice the surface rate. Yet the water-vapor content up there is falling. Therefore, the tropical mid-troposphere “hot spot” does not exist.
Bottom line: global warming is not a problem after all. Enjoy the sunshine climatologists forgot about.
Reviewers’ comments, and our responses
“Simply inserting emission temperature in place of anthropogenic surface warming in the equations, and proceeding as before, is a massive violation of energy conservation.”
Um, no. One of my co-authors, John Whitfield, built a test rig – effectively an analog computer – to verify the control theory underlying our argument. There was certainly no “massive violation of energy conservation”. Instead, the outputs from the rig, in 23 distinct experiments, confirmed our understanding in all respects.
To make assurance doubly sure, we commissioned a government laboratory to build a test rig to its own design and to carry out the same 23 experiments. The results agreed with what the theory had led us to predict, and did so to the equivalent of a tenth of a Kelvin in each case. If there had been any “massive violation of energy conservation”, it would definitely have shown up in the experiments. It didn’t.
Besides, the reviewer had provided no evidence or argument whatsoever to justify the nonsensical assertion that our method was a “massive violation of energy conservation”.
“Instead of feeding in the perturbation temperature and asking what the perturbation in the top-of-atmosphere energy budget is, they shove the whole temperature difference from absolute zero into the equation by fiat and without physical justification. It’s plain rubbish.”
The physical justification is this. Feedback processes, being inanimate, cannot discriminate between a pre-existing temperature and a perturbation of that temperature. They have no means of deciding not to react at all to the former and yet to react vigorously to the latter. Nor are those inanimate processes concerned with what might have been if the Sun were not shining. For the Sun – like it or not – is shining.
Feedback processes simply respond to the temperature as they find it. Let us see why by studying the block diagram for a feedback loop –
The reference temperature (i.e., the temperature before feedbacks act) comes in from top left and is input to the summative input/output node. From that node, the fraction of the output temperature represented by the feedback response goes round the feedback loop and is fed back to the input/output node, where it is added to the original reference temperature to give the equilibrium sensitivity.
Now, increase the reference temperature by some increment. Then the input to the feedback loop is a little larger than before. The feedback processes simply respond to that larger reference temperature. There is self-evidently no physical mechanism by which those processes can “know” that they must not respond to a somewhat larger reference temperature than before.
“The analogy to a Bode amplifier, on which the authors place so much emphasis, is not an identity. If it were a perturbation voltage that were isolated and it was the perturbation voltage on which the feedbacks operated, the analogy could be made more closely.”
To understand why the reviewer sees things this way, let us recall IPCC’s official definition of a “climate feedback” (IPCC, 2013, glossary, p. 1450) –
“Climate feedback An interaction in which a perturbation in one climate quantity causes a change in a second, and the change in the second quantity ultimately leads to an additional change in the first. A negative feedback is one in which the initial perturbation is weakened by the changes it causes; a positive feedback is one in which the initial perturbation is enhanced. In this Assessment Report, a somewhat narrower definition is often used in which the climate quantity that is perturbed is the global mean surface temperature, which in turn causes changes in the global radiation budget. In either case, the initial perturbation can either be externally forced or arise as part of internal variability.”
Notice that the word “perturbed” or “perturbation” occurs five times in this short and calculatedly inspissate definition. Let us draw the block diagram for the variant feedback loop imagined by official climatology –
Here, there is scarcely an absolute quantity in the entire diagram. So, what is going on? Well, the mainstream feedback system-gain equation used in official climatology states that the change in equilibrium temperature is equal to the sum of the change in reference temperature and the product of the feedback factor and the change in equilibrium temperature.
Now, climatology’s variant equation is a perfectly valid equation. In effect, it represents the difference between two successive instances of control theory’s mainstream equation, which states that the equilibrium temperature is equal to the sum of the reference temperature and the product of the feedback factor and the equilibrium temperature.
But the variant equation is not useful for finding equilibrium sensitivities, because one cannot reliably derive from it the Holy Grail of global-warming studies – namely, the feedback system-gain factor, which is the ratio of equilibrium to reference temperature.
For present purposes, though, it is necessary only to observe that, since climatology’s variant equation is a valid equation, so is control theory’s mainstream equation, from which the variant equation is derived.
Let us correct the official definition of a “climate feedback” –
“Positive feedback in dynamical systems amplifies the output signal. Negative feedback attenuates it. In climate, the input signal is the global mean surface reference temperature 
that would obtain without feedback. The output signal is the global mean surface equilibrium temperature 
after allowing for feedback. The feedback response 
constitutes the entire difference 
between equilibrium and reference temperatures, such that the feedback factor 
, which is the fraction of equilibrium temperature that constitutes the feedback response, is equal to 
. The system-gain factor 
is equal to 
, i.e. 
.”
Note in passing that the feedback-loop block diagrams (a) simplify to the system-gain block diagrams (b). What this means is that all one needs to know to find the system-gain factor 
for any given year is the reference temperature (before feedback) and the measured equilibrium surface temperature (after feedback) in that year. One does not need to know the value of any individual feedback.
“[Test rigs] are all very well, but simply show that one can construct systems for which the one-dimensional energy-balance equations are exactly true. There is no information contained therein to say whether these models are relevant to the real climate.”
If the feedback mathematics borrowed by official climatology from control theory is as inapplicable as the reviewer suggests, then there is no legitimate basis for climatology’s current mistaken belief that feedback response accounts for at least two-thirds of equilibrium sensitivity. Paper after paper (see e.g. Hansen 1984, Schlesinger 1985, Bony 2006, Roe 2009) uses feedback mathematics, explicitly referring to Bode. But these and suchlike papers use Bode in a fashion that prevents accurate derivation of the system-gain factor. IPCC (2013) mentions the word “feedback” more than 1000 times.
These and numerous other authors have accepted that feedback mathematics is relevant to the derivation of equilibrium sensitivity. Quite right too: for equilibrium temperature is greater than reference temperature, and feedback response constitutes the entire difference between them.
It is interesting to see how ready the reviewers are to ditch the “settled science” that has been in the literature for decades whenever they find it inconvenient.
“The energy-balance equation used by climate science is just a Taylor-series expansion of the difference between the global average top-of-atmosphere energy imbalance and the radiative forcing. Higher-order terms have been dropped. This is why emission temperature does not appear in the zero-dimensional energy-balance equation. I just don’t see any opposing argument that would change this view of the equation.”
Since climatology’s variant equation is a valid equation, there is nothing in itself wrong with it. It is validly derived from the energy-balance equation, and the fact that it is derived via a leading-order Taylor-series expansion does not in any way impugn our argument: for a Taylor-series expension is merely a mechanism for expressing the shape of a curve about a particular point.
But leaving out the sunshine term makes it impossible to derive the feedback system-gain factor accurately from the variant equation.
Nothing in the derivation of the variant equation from the top-of-atmosphere energy-balance equation tells us anything about the magnitude of the system-gain factor. It is precisely for this reason that climate modelers have spent decades futilely attempting to constrain the interval of Charney sensitivities, which, in IPCC (2013), was [1.5, 4.5] K, just as it was four decades ago in Charney (1979).
“The authors would do well to educate themselves on the literature evaluating the linearity or otherwise of feedbacks.”
Yes, some feedback responses are non-linear. The water vapor feedback is the prime example. As the space occupied by the atmosphere warms, it can carry 7% more water vapor per Kelvin. Indeed, close to the Earth’s surface, at a pressure altitude of 1000 mb, it does precisely that:
At 600 mb, however, there is no increase in the specific humidity with warming. And at the crucial mid-troposphere altitude 300 mb, the specific humidity has been falling. Why is this important? Well, official climatology regards all individual feedbacks except water vapor as broadly self-canceling. It is only the water vapor feedback that provides the pretext for the notion that because of feedbacks equilibrium warming is three or four or even ten times reference warming.
Yet the only altitude at which the predicted rate of increase the specific humidity is observed in reality is very close to the surface, where, as Harde (2017) has pointed out, the spectral lines of water vapor are very close to saturation.
Turn to Fig. 9.1c of IPCC (2007). There, the predicted tropical mid-troposphere “hot spot” – I had the honor to name it – is made evident in the fashion with which we are now wearily familiar: lurid colors –
So much for what is predicted. I could show dozens of similar images from various general-circulation models. In reality, however, the predicted “hot spot” is conspicuous by its entire absence –
Now, the U.S. Climate Change Science Program produced its real-world data showing no “hot spot” a year before IPCC persisted in its false claim that the “hot spot” exists. And why would it exist? For the specific humidity that would have to increase to deliver the predicted faster-than-surface warming has actually decreased.
However, using our method of finding the feedback system-gain factor, one does not need to know anything about individual feedbacks. All one needs to know is the reference temperature (before feedback) and the equilibrium temperature (after feedback) in any given year.
And to find out whether nonlinearities in individual feedbacks are varying the system-gain factor with time and temperature, all one needs to do is find the system-gain factor for two different years – one close to the beginning of the industrial era and one close to the end. So we did that. And we even made allowance for the imagined (and probably imaginary) “radiative imbalance” that may have delayed about a quarter of the manmade warming to date.
In both 1850 and 2011, the system-gain factor, to three decimal places, was 1.129. It didn’t change even in the third decimal place. It didn’t change because the combined temperature from the Sun and from the pre-industrial non-condensing greenhouse gases was 375 times bigger than the 0.68 K reference sensitivity between those two dates. Nonlinearity? Schmonlinearity.
“The fact that feedbacks, calculated properly from models, give the right range of climate sensitivity in models probably should have given the authors pause in their conviction it [their analysis] is fundamentally defective.”
And this, gentle reader, is our old friend the circular argument, the argumentum ad petitionem principii, one of the dozen commonest logical fallacies. From this fallacy the only valid conclusion that may be drawn is that the perpetrator is insufficiently educated to know any better.
To demonstrate the utility of the simple system-gain equation in studying equilibrium sensitivities, we had taken climatology’s variant of it and demonstrated that, using the range of feedback factors officially derived from the models by Vial et al. (2013), it would deliver the published interval of equilibrium sensitivities. But that exercise told us nothing of the correct value of the feedback factor, or of its cousin the system-gain factor. To derive the correct values of these variables, one needs to look outside the window, notice that the Sun is shining, and take proper account of that fact by using the mainstream system-gain in one’s calculations.
“The sensitivity of any climate model is what it is – it cannot change due to any post-hoc analysis of its feedbacks. In a model the CO2 level is doubled, the radiative transfer calculation alters, and temperatures, water vapor, circulation, clouds etc. all change. The simulated climate system eventually stabilizes and the resulting net change in surface temperature is the sensitivity of that model.”
And this is the fundamental fallacy of relevance known as the straw-man argument, the argumentum ad ignorationem elenchi. For we had not undertaken any post-hoc analysis of any model’s feedbacks. Instead of adopting the models’ doomed-to-failure bottom-up approach to deriving equilibrium sensitivity by making fanciful guesstimates of the values of individual feedbacks, we had adopted the far simpler and more robust top-down approach of finding the reference and equilibrium temperatures for two well-separated years in the industrial era, discovering that the system-gain factors derived from these values were the same, applying the system-gain factor to the reference sensitivity to doubled CO2 and demonstrating, beyond all reasonable doubt, that the equilibrium sensitivity to doubled CO2 is just 1.17 K, plus or minus less than a tenth of a Kelvin.
The reviewer is, in effect, saying that the models must be right. Well, however elaborate they are, they are not right. They are wrong, as our analysis has demonstrated.
“No physical arguments are given for why the sensitivity should be so small, and accepting this simple estimate as plausible would require rejecting all previous work by scientists to understand the physics of climate change, much of which has been proven beyond doubt. The analysis given is both rudimentary and fundamentally flawed and I cannot recommend publication by a reputable journal.”
See the analysis of the water vapor feedback, earlier in this article. The magnitude of that feedback has not been “proven beyond doubt”: it has been disproven beyond doubt. Consider, for instance, John Christy’s fascinating graph of predicted tropical mid-troposphere temperature change in 73 models from 1979-2012. All 73 models showed tropical mid-troposphere warming at a mean rate about four times the observed rate, and no model’s prediction was below the observed outturn –
It is very likely, therefore, that the chief reason why the corrected value of the system-gain factor, and hence of equilibrium sensitivity, is so much below all official estimates is the overegging of the water-vapor pudding in the models. But we don’t need to know what the models got wrong – it is sufficient to demonstrate – in our submission irrefutably – that wrong they were.
In one respect, though, the reviewer is right. We are indeed rejecting all previous work by scientists to derive equilibrium sensitivity, insofar as that work, however honest and diligent, is incompatible with the correct result which we have reached by a far simpler and more reliable method than theirs.
“Look back at the definition of the feedback factor above, and marvel at what they have done. The perturbation in climate forcing that they use to estimate feedbacks is, quite literally, Switching On The Sun. Start with the Earth at zero Kelvin. Now switch on the Sun, forbid any feedbacks, and we get a reference temperature of 255 K. Now allow feedbacks to perated, and in our current world we actually get to equilibrium temperature 287 K.”
Perhaps all climatologists are Scottish. For it comes as a great surprise to us, whenever we take the road to England – or the boat for the cold coast of Greenland, or the flight to almost anywhere – and we find, to our fascination and delight, that the land is often bathed in the holy radiance of a large, bright, warm, yellow object in the sky. We don’t see it that much in the Gaidhealtachd.
We do not have to Switch On The Sun. For, owing to the bounty of Divine Providence, it has already been Switched On for us (except in Scotland), and the angels – the intergalactic grease-monkeys whose task is keep the Universe unfolding as it should – are doing a splendid job of care and maintenance.
For the Sun, you see, is shining. Are we wrong to take account of that fact? We think not. The feedback processes operating today don’t care what feedback processes operated at zero Kelvin. They simply respond to the temperature as they find it. And that means it is better to take account of the fact that the Sun is shining than to ignore it.
It was not only the reviewers nominated by the journal who reviewed it. Somehow, a copy of our paper reached the Vice-Chancellor of the University of East Anglia, who, on reading the paper, summoned a meeting of all 65 Professors and Doctors of science in his Environmental Sciences faculty and yelled at them as follows –
“Monckton’s paper is a catastrophe for us. If the general public ever gets to hear of Monckton’s paper, there will be hell to pay.”
He ordered the faculty to drop everything and work on trying to refute our paper – which, at that time, was merely a 2000-word outline that has now been developed into a full-length, 6000-word paper. He later denied that the meeting had taken place, but we heard about it directly from one who was present.
Finally, here is a comment from a notoriously irascible skeptical blogger (not, of course, our genial host here):
“No, we’re not going to discuss Monckton’s result here. We don’t do simple.”
My reading in mathematics and physics has led me to imagine – perhaps wrongly – that there is more rejoicing in Heaven at the discovery of a simple method to derive a correct result than at the use of a pointlessly complex method to derive a result that, not least on account of the complexity, is incorrect.
Some final questions for those who have had the persistence to read this far. Are the reviewers correct, or are we correct? And would you like to be kept abreast of developments with occasional pieces here? The paper remains out for review and, in due course, we shall learn whether it has been accepted for publication. We have also been invited to write a book giving an account of our result and how we came by it.
And we have sent to IPCC a formal notice that all of its Assessment Reports are gravely in error. Though we have followed IPCC’s own published protocol for submission of alleged errors, we have been unable to obtain from the Secretariat the acknowledgement which its own rules require. So we are about to put the matter into the hands of the Bureau de l’Escroquerie, the Swiss Fraud Office, via the London Ambassador of Switzerland, the nation where IPCC is headquartered.
Before we call in InterPlod, are we right to think we are correct and the reviewers wrong?
For a 45-minute You-Tube presentation by me explaining our result, follow this link. I’m most grateful to John Charleston for having filmed the presentation in his own studio, and for having edited it and posted it up.
And here is the single slide, from my presentation at next week’s Camp Constitution in Connecticut, that brings the entire global warming foofaraw to an unlamented end –
As my noble friend the Earl of Seafield once put it, “There’s ane end to ane auld sang.”
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Lord Monckton,
For many reasons I’m firmly a climate change “skeptic”. My background is chemical engineering, which is a field very much concerned with feedbacks, but it’s been many years since I’ve practiced. Still, I think I’ve retained an intuitive sense for these matters, and something doesn’t sit right to me with your analysis. Or, more accurately, since you posit that this type of analysis is a theoretical underpinning in the field of climate change, then something doesn’t sit right with the overall theory (which, I believe, is the core of your argument). The argument I’m making here is that only perturbations in temperature are important when it comes to calculating feedbacks. The total contribution from the Sun, while obviously very important to establishing the absolute temperature of the Earth, is irrelevant to calculating the feedbacks and therefore the equilibrium climate sensitivity.
First, I think using temperature as both input and response to the feedback does not make sense. Temperature is a response to the rates of heat flow in and out of a system, including feedbacks, so a feedback model based only on the state function (temperature) rather than flow rates seems incorrect. Your concept of “switching on the Sun” also clashes with my intuitive sense of how feedbacks work. I decided to describe here a different, yet equally (or even more) simplistic feedback model. Rather than heat flow rates and temperature, I describe a model using gas flow rates and pressure. I do this simply because I think gas flow and pressure are concepts more intuitively grasped, whereas heat flow and temperature are more abstract concepts to the general public.
This simple model involves a System of fixed volume (analogy for Earth), with gas flowing IN (analogy for heat from the Sun) and out (analogy for radiation to the universe), and two different gas flow feedbacks as analogies for the heat feedbacks generated by CO2 and water vapor in the atmosphere. I’ll point out that the water vapor feedback can’t “feel” anything about what’s going on with CO2; it is only affected by the state of the System. The magnitude of the feedbacks are controlled by “valves” in this model, as described below:
At equilibrium, the flow rates IN = OUT. First, let’s assume there is only one feedback, a gas flow stream labeled CO2. The gas flow rate CO2 is a function of V1. For the sake of argument, let’s assume V1 is independent of the system pressure P. Feedback flow CO2 siphons some of the gas flow from OUT back into the System. If V1 is opened a little (say, by a man opening the valve a little bit), the pressure in the System rises until the gas flow rate IN = gas flow rate OUT again, and we’re back to equilibrium. The pressure P is higher than it was when V1 was closed. Now, let’s add a second feedback, labeled WV (water vapor). Unlike V1, V2 is not externally controlled, but is an unknown function f(P) of System pressure P. V2 (and therefore the gas flow rate of feedback WV) doesn’t care about the individual values of the gas flow rates IN, OUT (which always equals IN at equilibrium), or CO2. It is purely a function of P, and doesn’t know anything about how P is established. If the relation between P and V2 is positive, and P increases (for whatever reason, for example someone opening valve V1), then V2 opens by an amount dictated by the function f(P), and System pressure P increases by an additional amount, until the feedback function is established and once again gas flow rates IN = OUT. That’s the positive feedback.
Now to the question of equilibrium sensitivity. For simplicity, IN and OUT are known constants. CO2 is a known constant (based on how much we open V1). The equilibrium sensitivity is therefore dictated entirely by the unknown function f(P), which governs the WV feedback. At equilibrium, IN = OUT, and therefore these terms always cancel out in solving f(P).
It should be immediately clear that the question of sensitivity is only concerned with CHANGES in P. And in the real world, we’re talking about very small changes in P, around which we could strive to empirically approximate the incredibly complicated function f(P). The absolute value of IN (input from the Sun) is irrelevant to the solution, since it is always canceled out by the equal and opposite value OUT.
Now replace all this talk of pressure and gas flow with temperature and heat flow. This is why estimates of equilibrium sensitivity should only be concerned with perturbations of temperature. The absolute temperature in the absence of feedbacks (i.e. contribution from the Sun only) does not factor into the equation, so to speak.
Yes to be more accurate there should be fixed valves at the inlet and outlet of the System to establish the initial pressure P, but I’ve neglected them for the sake of simplicity. There would also need to be pumps to provide the pressure differential between the vacuum of the universe and System pressure P to establish the flow directions of the feedbacks back to the System. And of course the CO2 feedback is not actually a constant irrespective of the state of the System. But I digress.
I welcome all criticisms and corrections!
David, You invited comments.
In your new model you posit “Rather than heat flow rates and temperature, I describe a model using gas flow rates and pressure.” and “This simple model involves a System of fixed volume (analogy for Earth), with gas flowing IN (analogy for heat from the Sun) and out (analogy for radiation to the universe),”
My issue with your analogy is that the climate system is not a “fixed volume” system. If you start your model from a system pressure datum of zero, which is analogous to the thermal datum of absolute zero as explained by William C. Rostron (July 31, 2018 2:00 am), then the mass of the gas in your model must change with time as the system develops towards its current state of balance. Then it is clear that the pressure (your proxy for temperature) varies both as the retained mass of gas increases as well as the increase in pressure associated with the gas flow rate throttles (your proxy for heat flow) and so you are not dealing with a “fixed volume” (i.e. fixed mass) system and your analogy fails.
All planetary atmospheres have a tendency to “boil off” into space with the light molecular fraction gases being lost first due to their thermal ability to more easily exceed the escape velocity. Gravity, as determined by planetary mass, is the “pump” that retains the atmosphere under a given solar energy loading. (but I digress too).
“DavidR” has taken much trouble over his alternative feedback model, but unfortunately it is not on all fours, mathematically speaking, with the block diagrams in the head posting. And there is no attempt to analyze the system mathematically – any such attempt would at once have shown the deficiencies in the model.
The block diagrams in the head posting are the simplest way to represent a feedback-moderated dynamical system. Let us do the math.
The input signal (which may be an absolute value, a perturbation of that value, or the sum of the two to give a new absolute value) passes to the summative input/output node. Thence, the signal goes round and round the feedback loop, where, since the feedblack block is rectangular, it is multiplied on each occasion by the feedback factor f.
Thus, the input signal or reference temperature Tr, before feedback, is multiplied successively by f, f^2, f^3 … ad infinitum and the product of Tr and each power of f is summed at the summative node. Now, under the convergence condition | f | < 1, the sum of f, f^2, … ad inf. is simply the system-gain factor A = 1 / (1 – f). This is one of the best-known of the infinite series.
Therefore, for any given input signal Tr, the output signal Tq is simply Tr A. The feedback-loop diagram thus simplifies to the diagram marked (b) in the head posting.
Now, it is at once evident from this description that the feedback loop will act not only upon any perturbation of Tr but also upon Tr itself. But climatology does not know this, and its paid agents in these threads have gone to extraordinary lengths to attempt to deny it. The denials will do no good. This is basic control theory, and the secret is now out. It's only a matter of time before the climate Communists find themselves marginalized and ridiculed.
Disappointed by the peer review feedback. Climate scientists don’t seem to be able to offer a proper scientific refutation. I put that down to groupthink and insularity. They shielded themselves so well from any substantive discussion of GHGE for so long that their minds turned to pulp.
Mr Pawelek is right: the standard of peer review, even at leading climate journals, is lamentable. Nothing recognizable as a serious and scientifically credible criticism was offered, and there was a great deal of sneering.
just a Taylor-series expansion of the difference between the global average top-of-atmosphere energy imbalance and the radiative forcing.
There is huge complexity in that “just”. What is the TOA energy imbalance? What is the radiation forcing? Shouldn’t cloud around the equator be included somewhere?
Stokes and Monckton: It appears that Stokes and fellow climateers have been wrong footed all these years by the IPCC definition of climate forcing:
“Radiative forcing:
Radiative forcing is the change in the net vertical irradiance (expressed in Watts per square metre: Wm-2) at the tropopause due to an internal change or a change in the external forcing of the climate system, such as, for example, a change in the concentration of carbon dioxide or the output of the Sun. Usually radiative forcing is computed after allowing for stratospheric temperatures to readjust to radiative equilibrium, but with all tropospheric properties held fixed at their unperturbed values. Radiative forcing is called instantaneous if no change in stratospheric temperature is accounted for. Practical problems with this definition, in particular with respect to radiative forcing associated with changes, by aerosols, of the precipitation formation by clouds, are discussed in Chapter 6 of this Report.” from:
https://www.ipcc.ch/ipccreports/tar/wg1/518.htm
It looks as though when Stokes et al says with considerable verbal force, that climateers are only concerned with changes – they are only talking about an IPCC definition.
To use this definition to help explain the climate system is bound to fail.
Ask anyone who has worked with control systems. They understand that ALL inputs have an effect upon the system that you are measuring.
The fact that climateer scientists have dreamed up a bespoke terminology to describe how they believe something works does not mean that they are correct. Especially when they then make use of equations from other disciplines.
I would define the climate system overall to be a partial self regulating system.
Mr Richards will be interested in the definition of a climate feedback in the Fifth Assessment Report (see the head posting). There, the emphasis is relentlessly upon the fact that the feedback response is to a perturbation only. But the system-gain equation is quite clear – feedbacks respond to whatever input they find, whether it be the input signal or some perturbation thereof or the sum of the two.
However, radiative forcing is not the same thing as feedback, and it is correctly defined as a change in irradiance.
the feedback response is to a perturbation only.
======
What Mof B has discovered, and what climatology and the IPCC have overlooked, is that the understanding of climate has been hampered by the formal climate definition of feedback.
Because climate science and the IPCC define feedback as a delta, it has been assumed that the integral of feedback is 0 because it is undefined. However, this is mathematical nonsense. The problem is that climate science has no definition for the integral of feedback. That doesn’t mean it doesn’t exists, nor does it mean the value is zero. An integral is non zero unless the underlying term sums to zero.
to my mind a near perfect feedback analogy is a sailboat sailing into the wind. In sailing we use the term “true wind” and “apparent wind” to distinguish between the wind seen by a stationary observer and the wind seen by the observer on the boat.
Consider a sailboat sailing upwind into a wind. If the true wind increases, the boat speeds up. This increase in boat speed further increases what is called the “apparent wind” the boat experiences, which causes the boat speed to increase even further.
This extra boat speed that comes from the increase in apparent wind is feedback. It is extra speed that results not from the wind itself, but rather from the speed of the boat through the wind generating wind, similar to back radiation increasing surface radiation.
No sailor would assume that apparent wind only increases boat speed when there is a change in the wind. Apparent wind increases boat speed even when the true wind is constant. Likewise, even when the temperature of the earth is constant, the integral of feedback, which represents the total amount of GHG in the atmosphere, this integral is non-zero.
Even when the wind speed is constant, efficient sailing craft can use the apparent wind to sail faster than the wind, even downwind. Explain how a sail boat can sail faster than the wind downwind in a constant breeze if feedback only affects a change in wind speed.
I very much like this sailing analogy.
the feedback response is to a perturbation only.
======
where I take issue with M of B is perhaps on the matter of terminology. M of B says that feedback exists for an absolute temperature. Strictly speaking, this is incorrect. Not for physical reasons, but as a matter of definition.
The IPCC says that feedback is a response to perturbation only. As such, the absolute temperature of the earth is the integral of all perturbations and feedbacks since the formation of the earth billions of years ago. As such, what M of B is calling feedback for an absolute temperature is more properly called the integral of feedback in climate science, as a matter of definition (not physics).
What is lacking is a shorthand term for the integral of feedback. We use “speed” as a shorthand for the integral of “acceleration”, and distance as the shorthand for the integral of “speed”. What is required in climate science is a scientific term for the integral of feedback.
At present, because no such term exists, climate science assumes that the integral of feedback = 0. No proof of this assumption is given, and mathematically and physically it makes no sense.
Climate science maintains that feedback is non-zero and positive. As such, the integral of feedback cannot be zero. Since it is trial to show that the absolute temperature of the earth is the integral of the perturbations plus feedbacks, the integral of the feedbacks must equal the absolute temperature minus the integral of the perturbations. Since these last two are not equal and non zero, the integral of the feedbacks must be non zero.
As Karl Friedrich Gauss used to say when challenged on notation or nomenclature, “Non notatio, sed notio.”
I am simply doing the mathematics of a standard feedback loop, as follows.
Imagine a reference temperature 255 K in, say, 1850. Imagine that that reference temperature comprises the emission temperature of 243.3 K without any non-condensing greenhouse gases, plus another 11.5 K from the presence of those gases up to 1850. We know by definition that feedback has not acted on either of these quantities.
Now, imagine an equilibrium temperature in 1850. Was it indeed an equilibrium temperature? Yes. The linear trend to 1930, 80 years later, would be zero. Therefore, the equilibrium temperature is the measured surface temperature of about 287.5 K.
All of the difference between these two values is necessarily temperature feedback.
Therefore, the system-gain factor for 1850 was 1.13. As the head posting shows, it was also 1.13 in 2011.
But let us pretend that some of the difference between 255 and 287.5 K did not constitute feedback response. In that event, the system gain factor must be commensurately reduced, and equilibrium sensitivity with it.
No need to worry about what we call the feedback response (in Kelvin). Me, I just call it the feedback response. As the reference temperature grows, so the feedback response grows. And if, as we can prove for 1850-2011, the system-gain factor is pretty much constant, the growth in the feedback response will be proportional to the growth in the reference temperature.
Mathematically, why is this?
The output signal from a feedback loop (in climate, this is emission temperature) is the sum of the following series:
Input signal x feedback factor ^ 0 + input signal x feedback factor ^ 1 + input signal x feedback factor ^2 + … + ad inf.
Under the convergence condition that the absolute value of the feedback factor is less than 1, the sum of the series is simply Input signal x 1 / (1 – feedback factor).
From this description, it is self-evident that feedback processes must respond not only to some perturbation of the input signal but to the entire input signal. Q.E.D.
Non notatio, sed notio
============
Your understanding of the problem seems fine to me. What I’m thinking of is the understanding of others.
Because to me, if we were to call acceleration and speed the “accelerator response” because both vary when you press on the gas pedal, I think this would lead to all sorts of confusion.
It seems to me that there is a whole body of climate science that has been brought up to think one way and you are asking them to think contrary to what they have learned. This is a very difficult task for the human brain.
To my mind the problem stems from the above statement “the feedback response is to a perturbation only.” Climate science doesn’t have a definition for feedback outside of a perturbation.
So rather than argue this question, my approach would be to ask what happens if we integrate both sides of the question.
When we integrate the perturbations we get temperature absolute. And when we integrate the feedback response we get the “feedback integral “, which doesn’t have a name, but we could then create one such as “cumulative feedback response”, which is not a function of delta T, but rather of integral(delta T) which is T absolute.
This I think would turn the light bulb on for many currently in the dark. Not because your math is wrong, but rather because it is a leap too far for people trained to think differently.
And for those that became climate scientists via art majors, where “integrate” means something done with black and white children in school, maybe use something friendly like “sum up”. Though even that might bring to mind visions of a book review or a short couple of paragraphs.
Since many climatologists find calculus a challenge, it might be better simply to present a summary table showing the three equilibrium temperatures – in 1850, in 2011 and at 2 x CO2 compared with 2011 – and putting numbers on the feedback responses at each stage.
The feedback response in 1850 is 287.5 – 254.8 =32.7 K. The feedback response between 1850 and 2010 is 1.02 – 0.68 = 0.34 K (assuming the “radiative imbalance” is as big as They imagine). The feedback response upon doubling CO2 concentration is 1.17 – 1.04 = 0.13 K.
The assessment is flawed since it is based upon the premise of there being an equilibrium temperature, but that premise is flawed.
There is no equilibrium temperature as can be seen from the fact that the temperature of the Holocene has varied throughout its epoch, and there is no variation in temperature seen today that has not been seen in the past.
Further, we know that the temperature as at 1850 was not in equilibrium since, as I have pointed out above, if one accepts the data sets (unadjusted HADCRUT 3) there is a temperature change of about 1.2 degC form 1850 to 1879, when according to the Law Dome Ice Cores, CO2 rose by just 3ppm.
This 1.2 degC change in temperature is about the same as your assessment of Charney Sensitivity (1.17 degC), and we know from this that natural factors, possibly already built in as at 1850, can cause a rise in temperature of 1.2 degC.
We cannot separate the signal to CO2, if there be any at all, from the noise of natural variation, and one cannot make a proper assessment of the so called Charney Sensitivity unless there is an equilibrium state, but there is never an equilibrium state.
At the very minimum your assessment of the Charney Sensitivity must have an error bound of around 1.2 degC reflecting the natural variability which was in the system as at 1850, or was inputted into the system shortly thereafter and before there was any significant increase in CO2.
In response to Mr Verney, the error bounds for the HadCRUT4 dataset for 1850 are +/-0.35 K. One can use the upper bound, the mid-range estimate or the lower bound and the Charney sensitivity derivable by our method from the data for 1850 remains at 1.17 K. These matters were very carefully considered by our emeritus professor of statistics.
I hope others will join you in supporting your suggestion.
the feedback response is to a perturbation only.
==========
if feedback only works on perturbation, the following would be impossible.
In my analogy, the feedback force (back radiation) is the difference between apparent wind and true wind, resulting from the motion of the vehicle (ghg). The true wind is solar radiation, and the apparent wind is total radiation.
https://en.wikipedia.org/wiki/Blackbird_(land_yacht)
On July 2, 2010, Blackbird set the world’s first certified record for going directly downwind, faster than the wind, using only power from the available wind during its run. The yacht achieved a dead downwind speed of about 2.8 times the speed of the wind.[18][19]
On June 16, 2012, Blackbird set the world’s first certified record for going directly upwind, without tacking, using only power from the wind. The yacht achieved a dead upwind speed of about 2.1 times the speed of the wind.[18]
“they are only talking about an IPCC definition”
No, it is the standard definition of feedback in electrical engineering or control. Here is a Wiki diagram of feedback control:
Note the input – disturbance. Feedback control works by calculating the difference between a state and a reference state, and exerting a control proportional to the difference. Not proportional to the reference state itself, or any part of it.
Mr Stokes gets sillier and sillier in his desperation to try to confuse those who have read this far, and to try to shore up the collapsing catastrophist case. If he had read the head posting he would realize that climatology’s variant system-gain equation, which he rejected in an earlier comment here, has a perturbation (i.e., a “disturbance”) as its input signal and, therefore, a perturbation as its output signal. Now, if Mr Stokes rejected that equation then, why does he parade a circuit diagram in some ways equivalent to it now? And, given that a block diagram akin to his CreepyMedia diagram already exists in the head posting, why would he consider that his diagram somehow casts doubt upon that posting?
As the head posting makes plain, the variant equation used in climatology is a valid equation, whether Mr Stokes finds it expedient or not. It has to be, for it constitutes the difference between two instances of the valid mainstream equation, with the smaller of the two input signals subtracted out.
But let us go with Mr Stokes’ “disturbance” diagram and do things his way. There is nothing to stop the “disturbance” being very large and the input signal that is being disturbed very small. Indeed, there is nothing to stop the “disturbance” being so large that it constitutes the entire input signal. Therefore, there is nothing to stop the feedback loop from treating the entire input signal as if it were a “disturbance”, or vice versa.
The point of the head posting is that it is not possible to exclude by fiat any part of the input signal in the climate from being modified by the feedback loop. And once that is admitted, as Mr Stokes will eventually be compelled to admit it, then one may derive the system-gain factor – by definition the entire difference between the input signal (i.e., before feedback has acted) and the output signal (i.e., after feedback has acted) – from these two quantities by the not particularly difficult expedient of taking the ratio of the latter to the former. And that allows us to derive Charney sensitivity reliably by a top-down method a good deal more robust than the clunky, bottom-up method of trying to represent feedback processes (many of them at sub-grid scale) in complex climate models that are now shown to have failed.
“There is nothing to stop the “disturbance” being very large”
There is. Linear feedback theory is restricted to small disturbances, so that the first order expansion is admissible. It is true that for artificial conditions like the op amp circuit the range of linearity is large, but this is generally not true. But the key thing is that the amplification and feedback operates on the difference between the reference and disturbed states. You can’t include the reference state itself as a disturbance.
Linear feedback theory is not restricted to small disturbances of a pre-existing equilibrium. What Mr Stokes misses – I now think deliberately – is that feedback is capable of operating on a pre-existing state, so that any given equilibrium may already have a feedback response as a component.
In any event, our own analysis simply derives the feedback system-gain factors for two years close enough to one another, particularly when seen sub specie aeternitatis, to constitute a small perturbation.
It seems self evidently clear that any previous equilibrium state posited was based on raw input + feedbacks…since the climate system that produced those feedbacks also previously existed. Thus, additional perturbations, resulting in incremental feedbacks, should simply be added to this, not treated as stand alone.
Said another way, the surface temperature (or, total surface flux) achieved with a feedback system at 280ppm CO2, was already based on (solar input) + (back radiation of 280ppm CO2). Adding another 120ppm CO2 now produces a surface temp (or, again, total surface flux) based on (solar input) + (back radiation of 400ppm CO2). Right?
So, how could it be anything other than what CMoB is saying. The solar input (the sun shining) must be included or it doesn’t make any sense.
(In case I’m not being clear, I am simply saying I agree with CMoB…at least as far as my simple understanding can extend.)
rip
This block diagram has nothing to do with a climate model because there is no controller, there is no set point, there is no effector, and there is no computation of error.
Indeed, and that is my point. The view that feedback is something that operates on changes, not constant quantities, is not peculiar to climate, as claimed here, but is universal.
But anyway, a GCM does not have anything like the structure of an amplifier either. It is a totally different thing. It solves partial differential equations.
GMC may be a good approach to predicting weather in the short term but in terms of trying to predict climate the approach has many unresolved problems like the stability of the calculation. It is like trying to predict chaotic flow using laminar flow equations.
It is inherent in the mathematics of the feedback loop that the loop will run to equilibrium as an infinite series of powers of the feedback factor. Once the loop has run to equilibrium, the system will be in equilibrium, and yet feedback has operated on it.
What I would really like to see associated with your models are open loop and closed loop S domain transfer functions, Frequency response, impulse response, step response, and stability margins. If the system is unstable then it cannot be correct because for more than 500 million years the climate has been stable enough for life to evolve for after all we are here.
We can dispose of the first case raised by Mr Haas straight away. As will be evident from the head posting, we have taken the mu gain block as unity, removing it from the circuit. Any perturbation in the reference temperature is simply added to that temperature before it is input to the circuit. In the open-loop case, therefore, the reference and equilibrium temperatures are equal and nothing more need be said.
Your diagram is meaningless because it fails to include a transfer function for the climate system which is not unity. To be meaningful you need to produce a block diagram that relates changes in CO2 to changes in global temperature. An increase in CO2 concentration in the Earth’s climate system will not result in an instantaneous increase in global temperature. The feedbacks to a change in CO2 take time to develop so there is a fundamental delay in the feedback loop that your model ignores. To be meaningful your model needs to include an open loop transfer function.
Mr Haas is incorrect when he says there is no transfer function. The block diagram in the head posting embodies a transfer function A = 1 / (1 – f).
Mr Haas is again incorrect when he says we have not allowed for time-delays in the climate system. However, we have done so. Our first case is 1850, after which the trend in global mean surface temperature was zero for 80 years. Our second case is 2011, where we make explicit provision for the radiative imbalance caused by delay in the system.
Mr Haas is yet again incorrect when he says our model needs to include an open-loop transfer function. As explained in the head posting, setting the mu gain block to unity and including any perturbation of the input signal by addition to that signal before inputting it to the feedback loop is functionally identical to the Bode approach, and produces exactly the same output signal.
All you have is a gain value which is not in it self a transfer function. What we want to see is how a change in CO2 causes a change in global temperature because we are trying to compute the climate sensitivity of CO2. A step change in atmospheric CO2 will not cause an instantaneous change in global temperature because of the thermal capacitance or in other words the thermal inertia of the climate system. Your diagrams do not have anything in them that is a function of time. The theory is that an increase in CO2 causes an increase in the insulating properties of the atmosphere which in turn causes an increase in the surface temperature. That increase in the surface temperature will not happen instantaneously but takes time to develop largely because of the thermal inertia of the climate system. An increase in the surface and lower atmospheric temperatures will cause more H2O to enter the atmosphere which in turn will cause more warming because H2O is the primary greenhouse gas according to “official climatology”. That is the feedback element and it takes time for that feedback warming to take place. That feedback caused warming causes even more H2O to enter the atmosphere which causes even more warming and so forth. One has to be concerned about the stability of the whole process, Your diagrams do not show anything that is a function of time. You may have considered measurements that were taken at different points in time but that still does not change the fact that your diagrams do not have anything that is a function of time.
Mr Haas does not seem to appreciate that at equilibrium time is not an issue. In 1850 the climate had already settled to equilibrium. The emission temperature for a world without non-condensing greenhouse gases can be calculated without reference to time. The warming caused by the presence of those gases up to 1850, before accounting for feedback, can be calculated without reference to time, because the temperature response to a forcing, before accounting for feedback, is near-instantaneous. The equilibrium temperature in 1850 was the surface temperature then prevailing, and there was no trend in that temperature for 80 years.
From these three values the value of the system-gain factor as it stood in 1850 may be derived directly, and without reference to time.
I do not take issue with anything that you have said regarding 1850. My issue is that your model as represented by your diagrams is not realistic. At issue here is how changes in CO2 affect global temperature and your model does not show that. You need something that shows changes in CO2 as input and changes in global temperature as output.
I don’t need what Mr Haas is suggesting, since we have simply accepted all of official climatology except what we can prove to be wrong. Therefore, we have accepted that the reference sensitivity to doubled CO2 is 1.04 K.
The largest uncertainty in climate-sensitivity studies is as to the value of the system-gain factor. We find it to be 1.13. Therefore, the equilibrium sensitivity to doubled CO2 is simple 1.04 x 1.13, or 1.17 K. We do not need to know anything more about it than that.
“Frequency response, impulse response, step response, and stability margins.”
The components in the circuit should have no reactance or frequency-dependent behaviour, at least below RF. Nor should there be any stability issues at such frequencies, as long as 1-μ*β>0. It has no relation to climate, so there is no point in looking there for correctness.
Something must be wrong then because global temperature is a function of time and the feedbacks operate over a function of time. A change in the insulating characteristics of the atmosphere or of the input and or output energies effects temperature as a function of time. According to the AGW conjecture, an increase in CO2 causes an increase in the insulating characteristics of the atmosphere which causes the temperature at the Earth’s surface to increase which in turn causes more H2O to enter the atmosphere which supposedly causes more warming because H2O is the primary greenhouse gas. That additional warming causes even more H2O to enter the atmosphere which causes still more warming and so forth. To be significant your model has to take into consideration the thermal capacitance characteristics of the climate system which you are telling me it does not. You model completely ignores the temporal characteristics of a changing climate.
“You model completely ignores the temporal characteristics of a changing climate.”
It isn’t my model. And Lord M’s circuit has nothing to do with climate. It is just a feedback amplifier. It could be from any undergrad EE text.
But all the talk here about “official climatology” (never quoted) is misplaced. They don’t use this stuff either, except for the odd interpretive paper. GCMs do not use notions of feedback. They do a complete emulation of the time-varying atmosphere and ocean, updating two or three times an hour.
“They do a complete emulation of the time-varying atmosphere and ocean, updating two or three times an hour.”
while on planet earth the response is instantaneous.
“They do a complete emulation of the time-varying atmosphere and ocean, updating two or three times an hour.”
That’s the whole point. It is the wrong emulation formula.
No. It is the correct emulation formula, and easily demonstrated. I suspect some of the misunderstanding shown in these comments is a failure to recognise that linear feedback factors as applied and discussed in Climate Science already represent the integral of the gain from the feedback loop. The feedback factors are only applied once to a temperature increment, and unambiguously represent the gradient of flux change attributed to the drivers of feedback with temperature. It would have been better if climate science had NOT adopted the jargon of Control Theory outside normal usage.
Amen to that!
Integral with respect ot what?
William,
A change in temperature cannot directly “cause” a further temperature change. A change in temperature causes a change in the net flux imbalance which controls the rate of heating of the atmosphere and oceans, and which then controls the rate of (transient) temperature change in atmosphere and ocean.
The heating rate at any point in time is determined by the sum of the changes to net flux imbalance due to forcings plus the changes to net flux imbalance due to feedbacks. The feedback changes are changes TO FLUX which arise from the changing climate state, largely due to changing temperature. The main such feedback is the large negative Planck response, which is almost instantaneous. Most other feedbacks take hours to months to complete their work on net flux imbalance and can be deemed instantaneous if we are considering interannual data. (The exceptions include largescale changes to Earth system response, such as long term change of albedo due to planetary greening, but since such Earth system feedbacks are not the main issue here, I will leave them outwith the scope.
The total energy which has entered the system determines the temperature change at any point in time and this is given by the integral of the net flux imbalance over time – mathematically equivalent to integrating over time the sum of the forced changes in flux plus the changes in flux due to feedback. The transient temperature then IS WHAT IT IS at that point in time. It has already incorporated all of the temperature-dependent feedback effects on net flux upto that point. If, for a fixed forcing (as in, for example, the quadrupling of CO2 numerical experiments) you allow the system to stabilise over a very long time, then all of the net flux feedbacks are integrated over time, and all of the temperature gain due to temperature feedback on net flux has been fully accumulated.
You bring up time integrals but there are are none in the model. You apparently claim that there are no feedbacks. You apparently claim that there is no thermal capacitance in the Earth’s climate system.
William,
My goodness. The linear feedback equation is stated as a differential equation. The solution of the equation in Temperature or Net flux imbalance is ALWAYS via a process of integration w.r.t. time. Thermal capacitance terms are included when total heat uptake into the system is equated with the radiative imbalance at TOA. The exact form is subject to assumption.
To avoid the complexities of a non-constant feedback case, here I will consider just THE CONSTANT FEEDBACK SOLUTION.
The radiative imbalance, N, is equal to F – alpha* DeltaT where alpha is the constant linear feedback.
The heat uptake by the climate system (flux) must be equal to this at all points in time under 2LOT.
For a single-body ocean-heating model assumption, for exanple, this flux is given by C dT/dt and we obtain
CdT/dt = F – alpha*DeltaT
Note that
(a) this has just one THERMAL CAPACITANCE term in it, C; a multiple body version has multiple thermal capacitances defined.
(b) it is a differential equation which can be solved for T by the process of INTEGRATION, where T is the transient temperature at each point in time, t.
At each point in time, the feedback to net flux is fully incorporated into the net flux solution at that point in time. The history of net flux variation, specifically its integral, determines the energy content of the system and hence temperature. Hence both the net flux and the temperature solutions fully incorporate all of the feedbacks at that point in time.
However, if we only wish to talk about equilibrium temperature, we can get to the solution at infinite time of this equation by two methods. Solve the equation for T and let t go to infinity OR note that irrespective of the choice of ocean heating model, the LHS of the equation has to go to zero net flux as t goes to infinity. They give exactly the same answer, as you would expect. Hence we can find the solution at equilibrium via a shortcut, which is DeltaT = F/alpha for this simple constant feedback case. This equilibrium solution is valid for the single body and multiple-body heating assumptions and has integrated all of the accumulated temperature-dependent feedbacks into the final equilibrium temperatre result.
Forgive me, William, but I do not intend to pursue this further. It is somewhat evident that you need to deepen your understanding and I do not have the time to do it for you. Somewhere below, I included a conventional derivation of the linear feedback equation to try to ensure that people understood the assumptions that go into it. You may find it useful to peruse that post.
You are right, The block diagram that we are dealing with is missing all of what you are saying. A basic transfer function for the action of the climate system is missing so hence the block diagram we are dealing with is meaningless and has nothing to do with climate. What we really need here is a block diagram of how, according to “official climatology” a change in CO2, atmospheric concentration causes a change in global temperature. There has to be an open loop transfer function that relates how a change in CO2 will cause a change in global temperature. The change does not happen instantaneously.
The advantage of deriving a system-gain factor for a particular moment is that one need not do time integrations. All one needs to know is the reference and equilibrium temperatures (i.e., the input and output signals, respectively). The system-gain factor is then the ratio of the output to the input signal.
The system-gain factor for a particular moment is zero. If the CO2 percentage in the atmosphere were suddenly to increase the increase in the Earth’s surface temperature would be zero because it takes more than zero time for the temperature to increase. The differential equations involved do matter.
Mr Haas is not quite following our argument. In 1850, when the Earth’s surface temperature was at equilibrium and would show no trend for 80 years, we are able to derive the system-gain factor that corresponded to the feedback response that represented the difference between the reference temperature of 255 K and the equilibrium temperature of 287.5 K. Deriving system-gain factors in this way is perfectly straightforward and does not require the use of time-differentials.
However, in 2011 it is possible (though by no means certain) that not all of the warming induced by our activities had yet manifested itself. We used the standard method of allowing for this putative delay.
I do not take issue with what your measurements may be telling you but you have not produced a valid model that relates change in CO2 at the input and change in global temperature at the output. We are trying to determine the climate sensitivity of CO2. Apparently your measurements are telling us that the climate sensitivity of CO2 must be less than 1.2 degrees C and hence proposed positive feedbacks have little apparent effect. For many reasons, I believe that CO2 has no effect on climate but that is not really the issue here because it is contrary to “official climatology.
Mr Stokes makes the obvious point that models do not use notions of feedback. However, our approach provides a simple and robust method of calculating the feedback system-gain factor and hence equilibrium sensitivity. What we have shown is that the models, in attempting to represent processes – often at sub-grid scale- that give rise to feedback are not succeeding.
Before you can calculate the feedback system-gain factor you need a plausible system model which apparently you do not have. Climate change takes time to develop.
Mr Haas is incorrect. All one needs to find the system-gain factor for any year is the reference and equilibrium temperatures for that year.
In the head posting, two such years were studied: 1850 and 2011. The system-gain factors for each were found to be 1.13. Therefore, there is not much “development” going on, and one may take the system-gain factor as constant without much error.
Mr Haas does not appear to appreciate that, at a time of temperature equilibrium, such as 1850, it is perfectly possible to derive the system-gain factor as the ratio of the measured equilibrium temperature to the reference temperature that would have prevailed before accounting for feedback.
As for the position in 2011, due allowance was made for the fact that not all of the global warming we had induced had yet manifested itself.
William,
On the scale of eons, Earth’s temperature is not stable. That life has evolved is a tribute to its tenacity as much as to a “stable” environment, within wide limits.
Life has existed on Earth for about four billion years. During four eons, global temperature has been both much hotter and much colder than now. The range is on the order of -50 degrees C during Snowball Earth episodes to +25 degrees C or even hotter during Hothouse climates. Some think that the warmest parts of the Archean Eon were much hotter than now, but others disagree.
Within our own Phanerozoic Eon (the past 541 million years), it has often been hotter than now, but rarely colder. Only the depths of the Ordovician-Silurian, Carboniferous-Permian and present Icehouse climates have been colder.
Thus, ECS is not a constant for all geological intervals and atmospheric compositions. For “climate change” purposes, it must refer to the present arrangement of continents, amount of gaseous, liquid and solid water and makeup of our air, among other factors which change over the millennia.
The Earth’s climate has been stable enough over the past 500 million years for life to evolve. That is a fact. We are here. If the climate were truly unstable then the oceans would have boiled away at least hundreds of millions of years ago and the atmospheric pressure at the Earth’s surface would be greater that it is on Venus and the surface temperature would be hotter than that of Venus. Negative feedback systems are inherently stable and positive feedback systems are inherently unstable. The feedback diagram that is under consideration because it is missing a climate transfer function.
William,
Our ancestors from whom we evolved were also here four billion years ago.
The great transitions in the history of life on earth occurred as a result of unstable conditions, not because of stability.
This includes the Snowball Earth episodes, associated with the origin of eukaryotes, of sex and multicellularity, ie the appearance of slime molds, fungi, animals and plants. The so-called Cambrian Explosion also followed the less drastic Gaskiers glaciation and the mass extinction event at the end of the Ediacaran Period, when habitats changed drastically, due to the Precambrian seafloor cyanobacterial slime mats being consumed by evolving animals.
If the Earth’s climate were not stable, the oceans would have boiled away and the heat would have extinguished all life on Earth but that has not happened for at least the past 500 million years.
William Haas criticizes the missing time delays and open loop transfer functions and asks for frequency responses etc. we can address his concerns:
Time delays: We consider only equilibrium states where time goes towards infinity. All time delays are compared to infinity very small and can thus be neglected. Our model makes no statements about the rate at which equilibrium is reached after a disturbance (for that is not the scientific question we want to answer) but we can make statements about the nature of the equilibrium itself.
Mr Haas mentions the open-loop function. In control theory the open loop function is not a system without feedbacks but the transfer function from one point in the feedback loop along the loop (including feedback) until one ends up at the same point. It has no practical meaning except to test for stability, which is the propensity to attain equilibrium after a disturbance.
As for instability, we need not be concerned about it because a system becomes unstable when (according to Nyquist) the open-loop function has a gain above unity for a phase-shift above 180°. We do not have phase -shift information because we have ignored all the delays. But our open-loop gain function is essentially f, and f < 1.
No, open loop is the system without feedbacks. We are trying to compare the open loop gain with what the gain would be with feedbacks. We do not have any measurement data as time increases without bound. What is very important is ascertaining the stability of the system. The Earth’s climate system has been stable enough for life to evolve for at least the past 500 million years so to have a chance of being a possible valid representation of climate the system model has to be stable. In general negative feedback systems are stable and positive feedback systems are not. You do not have phase shift information because you do not have a valid model. What is f in terms of the climate sensitivity of CO2?
The curse of feedback theory is the absence of standard methodology. If Mr Haas is interested in the open-loop case, he should know that the approach we have taken is to set the gain block to unity and to add any perturbations of the input signal to that signal before it enters the feedback loop.
Except at the margins, feedbacks in the climate respond similarly to all temperature changes, whether they originated from CO2 or some other cause.
We do not need to concern ourselves with what happened 500 million years ago. We begin with a temperature equilibrium in 1850. From that equilibrium, and from the reference temperature for that year, we are able to derive the feedback system-gain factor for that year.
Unity does not adequately model the Earth’s climate system ignoring feedbacks. You need a model that has CO2 change as its input and climate sensitivity as its output.
Mr Haas has not understood our method. We derive the value of the system-gain factor from the reference and equilibrium temperature in 1850 and again in 2011. It proves to be 1.129 (to 3 d.p.) in both years. We then use official climatology’s variant system-gain equation to derive the equilibrium sensitivity to doubled CO2.
The reference sensitivity to doubled CO2 is 1.04 K (derived from Andrews 2012). We have simply accepted this and all else in official climatology that we cannot prove to be incorrect.
Therefore, the equilibrium sensitivity to doubled CO2 is the product of the reference sensitivity and the system-gain factor: i.e. 1.04 x 1.129, or 1.17 K.
OK then what you just related to me is your paper. So assuming that Andrews 2012 is correct, based on measurements, the climate sensitivity of CO2 is 1.17 degrees K and the feedbacks that are included have only a small effect upon the result. What I would like to add is that if you superimpose a warming trend caused by things other than CO2 as has happened in the past, the climate sensitivity of CO2 may be significantly less than 1.17 degrees K. Try doing a computation where you first assume that the warming cycle experienced during the thirties was caused by both CO2 and natural causes and then you make the same assumption as to the warming cycle of the nineties. Two equations and two variables to solve for should allow you to separate out CO2 based warming and Nature based warming assuming that they were both the same physically during both of those periods.
As explained previously, the feedback system-gain factor is derived from reference and equilibrium temperatures in 1850 and in 2011, under the assumption that all global warming between those two dates was anthropogenic. Very little would change if some of the warming were natural, because the influence of the Sun (through emission temperature) and of the pre-industrial non-condensing greenhouse gases overwhelms any tiny influence we may subsequently make.
The climate change that we have been experiencing is very similar to climate change that happened before the industrial revolution. The climate change that happened before the industrial revolution could not possibly have been caused by mankind’s use of fossil fuels. The climate change we have been experiencing since the beginning of the industrial revolution may have nothing to do with mankind’s use of fossil fuels.
It is of course possible that little of the warming since 1850 was anthropogenic. However, our paper concentrates not on what may be so but on what we can prove to be so. Even if all of the warming since 1850 were anthropogenic, the warming in response to doubled CO2 would be of order 1.17 K, assuming that official climatology has made no errors other than that which we have identified, formally demonstrated and quantified.
I like what you are saying here but there will be others who will say that you are cherry picking to achieve a desired result. I do not think that you have been doing that but others will say you did no matter how carefully you chose the dates because of other reasons. It would be interesting to see what climate sensitivity numbers you would compute as a function of which dates you chose. You could present the result as a two dimensional pseudo color image. doing so might help to sell your conclusions.
There is no cherry-picking, and it doesn’t make much difference what dates one chooses.
I believe that you were very just in the dates you chose but others may not. You could put the “cherry-picking” criticism to rest by plotting your results as a function of start date and the number of years between the start date and the stop date.
A flash of steel from the dark lords sword and the rats start running in circles, unable to escape the light of reason.
The Bright Lord, surely: for are we not the Army of Light and Truth?
After 10 years of reading here my first ever comment is to you sir, firstly thank you for your tireless efforts over many years, secondly as a layman, after 450 comments where I kind of understood your point, ferderple’s sailing analogy was a lightbulb moment. If you wish to engage a wider everyday audience in the future you would do well to incorporate it into your presentation.
I look forward to future updates on your paper.
Many thanks to Mr Dillon for his kind words. I agree that the sailing example is an excellent one. At present, our chief aim is to be sure that we have gotten the science right. Frankly, we had expected a more intellectually challenging set of responses than those we have received from the paid agents of climate nonsense. Fortunately, there are plenty of professors of control theory who know a lot more about it than the fumbling amateurs here, and more and more of them are getting in touch as they see the hilariously futile attempts of the trolls to pretend, for instance, that feedback does not respond to the entire input signal.
We shall not be doing updates in the near future, because the paper is now under review and we suspect it will be some time before the editors revert to us.
Lord Monckton of Brenchley, I too thank you for educating us on the error in application of control theory to the climate models. This is an important discussion as evidenced by the arrival of the “flying monkeys” from the castle. That observation alone convinces me that the meeting you described did take place.
In response to the Farmer, one can tell how worried the usual suspects are by the fact that they are lying repeatedly here to try to prop up their collapsing Party Line. Yes, the meeting took place. Yes, the University of East Anglia is in a panic. And yes, it will lose hundreds of millions a year in global-warming funding.
Lord Monckton,
One of your reviewers wrote the following.
““The energy-balance equation used by climate science is just a Taylor-series expansion of the difference between the global average top-of-atmosphere energy imbalance and the radiative forcing. Higher-order terms have been dropped. This is why emission temperature does not appear in the zero-dimensional energy-balance equation. I just don’t see any opposing argument that would change this view of the equation.”
The above statement is precise and correct, but from your many comments, you don’t seem to have grasped its import. Let me try to expand a little on the reviewer’s comment, using a conventional derivation of the linear feedback equation.
Assume that at some point in time (t = 0) the climate system is in steady-state radiative balance at TOA with a surface temperature of T0 deg K. The outgoing radiation is R(T0) and is exactly equal to the incoming solar flux, S.
Assume further that at time t = 0 the system is perturbed by a positive downward flux step-forcing of magnitude F Watts/m2 at TOA.
The new incoming flux is the solar flux plus the flux forcing. The outgoing flux is R(T) where T is the absolute temperature still expressed in deg K and which changes with time as T changes, increasing in time in this case.
The net flux imbalance is then given by the difference between the incoming and outgoing fluxes:-
N = S + F – R(T) Eq 1
Clearly at time t=0, T=T0, and R(T0) = S; hence initially the net flux imbalance is equal to the flux forcing F.
We make no assumption about the shape of the function R, but all continuous and differentiable functions can be expanded using Taylor series. Here we choose to expand about the point T = T0.
R(T) = R(T0) + R’(T0)*(T – T0) + 0.5* R’’(T0) * (T-T0)^2 + … Eq 2
Given that we are considering only a small perturbation in flux and temperature we will use a first order approximation of this series i.e. just the first two terms.
Our net flux balance in Eq 1 can then be approximated as
N = S+F – {R(T0) + R’(T0)*(T-T0)} Eq 3
Recalling that S is exactly equal to R(T0) and noting that R’(T0) is a constant, we can rewrite this expression as
N = F – alpha * (T – T0) Eq 4
NOTE THAT alpha IS UNAMBIGUOUSLY AN ESTIMATE OF THE LOCAL GRADIENTOF THE FUNCTION, R.
It is typically called the total linear feedback term and has units of W/m2/deg K. Note also that there is no requirement to invoke Control Theory in this derivation, with the risk of stretching the analogy (and indeed the analogue in this instance) too far.
As time goes to infinity, N goes to zero and the temperature T goes to the Equilibrium Temperature Te, (a misnomer, but too widely used for me to bother trying to change the term). We can then write
Te – T0 = F/alpha Eq 5
We can decompose alpha into its component feedbacks. More specifically we can decompose it into the Planck response and other feedbacks.
We write alpha = alpha_Planck + alpha_Other
Using Eq 5 separately to calculate the temperature change due to Planck alone and the temperature change due to all feedbacks, we find that the amplification factor is given by:-
(Change in Temperature due to all Feedbacks)/ (Change in temperature due to Planck response) =
F/alpha divided by F/alpha_Planck = alpha_Planck/ (alpha_Planck + alpha_Other)
There is no startling error in the above, nor has anybody “forgotten that the sun is shining”.
All of the above is intended merely to be an expansion of the reviewer’s concise but accurate comment. His last sentence is also very important. You wish to substitute a secant gradient passing through the origin at absolute zero for the estimate of the local gradient (local = around T0) of the function R which describes restorative flux. This would only make sense if you could present a theoretical argument why the functional form of R can be approximated as a straight line passing through the origin at absolute zero. In practice, there are several overpowering reasons to doubt that this functional form could ever be a good approximation of reality, the most obvious being that, while the Planck response can be very well approximated as a linear function over small temperature perturbations, it is highly non-linear with temperature change over an interval from zero to 290 deg K! Water phase change would additionally make your linear assumption highly unlikely.
I don’t doubt for a moment that median estimates of ECS of around 3.0 deg K are too high, but it is worse than useless trying to prove that with laughably bad methodology.
As explained in the head posting, we do not dispute official climatology’s derivation of the variant system-gain equation from the energy-balance equation via a Taylor-series expansion. We merely point out that, at any given moment, the feedback processes (denominated in Watts per square meter per Kelvin) respond to the input signal (in Kelvin) that they find – and not just to any arbitrarily chosen perturbation thereof.
Therefore, at any chosen moment, such as 1850, if one knows the reference temperature (before accounting for feedback) and the equilibrium temperature (after accounting for feedback), one may derive the feedback system-gain factor applicable at that moment.
The models, however, attempt to derive that system-gain factor as the product of the Planck parameter at that given moment (for, as you say, it varies with temperature, though very slowly) and the sum of the individual feedback processes. This bottom-up approach has failed, in that the observed rate of warming is approximately one-third to one-half of what was originally predicted.
Furthermore, it is evident that very nearly all of the exaggeration of equilibrium sensitivity in the models must come from overstatement of the feedback response.
The Taylor-series expansion that gives the variant system-gain equation unfortunately tells us nothing of the value of the feedback sum (in Watts per square meter per Kelvin), of the feedback factor (unitless) or the system-gain factor (unitless).
However, our method starts from the common-sense position, which our professor of control theory says is unquestionably correct, that at any given moment the feedback processes, whatever their magnitude, respond to the entire input signal they find, and not to any other or lesser or earlier quantity.
We say nothing about what feedback processes might have existed at some earlier time or at some lower temperature, or about how those processes might have responded. And the feedback processes currently extant, being inanimate, do not know what part of the input temperature they should respond to. They simply respond to the whole thing. From this consideration, our method follows.
If this consideration is wrong, please say why. In stating that feedback processes in the current age respond to the reference temperature they find, we are saying absolutely nothing about the slope of what you are calling alpha in any previous age, still less at zero Kelvin. We are saying no more than we found on our test rigs: that the feedback processes respond to the input temperature they find, and they neither know nor care how other feedback processes might have responded to any other temperature.
Lord Monckton,
Thank you for your response.
“If this consideration is wrong, please say why.”
I would agree with you that feedback processes in general must respond to the entire input. Let us consider though what that actually means in the context of the climate system.
The actuator for temperature feedback is always the net flux imbalance. A flux forcing causes a change in (surface) temperature. The change in surface temperature causes a direct increase in outgoing LW (S-B), a change in water vapour in the atmosphere, a change in cloud fraction and distribution, a change in the vertical temperature profile (lapse rate) and a change in albedo via cloud and ice distribution. Each of these changes then acts upon either the net received SW or the outgoing LW to change the net flux balance at the TOA. It is this change in net flux which then controls the further heating or cooling of the climate system, and hence the trajectory in time of further temperature change.
Now consider your system in 1850, which you were happy to assume ad argumentum was in a steady state. It was in a steady state because at that particular absolute surface temperature the ougoing LW exactly balanced the net incoming solar. The determinants of the incoming and outgoing radiation were the climate state variables at the time, being the effective atmospheric water vapour content, lapse rate, cloud distribution, albedo etc. How much temperature “feedback” is in that system at steady state?
IThe answer is that it is completely indeterminate and – unless you wish to postulate a forcing and feedback history to explain how each of the climate state variables got to where they were – completely irrelevant. What you do know is that a perturbation in those climate state variables will have an effect on the net flux imbalance, and in this sense, you do indeed have to base any calculation of variation on the absolute condition at the time because the absolute condition will determine the rate of change of net flux due to feedback with respect to temperature change for each of those climate state variables.
Once you have determined the local rate of change of net flux due to feedback with respect to temperature for those variables at the absolute condition prevailing you have already determined your best estimates of the feedbacks under first order assumptions.
It really is as simple as that.
You appear to be accepting the above when you write: “…we do not dispute official climatology’s derivation of the variant system-gain equation from the energy-balance equation via a Taylor-series expansion.” If that is indeed the case, then you should also understand that substituting a secant gradient estimate from the origin for the local gradient approximation (i.e. the derivative of total net flux change due to feedback with respect to temperature change) cannot represent an improvement over what is already the best available estimate under first order assumptions, and is highly unlikely to yield a valid answer.
Kribaez has failed to understand our argument. We are saying that in 1850 it can be demonstrated that the reference temperature (before the action of any feedback) was 254.8 K or thereby; that the equilibrium temperature (after feedbacks have acted) was 287.55 K; and that, therefore, the feedback system-gain factor was 287.55 / 254.8, or 1.13. We are not substituting a secant gradient estimate. We are simply stating the blindingly obvious.
Kribaez appears not to understand that feedbacks acted to bring up the surface temperature from the 254.8 K that would have obtained in their absence to the 287.55 K that actually obtained after they had acted. Thus, the difference between the 287.55 K equilibrium temperature and the 254.8 K reference temperature is the feedback response that was present in 1850.
Lord Monckton,
I assure you that my comments stem not from the fact that I don’t understand your argument, but that your argument has no validity.
It was only after I made all of my previous posts above that I realized from a comment by jhborn that this issue has been round the houses a couple of times. I Googled “Roy Spencer plus Lord Monckton” and was taken to two articles which appeared in March of this year.
Here: http://www.drroyspencer.com/2018/03/climate-f-words/
and here: http://www.drroyspencer.com/2018/03/lord-monckton-responds/
I found I agreed with almost everything that Dr Spencer wrote – with one exception. Being a pedant, I did not like his loose use of the term “energy imbalance” rather than “net flux imbalance”, which is the driver of all temperature change in time under the simplifying assumptions of Energy Balance Models. Temperature change does not beget temperature change. Temperature change begets a change in climate state variables which begets a change in net flux which begets a change in heating rate which controls the rate of total energy accumulating in the system which controls the trajectory of the transient temperature and ultimately the equilibrium temperature (again under the simplifying assumptions which underpin EBM’s. It is evident that if you did not accept Dr Spencer’s arguments at that time, then it is unlikely that you will accept similar arguments from me despite their “blindingly obvious” validity. I would however draw your attention specifically to the point that Dr Spencer made about the artificiality of your construct of 255 as a reference temperature without feedbacks.
“The 255 K radiative equilibrium temperature Christopher speaks of is physically impossible anyway (if there is no greenhouse effect, then there is no water vapor, thus no clouds, thus the Earth’s albedo will be different from that assumed when calculating the 255 K value). It’s an extremely simplified construct, based upon grossly simplified assumptions, of no value for computing climate sensitivity.
Another reason that 288K-minus-255K doesn’t measure the strength of today’s greenhouse effect is that 288 K is AFTER moist and dry convection have cooled the surface by about 40 deg. C from the extremely hot surface the greenhouse effect would caused without convective heat transport.
Yes, the models are wrong. But the reasons why cannot be deduced from unrealistic assumptions input into electrical circuit calculations.”
Quite so.
If Kribaez wishes to be a pedant, let it know that we are dealing not with fluxes but with flux densities.
If Kribaez thinks temperature change does not beget temperature change, let it inform the IPCC that it should not denominate its feedbacks in Watts per square meter per Kelvin of – er – temperature change.
If Kribaez thinks that doing the calculations in flux densities rather than in temperatures will materially alter the output, let it present the calculations.
If Kribaez’ half-understood repetition of an erroneous point by Dr Spencer represents his position, he should read the head posting, where he will notice that a careful distinction is drawn between condensing and non-condensing greenhouse gases. The equilibrium temperature for 1850 was derived by obtaining first the emission temperature without non-condensing greenhouse gases and then the warming (before accounting for feedback) caused by the presence of those gases to 1850.
kribaez:
Thank you for getting to the heart of the matter.
Unfortunately, you are but the latest of several (but disconcertingly few) commenters who over the last several months have done so but, as you have now seen, failed to get Lord Monckton to understand.
What is more concerning is the apparent inability of most WUWT denizens to understand the implications of the math that a few people like you have laid out. The fact that so many skeptics keep being taken in by such an obvious lightweight makes us skeptics look like buffoons.
(Your sweeping statement about what “denizens” of this forum think and say is unacceptable, You look like the buffoon” for doing it) MOD
jhborn,
Your comment is a clear example of concern trolling.
FYI
Concern troll
A concern troll is a false flag pseudonym created by a user whose actual point of view is opposed to the one that the troll claims to hold. The concern troll posts in Web forums devoted to its declared point of view and attempts to sway the group’s actions or opinions while claiming to share their goals, but with professed “concerns”. The goal is to sow fear, uncertainty and doubt within the group.[49] This is a particular case of sockpuppeting.
An example of this occurred in 2006 when Tad Furtado, a staffer for then-Congressman Charles Bass (R-NH), was caught posing as a “concerned” supporter of Bass’s opponent, Democrat Paul Hodes, on several liberal New Hampshire blogs, using the pseudonyms “IndieNH” or “IndyNH”. “IndyNH” expressed concern that Democrats might just be wasting their time or money on Hodes, because Bass was unbeatable.[50][51] Hodes eventually won the election.
etc.
ref. https://en.wikipedia.org/wiki/Internet_troll#Concern_troll
Richard
Richard S. Courtney:
You’re welcome to your opinion as to what my “actual point of view” is. I say it’s that increasing atmospheric CO2 concentration is a good thing and that for us who think that way to back charlatans like Lord Monckton is to lead with our chins. And it’s hard to imagine a “concern troll” on this issue writing a post like https://wattsupwiththat.com/2017/07/25/whos-afraid-of-sea-level-acceleration/.
Your choice, but you may want to consider actually checking out Lord Monckton’s math. It makes no sense. If you understand math, you won’t want to be associated with his.
jhborn:
I did not say the words you attribute to me in quotation marks.
Only a troll puts words in the mouth of another.
But that is OK because – as I said – it is very clear that you are a concern troll.
Are you obtaining remuneration for your trolling and if so then are you aable to say the source of the payments?
Eichard
PS I have checked the math (it is simple) and I strongly doubt your claims to mathematical ability.
My goodness, MOD, I do seem to have hit a nerve.
Look, I’m really okay with your not considering my statement acceptable.
But you may want to reflect on this site’s policy of persisting in featuring (now, six) head posts directed to a theory of mathematical and logical incoherence after several (but again, far too few) of your readers have explained its problems, and after other observers such as Roy Spencer and Steve McIntyre have made statements that would have served to wave you off if you’d had the wit to understand them.
But, by all means, go ahead and indulge your fantasy about whom those who really understand the math and logic would consider the buffoon.
Mr Born is, as usual, way out of his depth and is, as usual, spitefully petulant.
MOB wrote;
“Positive feedback in dynamical systems amplifies the output signal. Negative feedback attenuates it. ”
Not even wrong….
The gain stage (amplifier) consumes energy from a source other than the input signal (ie an external power supply) to create the output signal.
Negative feedback controls the amplifier so that the output responds as desired. It could be larger or smaller than the input signal. A larger output is most common since there are passive ways (a voltage divider made of resistors) to attenuate a signal.
Positive feedback causes oscillation. An oscillator is an amplifier with positive feedback.
The Bode feedback equations are not and never will be appropriate for understanding a passive system with energy flowing through it (IE the climate).
You are barking way way way up the wrong tree, but keep going you might make it to the top….
Cheers, KevinK
kevinK is, indeed, not even wrong.
The approach we have taken, as is evident from the circuit diagrams, is to set the mu gain block to unity, effectively removing it, and simply adding any perturbation to the input signal before inputting it to the feedback loop. Where mu = 1, the input and output nodes are equipotential and may be combined into a single node, as shown in the diagram.
Positive feedback causes oscillation if the feedback factor is unity, and not necessarily otherwise. The IPCC indeed imagines that a feedback factor of unity is possible, but we do not.
If the Bode feedback equations are not applicable to the climate, then there is no justification for the use of these equations throughout the literature on climate sensitivity from at least 1984 to the present (see e.g Hansen 1984, Schlesinger 1985, Lindzen 1992, Bates 2007, IPCC 2007 p. 631 fn., Roe 2009, Monckton of Brenchley 2015ab, Bates 2016), and there is no justification for assuming the very high climate sensitivities the greater part of which come not from directly-forced warming but from the feedback processes that kevinK says are inapplicable, in which event our conclusion that feedback responses may be ignored without significant error is correct a fortiori.
“The approach we have taken, as is evident from the circuit diagrams, is to set the mu gain block to unity, effectively removing it, and simply adding any perturbation to the input signal before inputting it to the feedback loop. Where mu = 1, the input and output nodes are equipotential and may be combined into a single node, as shown in the diagram.”
How you set the “gain block” does not remove the necessity of an amplifier (powered from an external “power supply” actually an energy supply) for the Bode feedback equations to apply.
Yes, you can “effectively remove” (with reference to the “gain block”)….. And this indeed makes the inputs and outputs in the circuit diagram “equipotential”……. But the Bode equations NO LONGER APPLY…… You simply have a bunch of passive components like resistors and capacitors. These are analyzed with Kirchoff’s and Thevenim’s theories, Bode does not even have to be in the room….
You may set the gain block to any value you wish, 1, -1, the square root of minus 1, pi, a prime number, tomorrows winning lotto number…… Does not make the Bode equation applicable…..
“Positive feedback causes oscillation if the feedback factor is unity, and not necessarily otherwise.” Not even wrong….. Positive feedback causes oscillation regardless of the “feedback factor”…. There is way more to the Bode equations than you realize, you should look up “phase margin”. It is possible to achieve oscillation with negative feedback if there is not sufficient phase margin. Bode was very bright, please take the time to study and understand his work completely before applying it where it does not belong…..
“If the Bode feedback equations are not applicable to the climate, then there is no justification for the use of these equations throughout the literature on climate sensitivity from at least 1984 ……………” DING DING DING WE HAVE A WINNER………
Correct at last…… I believe you are finally reaching the top of the tree, young man…..
You may now stop barking so much…… Too many words, way to many “seldom” used words. Prodigious verbiage does not make the analysis correct.
The conditions under which the Bode equations apply were detailed back about 70 years ago. They DO NOT apply to the climate….. The fact that folks with no proper training in the use of the Bode Equations chose to apply them to the climate does not make them applicable….
I have designed many circuits using feedback, funny thing, once I turn off the power supply all feedback’s (positive, negative, random, conservative, liberal….) stop and everything assumes the voltage (or temperature if you like) of the surroundings……
Cheers, KevinK (BSEE, MSEE, 40 years of experience with electrical circuits, a few patents)
Kevin K, like so many, has studied but not thought about the relevant science. The truth is that, whether he likes it or not, the feedback system-gain equation of which the Bode equation is an early instance is of universal application in modeling all feedback-moderated dynamical systems, of whatever kind.
Official climagology has at least understood that much.
Consider a simple feedback-loop block diagram, with an input signal. a summative input/output node, a feedback loop from and to that node and an output signal.
What is the relationship between the input and output signals in the presence of nonzero feedback factors. Provided that the absolute value of the feedback factor is less than unity, when the input signal enters the loop it will pass around it ad infinitum. Thus, the output signal is the product of the input signal and the sum of the infinite series {f^0 + f^1 + f^2 + … ad inf.}.
The sum of the infinite series is 1 / (1 – f). Therefore, the output signal is equal to the product of the input signal and 1 / (1 – f). Thus, 1 / (1 – f) is the system-gain factor.
The question is not whether this mathematics is applicable – for it very obviously is, and is recognized as such even by official climatology. The question is whether the output signal is the product of the system-gain factor 1 / (1 – f) and the absolute, entire value of the input signal, or the product only of the system-gain factor and some arbitrary fraction of the input signal.
In fact, the output signal – equilibrium temperature – is the product of the system-gain factor and the absolute input signal. And that’s an end of the matter.
Ah yes, “official climatology” improperly applies a equation from a field of study with which they have no relevant experience and therefore it is the “end of the matter”.
“the feedback system-gain equation of which the Bode equation is an early instance is of universal application”
So you say, I say SHOW US THE GAIN……………..
Where exactly is the temperature (energy content of the atmosphere) amplified ?????
“In fact, the output signal – equilibrium temperature – is the product of the system-gain factor and the absolute input signal. And that’s an end of the matter.”
Wait just one cotton picking minute (old American phrase, may now be impolitic)……..
First you claim victory by setting the “system gain factor” to 1.000000, unity, a single digit real number greater than zero and less than 2 to make your case, then you claim that the equilibrium temperature is the input temperature times 1.0000000……
So your argument comes down to; “I understand the Bode feedback equations better than Bode himself”…..
I do appreciate all you have done to raise critical analysis of the “Greenhouse Gas Hoax”, but you do everyone a disservice with your claptrap (sorry but that is a correct characterization of this nonsense) about how the climate science field is using the Bode equations “mostly correctly”, but You Know How to use them even better…..
CLAPTRAP and WORD SALAD……….
To summarize your math; The temperature after the “Greenhouse Effect” occurs is the temperature before the “Greenhouse Effect” occurs times a “gain factor” of 1.00000000000……………..
Your arguments have proven that there is indeed no “Radiative Greenhouse Effect” that causes any steady state increase in temperatures……
Please do not start designing any electrical circuits where loss of “Life and Limb” are a consideration.
Stick with those feedback equations, any bad thing (hot, cold, dry, wet, plagues of locusts. acne breakouts) is bound to be worse after a “system gain factor” of 1.000000 is applied…….
Cheers, KevinK
Kevin K’s comment is incoherent, even by his low standards. For a start, he confuses the system-gain factor (also known as the feedback amplification factor or the transfer function) with the direct-gain factor. It is the latter, not the former, that we have set to unity, adding any perturbation of the input signal to that signal before it enters the feedback loop. This approach is functionally equivalent to Bode’s feedback amplifier.
The system-gain factor is not unity. It is 287.55 / 254.8, or 1.13, as explained in the head posting. Do try to keep up.
At one point MOB sets the “system gain factor to unity”;
“The approach we have taken, as is evident from the circuit diagrams, is to set the mu gain block to unity”
Then later MOB sets the “system gain factor to”
“The system-gain factor is not unity. It is 287.55 / 254.8, or 1.13, as explained in the head posting. Do try to keep up.”
System gain factor (aka mu) is “unity” except when a mu of unity fails to explain things then mu magically becomes 1.13.
I am “keeping up” very well, you are positing multiple values of the “system gain factor” as necessary to explain this “shell game”…
Dear MOB, you are a “poser” you can’t discriminate your “system gain factor” from your own hind end….
Please stop pretending to be an accomplished electrical engineer that knows the proper application of the Bode equations. Mr. Bode would be laughing out loud at your silliness….
Cheers. KevinK
“Thus, the output signal is the product of the input signal and the sum of the infinite series {f^0 + f^1 + f^2 + … ad inf.}.”
I’m seeing this a lot lately on this thread. It is the tendency of those who quote Bode to make a hash of simple math. Feedback algebra just goes like this. You have an input I, an output O, which is partly fed back to the input. So the relation is
O = μ*I + f*O
where μ is the gain without feedback and f is the fraction fed back. All the fuss is about this simple linear equation. You can, if you wish, write it as
O = μ*I/(1-f)
expand 1/(1-f) as a geometric series and sum it again. But it doesn’t add anything.
Mr Stokes is not, perhaps, familiar with the sums of convergent infinite series. However, if he had any expertise in this field, he would know that the description of the system-gain factor as the sum of an infinite series is standard in control theory; he would know that, subject to the convergence condition that the absolute value of the feedback factor f be less than 1, the relevant series sums to 1 / (1 – f); he would know that 1 / (1 – f) is the system-gain factor; and he would know that this use of the sum of a well-known infinite series is equivalent to deriving the system-gain factor by the method he describes.
As he very well knows, the mathematics I have presented is in this respect entirely correct. It is he, not I, who has – as usual – made a hash of it. He should really try to recall some of the systems theory he once knew. If he can recall it just fine, then he should stop his deliberate misrepresentations of it. He deludes no one but himself.
I am very familiar with the theorems on radius of convergence of power series. I am simply pointing out that there was no need to create such a series in the first place. Simple linear algebra gives the right expression directly, with no need for summing infinite series.
Aha! Mr Stokes now concedes that, in saying earlier that I had “made a hash of simple math”, he was – as usual – lying. For lying in these columns is what he is, no doubt, well paid to do: for why would he otherwise bother to write such artful but arrant nonsense? He says that, after all, he knows about convergent series. That is an admission that he knew I was right about this particular convergent series all along.
He now concedes that the transfer function may be explained and represented as the sum of an infinite series; that, in my replies to one or two commenters here, I had correctly explained why the feedback loop generates that infinite series; and I had correctly summed the series. In short, he now concedes, abjectly, that there was nothing wrong with my math at all.
And when he gets around to reading the head posting he will find the linear algebra of which he speaks clearly set out in part (a) of the block diagrams, and he will also find the consequent simplification of those block diagrams in part (b).
He knows perfectly well that the infinite series is not mentioned at all in the head posting, and that I had added it in replies to one or two commenters as a way of helping them to grasp why the feedback loop works as it does. He may or may not find that explanation helpful: but it was not an explanation for him. For one suspects he is handsomely paid by some undisclosed vested interest or another to pretend not to understand these things, and only to admit them whenever – as on the present occasion – he finds hiself backed into a corner, having told an obvious lie to the effect that i had gotten the math wrong and having been caught out.
If Mr Stokes is not paid to lie here, then why does he lie? I think we should be told.
“In short, he now concedes, abjectly, that there was nothing wrong with my math at all”
I had never said otherwise. It is just dumb. As I pointed out, you can deal with the matter in just one line of math:
O = μ*I + f*O
with a second if you want
O = μ*I/(1-f)
And I said you can
“expand 1/(1-f) as a geometric series and sum it again. But it doesn’t add anything”
It is just pointless meandering.
As is your circuit, which adds nothing to the very simplest feedback circuit with one op amp. You can create such a circuit with exactly the same functionality as your much more complicated one. Neither has anything to do with climate, or needs to be built to determine its functionality. The ability of op amp circuits to implement feedback is not a scientific research matter.
Mr Stokes now lies about his lies. Recall that he had stated I had “made a hash of” my math. He now concedes, again, that my math was at all points correct. When he gets around to reading the head posting he is supposed to be commenting on, he will find the simple linear-algebra equation to which he refers. It is very plainly set out on not one but two block diagrams in the head posting.
Since he is calculatedly slow on the uptake, I shall explain to him again that the infinite-series point I had made in this thread was made to assist one or two commenters in understanding why the system-gain factor takes the form it does. He is now again compelled to concede that my account of the matter was, after all, correct and that I had not made “a hash” of it.
The truth of this matter is that Mr Stokes had tried, falsely, to give the impression that I had gotten the math wrong; he was caught out in his lie; and now, methinks, he doth protest too much.
However well paid he may be to lie here, his lies are not doing him or his cause any good at all. In future, let him hold fast to the truth, or be silent.
If Chris’ team’s result of 1.17 degrees C per doubling be correct, then positive and negative feedbacks in the complex climate system must effectively cancel out to net zero, since the no-feedback laboratory estimate of ECS is 1.1 to 1.2 K.
Which IMHO is about what actually happens.
Theo is more or less right. Derivable from Andrews (2012), the current CO2 radiative forcing is 5 ln 2 = 3.466 Watts per square meter, and the Planck parameter is 0.3 Kelvin per Watt per square meter, giving a reference sensitivity 1.04 K. The product of this value and the feedback system-gain factor 1.13 that we have derived is 1.17 K.
Thanks. That’s a bit lower than the figures I generally see quoted. Obviously, I’ve not derived it myself.
The reference sensitivity to doubled CO2 is an approximately logarithmic function of the proportionate change in concentration. The coefficient was 6.3 till IPCC (2001) cut it to 5.35, and it’s just 5.0 in the current generation of CMIP models.
IMO, on a homeostatic water world (at least between changes of state such as transitions into and out of glacial phases), net feedbacks are likely to be negative.
… but one can’t simply guess these things. Where equilibrium temperature in 1850 was 287.55 K, and where reference temperature in that year was 254.8 K, the system-gain factor was 287.55 / 254.8, or 1.13. And that means weakly positive feedback.
At 600 ppm Viscount Monckton will be judged by data a genius or a miscreant.
At 800 ppm we’ll know for certain.
My money is on the Viscount.
We shall contact Centrebet/William Hill today and suggest they make a book on it.
Unfortunately, we’ll probably never get to 800 ppm.
Many believe CO2 will exceed 500 ppm before 2050.
600 is likely too far out for the likes of William Hill.
Long-bets may be the go . . .
http://longbets.org/bets/
Best way to profit from the inside information that the global warming scare is about to come to an end is to wait till we know a leading climate journal is going to publish our paper and then short renewable-energy and other “green” stocks, such as Tesla, if it hasn’t gone bust already by then.
I am sure that if Hansen and his cohorts had studied Electrical Engineering in undergrad (instead of dreaming about ways to Save the Planet), the correct formula for closed-loop gain would have been drummed into his head
Lord Monckton – I watched your youtube presentation video.
1) I suggest you correct, as soon as possible, the errors in the slides which you noted verbally.
2) Please can you tell us the cost of the bill you avoided by agreeing not to name the government laboratory which undertook the tests for you? To my mind it is contradictory to sign a contract securing the right to publish results from a named test facility and then waive that right rather than pay the bill. Presumably the fee was agreed before the test took place and the reason for your contractual disclosure stipulation was in order to ensure credibility and verification of the results. To forfeit this important validation seems contrary to the whole thrust of your endeavor.
3) I suggest you produce an alternative, absolute minimum presentation of the essential theoretical argument with simple single colour slides and consistent font sizes and layout.
4) I suggest you produce a video of the experimental process too, with exact circuit design, specifications, procedures and test equipment to enable independent verification of your results.
Thank you.
Monckton & Co are working on this in their spare time without funding.
I agree with your desire for a professional presentation with polish; however, most academics rank presentation low. We employ academics (as consultants) on R & D projects so we know this first hand (the best minds are usually the worst at presentation).
I believe the lab bill is simply a matter of . . . ‘if you won’t put your name to it, we’re not paying the bill’. If you don’t have heaps of ‘other people’s money’ to throw around then any such saving is attractive.
In case you don’t know:
1. Big-oil won’t touch this stuff because all Big-oil strongly desire adherence to Paris hoping carbon trading will ensue so they can utilise (wrought) credits for significant corporate enrichment.
2. No Government will overtly support ‘denial’ or counter-research for fear of losing votes (including Trump).
3. All Western institutions are opposed to anything that curtails funding and global warming is the golden-pot of funding .
4. No academic or public servant will question any part of AGW theory for fear of being overlooked, demoted, victimised or dismissed.
Anyway, there may be hope for your desires . . .
Are you in a position to offer your time and expertise to undertake or assist Monckton & Co with any or all of your four (4) requests?
If so please let them know.
Thank you.
Well done, Warren! It’s all too easy to whinge about our presentation, but this is an idea that has a certain minimum of complexity attached. If we oversimplify it, people say it’s too simple. If we tell it like it is, people say it’s too complicated. But the furtively pseudonymous “slow to follow” is perhaps an exemplar of his self-description: too slow to follow our argument. Many others have commented on how clear they found that argument to be. One can’t please everyone.
(wrought) should be (rort).
Lord Monckton
1) Thanks for your comments on your slides – I disagree and I maintain that leaving a slide with a simple to correct error, as noted at 12mins 40 seconds into the video, is foolish and amateur.
2) I also maintain that the anecdote you tell at 28min 26 seconds to 29mins 52 seconds shows poor judgement on your part. Unfortunately, your low information content response does nothing to help illuminate the reasoning behind your choice.
3) As you say, one can’t please everyone.
4) If producing a video of the physical test is beyond your resources, I still suggest you publish the exact circuit design, specifications, procedures and test equipment to enable independent verification of your results: it is possible that an independent party could produce a useful video as a result.
The furtively pseudonymous “slow to follow” will have to put up with the presentation as it is for now. If it wishes merely to criticize, it need only do so once. At present our chief concern is to ensure that our argument is correct, and then to publish it in a suitable learned journal. Once we have done that, the resources to put together a professional presentation will, no doubt, become available.
As Warren has already pointed out, no one pays us to do our work on the climate. If “slow to follow” were to offer a substantial donation towards the cost of a professional presentation, that would be of more use than repetitive whining.
“At present our chief concern is to ensure that our argument is correct,” – apart from where a simple single slide edit is required or verification of sources is facilitated or where replication of results is enabled.
If your interest is really in sharing your results and work for scrutiny and testing, I suggest you put your effort into the dealing with the above instead of making much of the simple internet reality of the common practice of people posting with a pseudonym.
Don’t whine.
Don’t dodge.
Your avoidance of the simple substance of my comments and your childish responses undermine your credibility.
Good day.
Don’t whine.