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.”
Here is another version of my above proof:
If the feedback equation is true for an increase in temperature, then it is true for a decrease in temperature. Let T (abs) be the equilibrium temperature of the earth. Then if the sun was turned off and the earth was sampled n times as it cooled to 0 (abs) you would get:
T2 (abs) = T (abs) – delta T1
T3 (abs) = T2 (abs) – delta T2
…
0 (abs) = Tn (abs) – delta Tn
From this you can calculate the feedback for each delta (x) as:
feedback(delta Tx)
And from this the feedback at T (abs) as:
Feedback (T (abs)) = Sum (feedback(delta Tx)) for x= 1 to n
To compltet the proof reduce the number of samples to 1 and invert the sign.
It is really simpler than Mr Berple suggests. Set the mu gain block to unity, adding any perturbation of the input signal to that signal before inputting it to the summative node. Then the only elements in the circuit are the input signal, the summative input/output node, the feedback block in the feedback loop, and the output signal.
Follow the input signal round the feedback loop. It goes round and round and round an infinite number of times. Each time, it is multiplied by f and then added to the previous total. Therefore, 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.}. That is a well-kent series in mathematics. Its sum is 1 / (1 – f). That, then, is the system-gain factor A.
Therefore, the feedback-loop diagram simplifies to the statement that the output signal is the product of the input signal and the system-gain factor A.
Given that A is inanimate, and given that there is no sub-circuit or other process in the climate that permits A to decide that it will only multiply itself by some part of the input signal, it follows that the output signal is indeed the product of A and the entire input signal.
Note that this does not prevent climatology’s variant equation from being correct. One can call the input signal a perturbation and the output signal a perturbation.
But the advantage of the mainstream equation, using absolute quantities for the input and output signals, is that it provides a remarkably simple method of deriving the Holy Grail of climate-sensitivity studies – the system-gain factor. And that’s that.
LM’s characterization of the problem using process control theory is simply incorrect. The system input is not temperature, but heat in the form of solar radiation, which we can consider to be a constant. The system output (response) is the earth’s temperature. How the system (the earth in this case) responds is a function of its physical characteristics, which are not necessarily constant.
Mr Graney’s concern is understandable but incorrect. In mainstream climatology (not the most reliable sources, I agree), temperature feedbacks are just that: they are denominated in Watts per square meter per Kelvin of the temperature that triggered them. The product of the sum of these individual feedbacks and the Planck sensitivity parameter (in Kelvin per Watt per square meter) is the unitless feedback factor.
Mr Graney may like to read Roe (2009), where he will find a good pedagogical treatment of the question of temperature feedback, though of course that paper makes the same mistake as all other papers in climatology on this topic.
But let me be clear about what I mean when I say climatology has erred. Its error is one of missed opportunity. Its variant system-gain equation is a valid equation, but the emission temperature from the Sun and the warming from the pre-industrial non-condensing greenhouse gases has been subtracted out. Restoring these missing terms allows an immediate, robust, accurate derivation of the Holy Grail of climate-sensitivity studies – the system-gain factor.
you can do the calcs with temperatures or you can do them with fluxes. Either way the feedback mathematics works.
Quite right. There is very little difference between the two methods.
The statement
“Feedback processes, being inanimate, cannot discriminate between a pre-existing temperature and a perturbation of that temperature.” is accurate and describes why the feedback factor cannot be high enough for an ECS of 3 C. An ECS of 3 C would require a feedback factor of 3/1.1 = 2.72.
The input being the 1.1 C of forcing warming from the doubling of CO2.
If we assume a latency between input and output of Hansen’s 37 years, then the .2 C of pre 1940’s
warming would cycled two times through the feedback process.
So , (CYCLE 1).2 X 2.72 =.544 C (CYCLE2) .544 X 2.72= 1.48C.
Since the total warming is less than 1.48 C, that feedback factor with that latency
can be eliminated. The latency could be longer, but if we are going to attribute
and of the observed warming to greenhouse gas forcing, then the possible
amount of feedback factor diminishes.
Mr Bahm’s summary of the position is excellent. Indeed, the official position is even worse than he says, for the current mid-range estimate of reference sensitivity to doubled CO2 (i.e. the warming before accounting for feedback) is just 1.04 K (derivable from Andrews, 2010). And the mid-range Charney sensitivity (loc. cit.) is 3.37 K. So official climatology’s implicit mid-range estimate of the system-gain factor is 337/104, or 3.2, when the true value is 1.13.
One can also do things their way and use the variant system-gain equation. This won’t work for 1850, but it will work for 2011. They say there has been 2.29 W/m^2 net anthropogenic forcing to 2011, which, multiplied by the Planck parameter 0.299 K/W/m^2 (Schlesinger 1985), gives a period reference sensitivity of 0.68. However, only 0.75 K of warming occurred over the period (HadCRUT4). Allowing for the 0.6 W/m^2 imagined, and probably imaginary, “radiative imbalance” of 0.6 W/m^2 in 2010 (Smith+ 2015), the equilibrium warming for 2011 would have been 1.02 K. Now, the system-gain factor implicit in these two values is 1.02 / 0.68, or 1.5, which would give a Charney sensitivity of 1.04 * 1.5 = 1.55 K. Now, that is pretty close to our estimate of a system-gain factor 1.13, giving a Charney sensitivity of 1.04 * 1.13 = 1.17 K, and not at all close to the CMIP5 mid-range estimate of 3.2 and 1.04 * 3.2 = 3.37 K.
Are the “feedback theory only applies to deltas” trolls not saying, equivalently, that the sun was not vaporizing water until we started “dumping” anthropogenic CO2?
Mr Miller makes an excellent point. Indeed, Lacis et al. (2010), right from the heart of true-believing climate extremism, say that in the absence of any non-condensing greenhouse gases the albedo would be 0.418 compared with 0.298 today, and their albedo implies a waterbelt Earth, with an ice-free equatorial zone. Water vapor – treated as a feedback in climate studies – would then be free to enter the atmosphere by evaporation and convection. But, say the trolls, this feedback cannot have occurred because we cannot be blamed for it.
It’s enough to make you weep – another feedback, perhaps.
This is the fundamental point, isn’t it? Namely that the water feedback component begins to kick in at whatever temperature is such that the planet has open water, such that water starts evaporating and water vapour starts accumulating in the atmosphere.
Thus as at 1850 (or whatever date one wants to chose), there is already a considerable water feedback component acting, as a forcing, alongside the forcing of incoming solar irradiance.
The temperature as at 1850 must be made up of the forcing of solar irradiance + the forcing of then present water vapour + the forcing of the then present C02 + the forcing of the then present GHGs.
Mr Verney is almost exactly right. The water vapor forcing, however, is usually treated in climatology – and is thus treated by us – as a feedback forcing, and is called the water vapor feedback.
The first clue that something is wrong is that the feedback is greater than the forcing. This is the defining characteristic of an unconditionally unstable system.
Either they did their theorizing at night, at the Pole, or in Plato’s Cave. I think the latter. Along comes someone to tell the 7 chained cavedwellers it is the Sun casting shadows on the wall!
Of course the messenger was temporarily blinded by the Sun outside, so the 7 stoned him saying, look, he cannot see our thoroughly understood shadows anymore!
The 7 reviewers, peers all.
An explanatory video should be made about this.
It would be a great help for people who neither understand the despicable deception that has been perpetrated on them nor grasp its enormous significance.
Most grateful to Sasha. If she will persist and read through the piece to the end, she will see a link to a video made on my recent visit to Spokane, Washington.
And if anyone would like to hear an explanation of our result in person, he or she will be most welcome at Camp Constitution in Connecticut next week. Be there or be square!
He has made the video. Scroll up
I would love to get behind this, but after looking into it for ages I don’t see a basis to use zero Kelvin as a datum for feedbacks. It’s arguably more valid to use 255 Kelvin (the approximate temperature where water vapour feedback starts in earnest according to Clausius–Clapeyron) more like the IPCC.
The exam question is: what is the feedback at current global temperature (around 287K), i.e. if you force the temperature up 1°C from here how much will feedbacks add to this, perhaps another 0.1°C? or 3°C? That is the question.
Firstly note that many of the feedbacks present at 287K only function at warm temperatures. I.e. if you ask the same question in an alternative world with a very weak sun, so weak it only warms the earth to 50K (no feedbacks), then how much does water vapour feed add at that point? Answer: zero. Because there’s no water vapour in the atmosphere at that temperature.
So assuming feedbacks are constant at all temperatures from 0K to 290K doesn’t make any sense. It’s not unreasonable to assume there’s no feedbacks until 255K like the IPCC do. It’s not very accurate either, but not unreasonable. The feedbacks vary tremendously as a function of temperature, for example if temperature is forced 1°C up at the point ‘snowball’ early turns to warm watery earth then the feedbacks might be an additional 20°C (at the tipping point). The feedback parameter is function of temperature, so making the heroic assumption that feedbacks are constant from 0K to 287K it not helpful.
I’m sure Lord Monckton will come back saying I not qualified to express an opinion on this. But after much correspondence and contemplation I still cannot support this conjecture. Feedbacks are not constant from 0K through 290K and it’s not helpful to assume that they are.
The feedbacks vary tremendously as a function of temperature…
Indeed once the Arctic ice is melted the energy instead begins to raise the temperature of the liquid. Melting a kilo of ice uses the same energy that raises a kilo of water from 0 to 80C. That then changes global weather patterns.
Mr Palmes’ concern is shared by one of the reviewers. However, the math is ineluctable. Such feedback processes as exist at any given moment will respond to the absolute temperature they find at that moment. This is basic control theory; it is easily testable; we have tested it, not once but twice; and our Professor of control theory has confirmed it.
Feedback processes are inanimate. They have no mechanism by which they can decide not to respond to a reference temperature of 255 K, or decide to respond only to some unspecified and indeterminable fraction of it. They simply respond to all of it.
One might ask all sorts of questions about what the world would look like with a weaker Sun, or with an iceball Earth rather than the waterbelt Earth we have imagined. But we are humans and can envision these things. Feedback processes are inanimate. They have no power other than to respond to the temperature as they find it at any given moment. We simply selected two such moments – 1850 and 2011 – and did the math.
It is certainly not for me to say whether Mr Palmes is qualified to express an opinion on this or any topic. I myself have no piece of paper that qualifies me to talk about any of this. But I have an army of co-authors and pre-submission reviewers at my back, and some of these are the smartest cookies in the jar.
It’s important to understand that in saying that feedbacks respond to the 255 K reference temperature we are not saying anything about whether feedbacks would be constant at any temperature below 255 K. We are saying no more than that, where the reference temperature is in fact 255 K, then the feedback processes will respond to that reference temperature, regardless of what might have happened at some other temperature or in some other world.
By the same token, we are certainly not assuming that the feedback processes would be the same as today’s at temperatures appreciably below today’s. They wouldn’t. But the feedback processes in the climate today, whatever they be (for we don’t need to know in our method), will react to the temperature in the climate today, just as they did in 1850, for the difference in the climate between the two dates is not enough to throw off the calculation by very much.
The different phases of ice are important in glaciers and ice caps that are huge.
“The exam question is: what is the feedback at current global temperature (around 287K), i.e. if you force the temperature up 1°C from here how much will feedbacks add to this, perhaps another 0.1°C? or 3°C? ‘
Lord Monckton has answered that question. It is 0.129K
Many issues arise including partial pressures.
But the idea that there would be no water vapour feedback if this planet had an average temperature of 255K, seems to over look the concept of average. With such an average temperature, there would still be large areas of open water which would absorb incoming solar irradiance, leading to evaporation and hence water vapour in the atmosphere.
The temperature of the planet would be far from uniform with the poles been ridiculously cold. Likely the Tropics would still have open ocean water and incoming solar irradiance would likely keep it ice free, produce water vapor and form clouds. Winds and atmospheric convection would move this around the planet. Even during the snowball Earth era it was thought the planet still had open ocean water around the Tropics.
Matt G is correct: that is precisely the scenario we have modeled, using data from Lacis et al., 2010.
There is a fly in the ointment in that while IR emission varies with the absolute temperature raised to the 4th power, the phase changes of water at discreet temperatures complicate things by sequestering, transporting, and releasing energy. I’m not sure that the models are that sophisticated. It is well known that energy exchanges in clouds are not handled at the same scale as other parameters, and hence a lot of assumptions are built into the models to handle clouds.
I think that you are probably correct to assume that feedbacks are not constant. They also are probably not linear and may not even be monotonic functions. Feedbacks may well have step transitions because of phase changes in water.
No fly in our ointment, for our calculations span only the period from 1850-2011, during which the state of the atmosphere did not change enough to mess up the calculations.
I only see 2 points, 1850 and 2011. Do you have a graph that looks at multiple points across time. IMO, it would be more powerful if you show the relationship across time. I would like to see that the recorded Tr/Tq ratio holds up across time, and that 2011 wasn’t just a one off.
Dr Deanster raises a fair point. In fact, we found ten dates, all of them since 1850, where reasonably reliable official estimates of the anthropogenic forcing to those years were available, and we conducted an empirical campaign (it took months) to investigate each one and tabulate the results. The answer is that equilibrium sensitivity derivable from each of the ten cases was 1.17 K.
“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.”
From the ‘manmade warmings’ that triggered them? steady on chap.
Since the mid 1990’s, changes in atmospheric circulation have driven a warm AMO phase, declines in cloud cover, and changes in the vertical distribution of water vapour. All have driven surface warming, ocean heat content has increased, and CO2 uptake has reduced. Increased water vapour at lower levels increases the GH effect, decreases in water vapour at upper levels increases the penetration of solar near infrared to the surface and lower atmosphere. Given that the leading climate modes of AO/NAO are negative to drive such states, it’s all of the wrong sign to associate with rising CO2 or any net increase in total climate forcings. But closely follows the decline in solar wind temperature/pressure.
Ulric Lyons may or may not be right that natural variability is the cause of recent warming. However, ad argumentum we have accepted all of official climatology except what we can prove to be false. That way, we have succeeded at last in focusing the discussion on to our principal result: that, since feedback processes respond to whatever input temperature they find, it is possible to derive the system-gain factor and hence Charney sensitivity very simply and reliably.
“since feedback processes respond to whatever input temperature they find”
They do not, they respond to net changes in total climate forcing, within limits regardless of the absolute temperature, and appear to be strongly negative. Which is what one should expect given the relative stability of Earth’s temperature.
“However, ad argumentum we have accepted all of official climatology except what we can prove to be false.”
The climate system has already proved official climatology false, with the increase in negative NAO/AO from the mid 1990’s that wasn’t supposed to happen according to rising CO2 forcing models, and that actually drove the AMO and Arctic warming.
http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch10s10-3-5-6.html
They do not, they respond to net changes in total climate forcing, within limits regardless of the absolute temperature
==!===
Don’t agree. Due to phase change of water feed back will be nonlinear for large delta T. This means that the feedback must vary as a function of T absoluteabsolute.
Which means that climate sensitivity to a doubling of CO2 is not a constant!!!
ferdberple: Ocean phases act as negative feedbacks to net changes in climate forcing, which drives the changes in water vapour. That happens irrespective of the global mean surface T.
Mr Lyons is incorrect. Feedback processes respond to the input signal they find, not merely to some change in that signal. Look at the block diagram and think.
“Look at the block diagram and think.”
Having built audio op amp circuits, I think that it’s baloney. You have no amplification, and you have confused feedback with amplification. In doing so, you have also excluded the possibility of a negative feedback, and hence of a relatively stable climate. Bode would not be amused.
Mr Lyons should recall that one of our co-authors is a professor of applied control theory, and two more are electronic engineers familiar with the relevant control theory.
The block diagram for the feedback loop shown in the head posting has no gain block. Now, why is this, do you suppose? The reason, of course, is that if one wishes one may simplify the math by setting the value of the gain block to unity, and simply adding any perturbation of the original input signal to that signal itself before passing it into the feedback loop. But then the input and output nodes are equipotential, in which event one may represent them as a single node.
This approach is functionally equivalent to the Bode diagram, where the amplification is fed in via the mu gain block rather than as a simple addition to the input signal.
Look at the block diagram, and think.
“simply adding any perturbation of the original input signal to that signal itself before passing it into the feedback loop. But then the input and output nodes are equipotential, in which event one may represent them as a single node.”
Sounds like you can dispense with your feedback loop then from that. The requirement for your postulate though is simply an amplifier with a fixed gain of 1.13.
“Mr Lyons should recall that one of our co-authors is a professor of applied control theory, and two more are electronic engineers familiar with the relevant control theory.”
So what, I got my lessons on servo control and missile guidance systems and negative feedback when I was still sharing baths with my father who was at the time head of Guided Weapons at the RAE in Farnborough.
Right. Let Mr Lyons explain this. How can inanimate feedback processes receiving an input signal decide that they will ignore the greater part of that signal and respond only to some arbitrary perturbation of it?
The ‘greater part’ of the signal is being amplified by the greenhouse effect, that is not a feedback. The perturbations in the signal are not arbitrary, they are driving change, which will have a feedback, either net positive or net negative, and which could also exhibit overshoot.
Amplification is another term IPCC scientists use for feedback. The core GHG effect itself is not an amplification. The main positive feedback is supposed to happen because as a) CO2 makes temperatures warmer, and b) the system acts to keep water relative humidity constant (the catastrophists’ conjecture), c) but this H2O relative humidity changes with temperature, d) so H2O absolute humidity increases (that is: more H2O will dissolve in the atmosphere), e) this extra H2O is the IPCC feedback, or amplification. This small hypothesized fraction of the GHG is the GCM positive feedback (their amplification).
Fine and dandy in theory, but not observed in practice in the part of the atmosphere where it matters.
“Water vapour, water vapour. Our kingdom for more water vapour.” — Climate ‘scientists’ are heard to mutter as they lose their final battle and face imminent extinction.
If Mr Lyons reads the head posting with sufficient care, he will see that any perturbation owing to the greenhouse effect is accounted for by adding it to the input signal Tr before passing that signal to the feedback loop. This approach is functionally equivalent to the Bode feedback loop.
“Mr Lyons should recall that one of our co-authors is a professor of applied control theory, and two more are electronic engineers familiar with the relevant control theory.”
I find it funny when I see attempted refutations of large slabs of science, roundly and heartily rejected by journals and a great body of scientists, and the defence is
“but our man X says so, and he has qualifications!”
Greatly inflated here.
Mr Stokes is disingenuous. He knows quite well that laymen such as me are held in contempt by climatologists if we indicate we are not prepared to toe the Party Line. Well, now I have a growing academic army at my back, which is one reason why he is having such a hard time coming up with plausible reasons to suggest that our result is incorrect.
He has failed and failed and failed again to explain how inanimate feedback processes can “know” they should respond to some arbitrary perturbation of the input signal and not to the whole thing. His failure is being widely noticed, and not just here.
“to explain how inanimate feedback processes can “know” they should respond to some arbitrary perturbation of the input signal and not to the whole thing.”
It is built in to the term “respond” A system responds to something that happened. It can’t respond to something that always was. You can ask, how should the government respond to a rise in sea level? Build seawalls, higher docks etc. How should the government respond to sea level? ???
Nick Stokes,
You assert,
“A system responds to something that happened. It can’t respond to something that always was.”
Really? I suspect you respond to being in a breathable atmosphere by breathing. But you have always been in a breathable atmosphere so perhaps you should stop responding to it.
Richard
The air has always been breathable, and I have always been breathing it. So where is the response?
Does it make sense to say that the fires in California are a response to the presence of oxygen in the air?
Mr Stokes continues to ignore the simple mathematics of the feedback loop. At its simplest, it comprises an input signal, a feedback loop and an output signal. It is inherent in the mathematics of that simple loop that 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.e., the product of the input signal and the system-gain factor 1 / (1 – f), under the convergence condition – applicable here – that | f | <1.
The input signal, therefore, may be an absolute value, a delta or the sum of the two. It is as simple, and as undeniable, as that. The feedback factor f, which tells us what fraction of the output signal is feedback response, is inanimate. It cannot decide for itself that it will refuse to respond to most of the input signal and that it will suddenly respond to only some minuscule perturbation of it. It will respond to the entire input signal.
Nick Stokes:
You could have ignored my joke but instead you wrote this,
“The air has always been breathable, and I have always been breathing it. So where is the response?”
Oh! So, having contributed to the trashing of climate science you are now attempting to trash medical science, too?
Richard
Monckton of Brenchley creates a tiny choke with his loop. With no amplification between the input and output, the feedback loop will make zero change to the input.
But some of the output is going back into the input making that bigger… oh that just makes the output smaller duh!
“Does it make sense to say that the fires in California are a response to the presence of oxygen in the air?”
It makes as much sense as saying the fires in California are due to CO2 in the atmosphere. If prudent, one would consider the history of fires in the US, the effects of forest management on fuel accumulation, the increase in human-caused ignitions, etc.
“A system responds to something that happened. It can’t respond to something that always was.”
Nick – is it possible that the system already responded at sometime in the past and you weren’t around to make the observation? What results would you expect from a laboratory experiment? Would the system stop responding once the simulated condition was below the natural occurring condition?
“Nick – is it possible that the system already responded at sometime in the past”
Yes. That’s my point. Whatever response it made in the past is part of the reference state which is being perturbed. It isn’t going to respond again.
Nick Stokes,
You are being obtuse. Nobody claims the system will “respond again” to a change that happened in the past.
You are refusing to recognise that the system maintains its response to a change that happened in the past until something alters or removes that change.
Richard
Yes there is error. But it is much greater than you think. CO2 contribution to warming is near zero.
What are the photon absorption bands of CO2?
What are the photon absorption bands of water vapor?
What is the overlap?
What does it mean?
Mr Simon is asking all the right questions about CO2, which, however, was not the subject of our exercise. We simply accepted ad argumentum the current official estimate of the reference warming from doubled CO2.
It is very clear that at or near the surface extra CO2 in the air will make little difference, in that its principal absorption bands are overlain by those of water vapor. The same cannot be said of the upper troposphere, however, where it is much drier and a warming from CO2 can plausibly be expected to occur.
How? I had calculated that a reasonable average mass absorption coefficient for transmission from CO2 around the wing lines of 15 microns which is where we are concerned is quite weak, at 1.69 m^2/Kg. If you increase CO2 to 720 ppmv there is still transmission of around 37% at 6800 meters of height, and that’s using a standard earth atmosphere pressure at seal level to calculate the coefficient, meaning it is even less at 6.8 Km.
There would be considerable interference run by the hydro cycle because of this at the surface and additional cooling in the upper troposphere from the increased emissivity of CO2.
Bottom line is increased moist convection from any realized ( and weak) surface forcing in clear sky which is just another negative feedback with respect to surface temperature. Increasing solar irradiance by changed albedo or the suns energy output to the surface is the only way to change the tempertaure in the presence of the hydrological cycle unless solar magnetic has some other influence on temperature that is not yet apparent.
I’m afraid I refuse to be drawn. Ad argumentum, we have accepted all of official climatology except what we can prove to be wrong. Whether or not CO2 is a greenhouse gas is off topic.
Christopher: The problem with your answer is that it has not been demonstrated at any level just what caused delta(q2) ‘s value to be +1 degK.
If this was a clear sky only problem, it would be much more straightforward than it actually is. The “climate establishment” is a cabal of people like Michael Schlesinger was that made assumptions and claimed them to be true without ever demonstrating this, against what the founding principles in atmospheric science suggested about CO2’s effects in the presence of the earth’s hydro cycle were on temperature which was negligible. It is up to this group to prove their assumptions correct, not the established physics that stated otherwise from the founding work and that were accepted before the modelers showed up.
I’ve asked many times how the Schlesingers of the world separate solar insolation from IR radiation over the oceans and the question never gets answered because they can’t determine it with enough specificity to sort out the forcings in proportion to each other that would apply to delta(q2) .
So while your calculative method is straightforward, it assumes delta(q2) was caused by the RF from CO2 and obtains a climate sensitivity of 1.129 as a result. The founding principles suggest it is not possible to obtain such a sensitivity because the optical depth of the troposphere is maintained by solar forcing and the hydro cycle.
I’m on your side that the “sensitivity” from CO2 to temperature on earth is very low, but I’m unconvinced it is the value you state for the very reasons I gave, in that delta(q2) has not been determined with enough specificity to portion out the small RF from CO2.
Without that information, or proof that founding principles in atmospheric science are wrong, I maintain the sensitivity of CO2 on earth tempertaure in the presence of the hydro cycle is negligible as founding principles suggest.
Mr Wiese has not, perhaps, understood the basis on which we have written our paper. To remove the endless, futile arguments about questions wholly irrelevant to our present research, such as the extent of the CO2 forcing, we have simply accepted ad argumentum that all of official climatology is correct except what we can prove to be false.
One of the tactics used by the climate Communists is to attempt to intoduce useless complications of this kind, until they have driven us back on to accepting that the only way to deal with so complex a question as climate sensitivity is to fall back on the computer models that are just about entirely within their control.
What we have done is to cut through all that nonsense by saying that, for the sake of argument, we shall simply accept the official outputs of the climate-Communist models, except where we can demonstrate that they are manifestly incorrect.
In the matter of feedback, we can prove that the official definition of “temperature feedback” in climatology is incorrect. We can quantify the effect on equilibrium sensitivities of adopting the correct definition, which at once allows derivation of the Holy Grail of climate sensitivity studies – the feedback system-gain factor – by the very simplest and most robust of methods.
In short, we have found the answer They have been doing their very best to conceal. And it matters not whether the global warming in response to doubled CO2 is zero or 0.5 or 1 or 1.5 K. As long as it is not appreciably above 1.5 K, it becomes a mere curiosity, of no great scientific or policy relevance. And that’s game over.
Honestly, as a working-stiff forecasting meteorologist, the mathematical argument is a bit over my head. The rational argument, however, is pretty clear. The alarmists have always ignored the vast arena of rational arguments in order to convince us that their math is correct, which is why I became a skeptic in 1989.
It is clearly true that the climate has no ability to react differently to a change in temperature that is brought about by human CO2 emissions than an equal change in temperature brought about by some other means, yet that is precisely what the CAGW argument has maintained from the very beginning, and why I became a skeptic. (Also, their ‘math’ suggests that a ‘runaway’ (highly amplified) greenhouse effect is possible on Earth with relatively minor changes in atmospheric CO2 concentrations, but it has never happened in billions of years, despite great changes in CO2 concentrations. This indicates that their math is missing something obvious, and I think Mockton et al, are probably on to it.)
The skeptical position has been continually bolstered by the continuous observational evidence showing that catastrophic man-made global warming is not happening in any way, shape, or form resembling what the models predicted! It doesn’t get any simpler than that. It just isn’t happening! What IS happening is just what has always happened, and extremes are being cherry-picked and grotesquely hyped as evidence of a new normal. But they continue to be nothing more than the usual extremes of the old normal.
I am most grateful to Mr Clarke for his comment. Actually, our math is not at all difficult. Indeed, the reviewers were aghast at how simple it is. All you need to know about feedback is that the system-gain factor is the ratio of equilibrium temperature (after accounting for feedback) at a given moment to reference temperature (before accounting for feedback) at that moment.
In 1850, the reference temperature was 255 K and the equilibrium temperature was 287.5 K, so the system-gain factor was 287.5 / 255, or 1.13.
The only other figure you need to know is reference sensitivity to doubled CO2. The current mid-range estimate is 1.04 K. The product of the system gain factor 1.13 and the reference sensitivity of 1.04 K to CO2 is 1.17 K. And that’s it, really. Not 3.37 K, not 4.7 K, not 10 K, just 1.17 K. Not enough to be worth worrying about.
Oh, and our result is consistent with observed temperature change since 1990, while the official estimates are manifestly way over the top.
An alternate calculation gets the same result, but instead of expressing relations in terms of temperature, it’s expressed in terms of power in order to take advantage of the intrinsically linear relationships among Joules and extend the applicable range of the calculation.
The SB emissions corresponding to 255K are 239.74 W/m^2 and at an average temperature of 287.5 K, the SB emissions are 387.38 W/m^2. The power gain is then given as 387.38/239.74 = 1.616, thus each W/m^2 of input power contributes to 1.616 W/m^2 of output power corresponding to the average temperaure.
The IPCC asserts that doubling CO2 is equivalent to 3.7 W/m^2 of forcing. Multiplying 3.7 times the gain of 1.616 results in 5.98 W/m^2 which when added to the starting emissions of 387.38 W/m^2 become 393.36 W/m^2.
The SB equivalent temperature of 393.36 W/m^2 is 288.60 K which when subtracted from the 287.5K starting temperature becomes 1.1 C. This is slightly lower than the 1.17 C calculated by the ‘temperature gain’ owing to how 3.7 W/m^2 of ‘CO2 forcing’ was turned into an 1.04 C increase at TOA (255K -> 256.04K) which requires an equivalent increase in solar forcing of 3.94 W/m^2 and not the 3.7 W/m^2 stated in the AR’s. Using 3.94 W/m^2 instead of 3.7 W/m^2 in the power gain calculation gets exactly the same 1.17 C increase.
The difference between the two calculations is that the temperature centric gain calculation is valid at only one reference temperature and small deviations on either side, while the power centric gain calculation works across a wide range of reference and final temperatures, spanning all of the temperatures found on the planet.
It is useful to have confirmation that, whether one does the calculations in Watts per square meter or in Kelvin, the result is much the same. One would not expect otherwise.
As I recall, the use of temps rather than power is one of the sleight of hand “tricks” employed to arrive at a much higher sensitivity. That the calculation with power achieves a result so close to CMoB’s, it should be considered independent confirmation in his fundamental accuracy of approach. Right?
rip
The slight of hand is to use W/m^2 in and degrees out for the gain block. W/m^2 in and W/m^2 out works. Degrees in and degrees out also works, although the gain is not constant across different reference T’s. W/m^2 in and degrees out does not work at any reference T unless you analyze the system as W/m^2 in, W/m^2 out and convert the resulting before and after output from W/m^2 into degrees using the SB Law and subtract the results to get a delta T. What is done instead is to guess about a delta T and then fail to sanity check against the required change in W/m^2 allowing them to plausibly claim a arbitrarily high sensitivity.
Hi, just breaking into the discussion; I can appreciate Jim Clarke, the meteorologist, saying the ‘mathematical argument is a bit over’ his head. This is sort of my feeling too, enough so that I almost feel like calling ‘bulls–‘ on *all* climate theorists. Of course it may be that I just don’t fully “get” something compelling or reasonable to drive these math models. A big issue that I have is how much of this seems “counterfactual” or suppositional, really. Not at all like measuring voltages in a circuit, nor like measuring actual temperatures at the physical stages of a real flow flow system (say a steam turbine or what have you).
To illustrate, think about trying to understand the application of control theory to the estimates of future climate temperatures and forcings, as in Moncton’s model and/or his explanation of the “standard” climate models. To start on this, I was interested to read the two page handout from the link provided at the beginning of Christopher Moncton’s article.
In this Summary handout, PDF, or “cheat sheet”, for instance, we have near the end (as part of the essential initial equilibrium calculation), someone’s estimate of ground emission temperature? Then we have an estimate of the warming temperature *increment* or contribution from “pre-industrial non-condensing greenhouse gases”. After that, we have the ensuing statement “that without pre-industrial non-condensing greenhouse gases the Earth’s surface emission temerature would be 243.25 K” (or words to that effect). Then, another, apparently essential, step is to very carefully add in the presumed “flat” (or non-feedback amplified) effect of the “non-condensing greenhouse gases” (just the CO2 effect but *not* the CO2 *feedback* effect, does this mean?), *that* step gets us to a temp of 254.8 K. This last is really the start of the “simple” feedback calculations, as the 254.8 K is the all important (yet strictly counterfactual) Reference Temperature, i.e., it is the “TR1” temperature.
Now what would happen I wonder, if we were all to go through life making models or decisions in terms of ideal or counterfactual reference points, relying on someone’s simplified model estimate of what all the true reference numbers in the world must really be? Here are a few examples of interesting reference level concepts that might turn out to be vital to our understanding of the world around us.
Example 1: Choose a specified voltage level in a lab test circuit, defined as what the voltage *would be*, “if only the atmospheric composition in the lab were somehow different (like no CO2 in the lab, or maybe a pure nitrogen atmosphere).
Example 2: Specify an assumed rotation rate for the planet Earth, defined as “what it would be if only the Moon (Luna) had never formed”.
Example 3: Specify a reference average weight for adult human beings, defined as “what it would be if only doughnuts had never been invented”.
Example 4: Specify the total reference population of mice in the world, where the true reference mouse population must be calculated as “what it would be if cats had never existed”.
Now, please note, in listing some possible “everyday conterfactual” references, I am not necessarily saying that I’m completely uninformed about how climate theorists tend to think sometimes! In the past, for instance, I know I’ve read on Dr. Roy Spencer’s web site, some sort of estimate of the “Earth’s temperature assuming no persistent greenhouse gases (or similar wording).
Thinking of such estimates of what happens to the model temp. of the “Earth if bare of greenhouse effect”, what is one to make of it? My problem is, I’ve never been impressed with the reliability of such hypothetical model based statements, *especially* when important particulars never seem to get mentioned! For instance, if non-condensing or persistent greenhouse gases are supposed to be removed in the model, to get that sort of estimate, what does that say about water, H2O, a known greenhouse molecule? Does removing the IR active gases also imply that all oceans and water must be removed from the model Earth, so as to also make sure to get rid of all that pesky, IR aborptive H20 vapour? You know, that regular vapour stuff that would otherwise make the planet a lot warmer than the “bare” estimate would seem to say?
Whatever the usual application of hypothetical control theory levels, one can only hope that Moncton’s ideas are a rationalization of or improvement on the practice of this kind of thing so far? Also, if it comes to that, surely it must also be possible to build a energy flow model or physics systems model that deals solely in actual real real world quantities, like average temperatures in clouds, at different altitudes, etc.?
For myself so far, then, I just have to say that I don’t quite see a compelling reason for treating everything as a “deviation” (from an attenuated or pre-amplifier staged “level” of sorts).
David,
In the absence of any GHG effect (i.e. no water and no atmospheric GHG’s) the Earth’s temperature would be about 271K. This is a trivial calculation based on the accepted calculation of the Moon’s average temperature.
Without GHG’s, the albedo would be the same as the Moon at about 0.1, instead of the 0.3 it is now. This makes the solar forcing 307 W/m^2 and not the 240 W/m^2 it is when the albedo is 0.3. Converting 307 W/m^2 of average emissions into a temperature using SB results in an average temperature of 271.3K.
GHG’s both cool (specifically water) from 271K to 255K and warm from 255K to 288K, for a NET warming of 17C increasing the temperature from 271K to 288K. The warming can not be separated from the cooling, but often is to make the NET GHG effect seem much larger than it actually is. This is the consequence of defining forcing to be after reflection by albedo, effectively obscuring the negative feedback like effects from the dependence of albedo on water.
Technically, the arriving solar forcing is 307 W/m^2 and not 240 W/m^2 as the reflection that reduces 307 W/m^2 to 240 W/m^2 is part of the response of the system to solar forcing. This is ignored because it’s a negative feedback like effect that they don’t want to have to explain.
Thanks for the comment “co2isnotevil”.
So, reflection of sunlight (due to clouds, I think you mean), “is ignored because it’s a negative feedback like effect that they don’t want to have to explain”. In other words, the reflection *is* taken into account in terms reducing the solar ground level input, but *not* taken into account as a negative feedback in the “response to a hypothetical starting point” type of model? Hehe, if they did *that*, it would require an entirely annoying and unseemly rethink of where the reference temps should be assumed to be? Lindzen Iris Effect, anyone?
David Blenkinsop may like to understand how the emission temeperature and pre-industrial greenhouse-gas warming are calculated. First, he should read Lacis et al. (2010), which considered the question what the albedo of the Earth would be today with no non-condensing greenhouse gases present. The albedo is 0.418. Today’s insolation being 1364.625 W/m^2, one can use the Stefan-Boltzmann equation to derive an estimate of the emission temperature under those conditions. it is 243.3 K. We then allow a generous 5% variance either side of this value in our calculations.
Calculating the contribution of the pre-industrial non-condensing greenhouse gases is more difficult. In the underlying paper, we use three distinct methods, one giving 8.9 K, another 11.5 and a third 13.5. We use all three of these values in our calculations.
Even with these quite wide variances, there is remarkably little effect on final sensitivity, which comes out at less than 1.5 K under just about all circumstances. With the variances mentioned above, the interval to 95.4% confidence is 1.08 to 1.25 K, with a best estimate of 1.17 K.
One point that Mr Blenkinsop may not have appreciated is that because the feedback response attributable to the Sun and to the pre-industrial greenhouse gases is so very much larger than the feedback response to our tiny anthropogenic perturbation, great precision in the underlying data is simply not necessary.
For instance, one could even begin the calculation with an iceball Earth of albedo 0.66, and the Charney sensitivity would still only come out at about 1.5 K.
Thanks, Christopher Moncton, your comments above and also your responses to “co2isnotevil” certainly answer some of my questions and concerns about the meaning of Earth temperature estimates when CO2 is removed from the estimates of climate warming.
I do still have my doubts about the verifiability of such temperature estimates. For instance, laboratory enclosures with CO2 in them, and any associated measurements, are patently so *different* from the situation of CO2 in an open planetary atmosphere. Developing a statistical spread or probability distribution to encompass responses of the whole planet to various energy “forcings” makes for interesting theories, but where is the proof that the overall atmospheric response to any given level of added CO2 is really a known quantity?
That said, I accept that you may be on to something when you say that “feedback response attributable to the Sun and to the pre-industrial greenhouse gases is so very much larger than the feedback response to our tiny anthropogenic perturbation”. Seeing that you’ve been able to confirm this basic idea on an analog computing rig, this certainly sounds like a worthwhile approach! While there’s no guarantee that an analog circuit represents reality, at least that kind of circuitry should have an internal physical consistency that might easily get missed by the purely digital formulaic kinds of models. Again, to the extent that the analog represents reality, now maybe you’ve got a kind of concrete version of all those “what-ifs” that I was complaining about as getting too far removed from actual facts or measurements?
The caution here again, is the model is literally not reality, so don’t always attribute temperature rise to CO2 rise! I mean, does someone else have a circuit that gets the temperature rise a different way?
In response to Mr Blenkinsop, the mathematics of feedback is universal and applies, therefore, to all feedback-moderated dynamical systems, from electronic circuits to the climate. Therefore, if one builds a simple feedback-loop circuit, one can test the conclusions we have drawn here about how feedback in the climate works, because it will work just as it works in an electronic circuit.
CO2isnotevil is starting his calculation from the wrong point (the Earth without water) and then using the wrong method (a single Stefan-Boltzmann calculation). The correct starting-point, as set out in Lacis et al. 2010, is the Earth with its present ocean but without the non-condensing greenhouse gases.
Even then, it is not correct to perform a single Stefan-Boltzmann calculation. The reason, of course, is Hoelder’s inequalities between integrals, given that the SB equation is a fourth-power relation. As an exercise some months ago, I performed a hemispheric integration of temperatures at various Lunar latitudes on the dayside, took the Diviner data for the nightside, averaged the two and calculated that the lunar mean surface temperature is about 200 K, not the 270 K imagined in Nasa’s Moon fact sheet on the basis of their single SB calculation.
On Earth, the error is in the opposite direction, owing to the presence of the ocean, which retains heat at night (the upper 7 m, treated as a slab, loses only 0.25 K overnight).
Calculating the average temperature on the Moon is a little tricky due to its 672 hour day. The Earth spins fast enough that the maximum possible temperature that could arise from solar input is never achieved during the day and the minimum possible temperature is never achieved during the night. Once these conditions occur, it’s like an amplifier clipping and trying to figure out the average temperature gets a lot trickier. This condition occurs across all of the Moon’s surface and to a lesser extent in Earth’s polar regions.
Where this gets tricky is that the geometrically weighted average of the ocean temperature gets the right answer if the participating ocean water were to be well mixed together, owing the the linear relationship between temperature and stored energy, however; the geometrically weighted average of temperature is not a valid metric relative to emissions, the sensitivity and/or any temperature with a physical connection to the average forcing.
If you define the average temperature to be the temperature of an ideal BB emitting the average emissions, then it has a physical correspondence to the energies involved and is the only quantification of the average temperature that has any correspondence to the energy driven physical processes. For the purpose of calculating average, emissions can be validly summed with geometric weights.
My starting point is for determining the NET effect of all GHG’s, including water vapor which can’t exist at the relevant temperatures without liquid and solid forms existing as well.
How does taking away only non condensing gases for the starting point help us understand anything? The functioning of these gases is far better understood than the net effects of water, so a lot of uncertainty still exists in any results or conclusions.
The Moon’s mean surface temperature is some 70 K below what co2isnotevil thought it was. For one must allow for Hoelder’s inequalities between integrals.
As for the Earth, he should study Merlis (2010), who has a useful consideration of Earthlike aquaplanets of different rotation periods and of albedo 0.38, similar to the 0.418 considered by Lacis+ (2010). Put simply, during the day the incoming sunlight dominates the picture, and during the night the vast heat capacity of the ocean dominates. One can, therefore, to first order, do a hemispheric integration to find the dayside temperature, which works out at about 275.2 K. The nightside temperature is around 250 K in Merlis: call that 245.2 K to take account of the slightly higher albedo in Lacis. The mean terrestrial temperature, therfore, is about 260.4 K. Ad 11.5 K for the non-condensing greenhouse gases in the pre-industrial era to 1850 (for water vapor is treated as a temperature feedback) and the reference temperature in 1850 before feedback is 271.9 K. Therefore, since the equilibrium temperature in 1850 was 287.55 K, the system-gain factor was 1.06. The product of 1.06 and the reference sensitivity 1.04 K to doubled CO2 is 1.1 K, rather than the 1.17 K calculated in the head posting.
Interestingly, therefore, after allowing for Hoelder’s inequalities between integrals the Earth’s true mean surface temperature for a given albedo and insolation is some 17 K higher than a single global use of the SB equation would mandate, and the Moon’s true mean surface temperature is some 70 K lower. The reason for the difference is that the ocean has a greater heat capacity than the regolith by three orders of magnitude.
The reason why one starts, as Lacis (2010) did, by removing the non-condensing greenhouse gases from the atmosphere and deriving the emission temperature that would then prevail is that, like it or not, there is an ocean on the Earth today, and removing that introduces a complication so large, as well as needless, that no useful conclusion as to Charney sensitivity can possibly be drawn from it.
To answer CO2isnotevil’s final question, the reason why one removes the non-condensing greenhouse gases is precisely that we can quantify the warming they cause to within quite a reasonable margin. Taking them out, estimating with a GCM the albedo that would result and then simply deriving the resultant global mean surface temperature at today’s insolation and at an albedo of 0.418 (from Lacis) is very easy. One then adds back the warming from the pre-industrial non-condensing greenhouse gases to obtain a reference temperature that is remarkably well constrained. It is about 254.8 K, and it can vary by quite a bit either side of that value without much affecting equilibrium sensitivities.
If the Moon’s average temperature is only 200K (70K less than the 270K I claim), the Moon’s average emissions given by SB are only 91 W/m^2. The albedo is about 0.11 making the AVERAGE incident energy 304 W/m^2, so what’s happening to the remaining 213 W/m^2?
This illustrates the problem with applying a geometric mean to wide range of temperatures and that the geometric mean of temperature across a planet is a meaningless concept relative to the energy involved. In fact, it’s the Hoelder’s inequality between integrals that makes the geometric mean of temperature so meaningless and not the other way around as you’re suggesting.
I get that you’re trying to frame this in the terminology of consensus climate science which is focused on temperature, rather than energy, but it’s this focus that’s keeping climate science so broken.
CO2isnotevil continues to have difficulty in understanding some elementary concepts. First, he borrows from NASA the incorrect estimate that the mean lunar surface temperature is 270 K when it is closer to 200 K. Secondly, he appears not to understand that the 270 K value is derived by the naive method of using the fundamental equation of radiative transfer based on today’s insolation and a lunar albedo 0.11. Thirdly, he appears not to understand that it is precisely because of Hoelder’s inequalities between integrals that the 270 K value is incorrect. One must perform a Stefan-Boldzmann calculation for each dayside latitude, and then take a reasonable average for the night-side, and average the two.
I frame the discussion in terms of temperature because that is what we are talking about when we are talking about global warming.
See the December 2017 article by Australian doctoral-engineering candidate Robert Holmes, as reported by climatologist Kenneth Richard [Rick Cina] in Pierre Gosselin’s estimable “No Tricks Zone” blog-post for 02/05/2018: For any planet in Earth’s solar system, Temperature T = PM/Rp, where R is a given planet’s Gas Constant (varying by each world’s density and size).
With Mar’s exception due to special circumstances, Holmes’ equation derives planetary temperatures with virtually zero difference from century-old astronomical observations. Because this metric includes no carbon dioxide (CO-2) component whatsoever, all “greenhouse gas” and other extraneities become irrefutably, objectively irrelevant.
Needless to say, Holmes’ findings as an engineering candidate are as welcome as a nest of serpents at kiddies’ Teddy Bear Tea.
Prythroes’ point, while interesting, is not quite correct. For the atmospheric pressure of a planetary body is dependent inter alia on temperature, and temperature is dependent inter alia on the concentrations of greenhouse gases. All that Kenneth Richard is really saying is that the ideal-gas law works.
More here:
http://article.esjournal.org/pdf/10.11648.j.earth.20180703.13.pdf
The sun via solar radiation of course has an feedback and the major elephant in the room being the oceans. The oceans heated up by the sun regulate the energy output and so become a huge feedback over time. What would had been outputs of the climate system are routed back into the atmosphere as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The greenhouse effect and climate models are all wrong because the oceans being the main feedback of the sun aren’t taken into account.
The depth of the delusion among those who accept CAGW is astounding. The problem is that there’s not just one error, but a web of many errors all of which depend on and support each other. Circular reasoning was mentioned as driving one of the vacuous comments by the reviewers, but it’s far more pernicious and is at the core of almost all of the reviewers comments. Without circular reasoning it would be impossible for any competent scientist to accept the IPCC’s fake science.
Climate feedback embodies many fatal errors and the result of my research points to the broken Hansen/Schlesinger feedback model as the keystone of broken climate science. These errors comprised the primary theoretical justification for the formation of the IPCC and is the scientific malfeasance enabling a financial fraud against humanity that makes Bernie Madoff look like a petty thief. For a long time, I wanted to believe that it was just incompetence on the part of Hansen and Schlesinger, but the more I investigate, the more it seems like purposeful deception driven by collusion among the lead authors of AR1.
Casting the sensitivity as ‘incremental’, which is how accumulated forcing from the Sun gets ignored, is just one of the many errors. Others include the failure to conform to Bodes primary preconditions for using his LINEAR FEEDBACK AMPLIFIER analysis, that is strict linearity (implies no difference between incremental and average gain) and the requirement for an implicit, internal and infinite source of Joules to power the gain (which can not also be the forcing input and the Sun IS the only actual forcing influence). Casting the sensitivity in the non linear units of degrees per W/m^2 and calling it approximately linear is yet another level of obfuscation. Confusing the feedback factor with the feedback fraction is another error. The temperature feedback coefficients’ that convert degrees K to W/m^2 are nothing but untestable wildly guessed fudge factors with no correspondence to any physical reality.
In the Schlesinger feedback model, he multiplies the input to the gain block by Go to produce the output and then divides the output by Go and scales it by a dimensionless feedback fraction to determine the W/m^2 of feedback to add to the forcing. In effect, Go (the ‘amplification’ of W/m^2 into degrees K) is canceled out relative to feedback making the feedback a fraction of the input to the gain block implying unit open loop gain, which Schlesinger denies. In fact, the Go he claims to be the open loop gain is just the SB Law, which he also denies. His denial of these obvious modeling flaws and his proclamation to me that he’s the foremost expert on climate feedback was one of many factors that led me to suspect malfeasance, rather than incompetence. If he understands this as well as he claims, then his errors were based on ‘the ends justifying the means’ relative to identifying plausible theoretical support for an ECS high enough to justify the formation of the IPCC and that he expected real science to eventually support his preconceived position.
Co2isnotevil: Thanks for this. I’m not sure if you’re aware of this but Michael Schlesinger passed away last April at age 75.
He was new faculty that arrived on the Oregon State Unviversity campus in the atmospheric science department in the late 1970’s when I was going thru their undergraduate program. I had Schlesinger in one of my atmospheric dynamics courses back then and I will state he was a skilled mathematician. But I wasn’t willing to go so far as to calling him a great atmospheric science professor. He was more concerned about the class’s ability to perform complex mathematical operations than he was understanding or explaining to any detail what the physical significance of the equations we were deriving were.
At that time, his attitude was that he and his colleagues were going to slay the climate dragon and be able to tell human kind what the climate of the earth would look like centuries from now as that was the next frontier to conquer in atmospheric modeling.
If you read the comments from his daughter in his OB, she had stated that he was an environmental activist of sorts while in graduate school at UCLA, where he was getting a masters in mechanical engineering before going onto getting a PhD in atmospheric science and had preconceived notions back then that CO2 was changing the climate before he even studied any atmospheric science. The fact that his math skills allowed him to sail thru a PhD program in atmospheric science without any other degree in it always made me wonder just how many of the founding concepts he was actually familiar with by the time he left there and came to Oregon State University with a PhD in atmospheric science, so your comments and direct experience with him are quite interesting comparing to the way he looked at things when I took course work from him.
Chuck,
I was unaware that he had passed.
His emphasis on complicated math explains why he couldn’t see the errors mapping the climate to the feedback models math, as he was adhering to the math, it’s just that the system he was modeling didn’t conform to the prerequisites for using the model.
He was definitely an environmental activist and an unwaivering proponent of the CAGW hypothesis. I was on his propaganda email list for a while and observed what he thought was important, until I started responding and pointing out errors and/or contradictions and was removed from the list.
He sent me his feedback paper when I requested information on the theoretical basis for massive amplification from positive feedback. I was referred to him by Mike MacCracken, who seems to be the liaison between the Democratic party and the IPCC. Oddly enough, MacCracken was one of the reviewers of Schlesinger’s feedback paper whose timing seems to indicate that it was rushed through review in order to get into AR1 and correct errors in the Hansen paper which was to have have formed the theoretical basis for an ECS high enough to justify the formation of the IPCC.
After he rejected my analysis of his feedback paper, I suggested that he consult with an EE colleague to help him better understand Bode’s linear feedback amplifier analysis to verify my concerns. He responded that he didn’t need to because he had the necessary EE knowledge. It seems that the extent of this was that he new how the math worked in the abstract, but not how the system being modeled by the math worked in a physical sense. I tried to explain how to make the model more correct, but was never able to get past his preconceptions as he could see that the more correct linear model with W/m^2 in and W/m^2 out operating on all solar forcing at once didn’t support the ECS he needed.
By confining our analysis to the period 1850-2011, we have been able to use Bode’s linear analysis with very small error: indeed, we have demonstrated that to three decimal places the feedback system gain factors for 1850 and 2011 are identical. Not much nonlinearity there, then.
And we have adopted climatology’s practice of setting the mu gain block to unity. If one them simply adds any desired perturbation to the input signal, the output signal is exactly the same, but the math is much simplified.
CMoB,
Thanks for your persistence in this.
I believe you are self-evidently correct regarding your central contention that the feedback analysis must include the input signal. If one steps aside from the maths for a moment, and considers the “physical”* phenomena, I think becomes even more clear. (Well, at least “clear” to me in my current understanding. It could be that my understanding is profoundly wrong, and that upon further reflection, I’ll find all sorts of wholes in it, but for the moment, this is the fanciful scenario I’ve come up with.)
In the earth system we’re talking about, the input is not really sun, it’s the surface, and the feedback mechanism is the atmosphere, and the output is the top of atmosphere. What we understand to be “physically” occurring is:
– photons being emitted from the surface,
– interacting with the atmosphere,
– exiting the atmosphere.
The feedback in this system is the portion of those photons being returned to the surface via back-radiation, and from there back into the atmosphere.
The key point in this description, though, is that once a photon has been returned to the surface via back-radiation it becomes part of the surface emission. But, since there’s no way to distinguish this photon from any of the others being emitted from the surface, it’s simply part of the general input signal (again). Thus, we have a “physical” description to match the numerical one above.
(Obviously, this description leaves out the effect on the feedback system from those photons whose energy becomes thermalized to the surrounding non-GHGs. But, my argument there is simply that the probability of thermalization from GHG to non-GHG must be precisely matched by the probability of thermalization from non-GHGs to GHGs. So, a net 0 effect.)
*I say “physically” even though the understanding of photons and the current atomic models are simply that, models, and may or not be reflective of actual physical reality.
(Note, I am more than happy for anyone, who’s persevered enough to read through to the bottom of this thread, to correct any error in my understanding, as I’m offering the above description as much to see whether I’ve understood correctly…and my ego, fragile though it may be, is thankfully not tied to my having understood this difficult concept correctly.)
rip
“The feedback in this system is the portion of those photons being returned to the surface via back-radiation, and from there back into the atmosphere.”
Don’t think so. Feedback in the real system has to take place through energy dynamics within the system – involving water.
Moncton’s elegant argument summarizes for me that the system already exhibited a significant feedback effect before we ever burned any fossil fuels. We can see it in the atmosphere’s water vapor content, which certainly isn’t too different now than 1850..
AGWScience just failed to consider that when they tried to use math (Bode) that was much too deep for them.
If the output is the surface, feedback is formally defined as the fraction of the output from the surface that when added to the input from the Sun sustains a higher surface temperature resulting in more output than can be replaced by solar input alone. Any other definition will not conform to Bode and can not legitimately cite his analysis.
The input forcing is expressed in W/m^2 and you can’t add temperature to forcing, thus the only proper quantification of feedback is W/m^2 and the feedback fraction is the fraction of output W/m^2 added to the input. W/m^2 and temperature can be converted between each other using the SB Law.
It doesn’t make much difference whether one does the feedback-loop calculation in Watts per square meter or Kelvin: but it is useful to recall that we are dealing with temperature feedbacks denominated in Watts per square meter per Kelvin.
It’s difficult for me to understand how we can describe the feedback system as anything other than the atmosphere, and the input to that system as anything other than the surface of the earth. The fact the original source of energy for the earth’s surface is solar, to me, is not relevant for this discussion, since we’re essentially discussing the difference between bb’s and balloons. (Sorry, I mean, I explain to my children that the difference between solar radiation and surface emitting LWIR is like the difference between bb’s and balloons. Thus it’s easy for them to visualize how sunlight passes through the atmosphere, but upwelling IR doesn’t.)
The surface emits, the atmosphere feeds back to the surface, and this results in a slightly higher surface flux. WV entering the atomosphere, or additional CO2, is a change in this feedback system resulting in even more surface flux. Seems simple.
Perhaps the mistake people make is assuming too high of a surface flux due to direct solar input. Whatever surface flux we’re reading already includes the feedbacks from back radiation from the atmosphere.
I don’t know. Perhaps I have a fatal misconception here, but my understanding of the physical process perfectly aligns with CMoB’s numerical conclusions, so I’m satisfied.
rip
Ripshin should surely take account of the fact that the Sun is shining. Feedback processes that respond to tiny perturbations in global temperature must a fortiori respond to the large pre-existing temperature. The system-gain equation requires it.
Monckton of Brenchley says, in the article, “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.” If I understand your previous articles and comments correctly, it is for the sake of argument that you make this statement. Surely you would allow the possibility that most or even all of the warming since 1850 could be from causes other than a rise in CO2 concentration, would you not?
Mr Dibbell is correct: we have accepted ad argumentum all of official climate science except what we can prove to be incorrect. But what we have proven to be incorrect is enough to bring the climate scare to an end.
Yes, and No.
Yes in that if your paper is accepted, you have shown that the Charney Sensitivity is far lower. No in that the Charney Sensitivity concept could be ditched altogether, and models could still be made not utilising the Charney Sensitivity (indeed, it is not clear that they do in any way utilise it), and these models could still project alarming warming. As long as temperature records are tampered with, observational evidence will not suggest that Climate Sensitivity is only around 1 degC per doubling, and politicians have already decreased the catastrophic warming from 2 degrees to 1.5 degrees, and it will not be long before it is reduced to 1.3 degrees, with GISS claiming that we have already seen a 1.1 degC rise such that we are just on the cusp of Armageddon.
Don’t underestimate the movement that you are dealing with. This Science is all about the models, and until such time as it is accepted that the models are flawed, the cargo cult will continue.
Mr Verney continues to say that nothing can be done, with the implication that nothing should be attempted. That, with respect, is not the way I was made.
If the feedback of water vapour doesn’t start till the temperature gets hot enough to have water vapour in the air, aren’t you wrong in including the 255°K? You are throwing a constant into the division, or something. I see it all starting at the temperature it would have without GHGs, and try to measure the change in temperature as water vapour increases, (only) per degree of increase from that point.
You can’t divide water vapour’s effect into something it isn’t having an effect on. If that makes any sense to my query.
I’m on your side.
I hope you are not telling people they ignore the sun and you are ignoring the melting point of water on the water planet.
I know I must be wrong because others would have told you. And it is common sense.
Feedback, as we confimed with our test rigs, responds to the input temperature it finds, and not to any other temperature. Feedback processes, being inanimate, cannot imagine that they might have responded differently had the temperature and ambient conditions been different. The temperature and ambient conditions are as they are. In 1850 the input signal, reference temperature, was 255 K. The output signal was 287.5 K. The feedback system gain factor is the ratio of the latter to the former.
Feedback processes can’t pick and choose, respondong only to some part of the input signal. They respond to the whole thing.
Joe Adams – FYI water vapor is present in very cold air well below freezing (it does snow after all). The NOAA vapor pressure (VP) calculator shows saturated vapor pressure of 0.01 mb HG at 204°K. Feedback would likely be non-detectable at this low VP but would become detectable as the temperature rises. VP as a function of temperature has an exponential behavior.
Well, it’s complex enough that I wouldn’t ask Bill Nye to run a table-top demonstration with a heat lamp.
A brave and laborious effort from Monckton of Brenchley and his team. But the scientific process will require, — no, demand! — for the dialectic process to continue: by peers, challengers, the battle of authorities and so on. This effort can only be the beginning. But it should not be ridiculed or ignored as nobody can afford it, no matter what the truth of it turns out to be.
In the mean time, I’d look forward to a little analysis of how this “startling error” came to be, its path, how it wormed through the atmospheric sciences, the papers, the congresses and all the echoing halls. The anatomy of the error, as it were. Claiming to detect an error is one thing, understanding how it came to be despite the will, scrutiny and the intellectual power of many, is a whole other thing. And one of the most educative aspects of it in my view, especially when devising a plan on how to continue in the realm of ideas, symbols and formulas.
Truth and reasons persist, they always win out. Lets cut this journey a bit shorter though, seeing what might be at stake, after all.
This “startling error” came to be because it suited those scientists who fell into an entrenched position, it suited the environmental terrorists to push their agenda and raise funds to keep them in “work”, it suited the politicians who want to increase taxes, divert people’s minds from difficult real problems, push for a world government, gain popularity from people who “know” that successful big business is evil and devoted to destroying said people to make “obscene” profits and it suited those who profit from a multi-billion pound global warming industry. I left some out, but you get the picture.
Thanks for the answer, Andrew. But I’m mostly interested in the process of how “those scientists” appear to have massively fallen into positions. Because that very claim implies a bigger problem, potentially more serious and threatening on short term than any alarmist climate scenario could ever do. If the process of science is not allowed to run its course, as is part of the implication, it would mean the institute, the principle itself would now be in question. It means that for the most highly complex, important issues, we cannot guarantee anymore that any good methodology is being followed? Or is it limited to one scientific discipline only? This is what I meant with the “anatomy of the error”. The existence of this error in the very place where scrutiny and due process should be at its finest, would describe a bigger crisis of the mind and the collective effort. That in itself might dwarf any problem of climate change and threatens the future of our minds, and way faster, “like a river that wants to reach the end, that no longer reflects, that is afraid to reflect”.
John,
As best as I can tell, the anatomy of this error is as follows:
Hansen wrote the first paper applying Bode to the climate in 1984. This paper was written to be destined as the theoretical foundation for a climate sensitivity high enough to justify the formation of the IPCC 4 years later which was something Hansen was aggressively pushing for.
Hansen has little understanding of feedback networks and made several fatal errors in his paper, among them were swapping the roles of feedback and gain, the unacknowledged assumption of unit open loop gain and of course failing to conform to Bode’s simplifying assumptions of strict linearity and the existence of an implicit, internal power supply.
The preparations for AR1 were ongoing before the IPCC was actually formed and among the principle collaborators working to get the IPCC formed were Hansen and Schlesinger. Along the way, Schlesinger identified the feedback/gain swap and unit open loop gain assumption in Hansen’s paper and they suddenly needed a quick fix to establish plausible theory for an ECS high enough to justify the formation of the IPCC.
Schlesinger stepped up and wrote a paper that identified and ‘fixed’ the problems in Hansen’s paper. If you look at AR1, both the Hansen and Schlesinger papers are cited together as the theoretical foundation for a high ECS. The Schlesinger paper was rushed in order to be there in time for the formation of the IPCC and was not subject to sufficient peer review. He properly corrected the swap of feedback and gain, but ‘corrected’ the unit open loop gain assumption by casting the gain block as forcing in and temperature out and asserting that the conversion from W/m^2 to degrees K was the open loop gain. However; if you follow his math, the open loop gain he claimed was canceled out when calculating the feedback term, since feedback had to be in W/m^2 in order to be summed with forcing, reverting the system back to the unit open loop gain assumption. He either missed or ignored the other errors where Bode’s simplifying assumptions were inconsistent with the system being modeled.
Nobody caught these errors because nobody was looking, nobody wanted to look and nobody in the cabal had the specific expertise to identify them anyway. These errors then became canonized as ‘settled’ science and climate science has been broken ever since.
Thanks John. I know what you’re looking for, but when the peer review process is so poor that Michael Mann can get his broken hockey stick paper published, Amman and Wahl could get their paper published and so many research teams now feel the need to end every paper with a tenuous link to “climate change” in order to ensure future funding, I think it’s very clear that science currently has a serious problem. We know the process was still functional when polywater was discovered, because it didn’t take too long for that to be disproved. I’ve thought for a long time that the whole climate change thing would follow the polywater pattern with a bell shaped graph of increasing numbers of papers being published and then quickly declining back down the other side, but it’s been a frustrating watch waiting for that to happen. Perhaps, at long last, Lord Monckton of Brenchley’s team’s paper will trigger the much needed decline.
The problem in science is certainly not limited to climate science. Large areas of science regularly misuse statistics to make illegitimate claims. By applying cargo-cult statistics. In fact, a paper may merely state a possible correlation. Its’ press release often spins this into 95% chance that A causes B. Only 50% of journalists reporting science read the original paper. The other 50% just rewrite or copy the press release. We’ve know for at least 12 years that about half of scientific studies cannot be replicated (independently repeated to get the same result). This is part of a so-called crisis within science.
In response to Mr Dowser, first we must get our result published, so that the scientific community is forced to take note of it. Then we must wait to see whether any obvious error is found. We think that possible but increasingly unlikely. The paid trolls here have had a particularly difficult time trying to refute our argument, and they have come up with a series of point which, even by their low standards, are risible.
If no error is found, then what we have discovered is a formal proof that equilibrium sensitivity will be low. The advantage of such a proof is that it no longer requires debate: it is so, just as Pythagoras’ theorem is so (on the Euclidean and hyperbolic planes, at any rate). Do not underestimate the power of an absolute proof to bring a previously acrimonious scientific debate to an end.
We have seen with multiple demonstrations that running the Oz machines ( climate models) have resulted in gross failure of being able to predict earth temperature with any success. That could have been deduced by simple logic years ago, in that the limitations because of the mathematics of earth geometry grid sizing and a host of other problems too lengthy to get into here would lead to such a failure. It is a shame that those like Ben Santer, Hansen et.al have been far less than candid to the political class that funds them and relies on their junk science the model output gives and has led to disastrous public policy making from modelers like this that are not being honest
That being said, Christopher Monckton is on a far more sensible path in estimating impirically the effect of doubling CO2 on temperature on the earth.
I would only add, that when speaking about climate feedbacks, that founding principles in atmospheric science also impirically deduced many years ago that the net effect from CO2 on temperature in the presence of the earth’s hydrological cycle for planet earth is zero, in anticipation of a negative feedback, or attenuation, as Monckton puts it.
To see this, one need only determine the radiative equilibrium temperature lapse rate from water vapor alone to see that warming near the surfcae and resulting rapid cooling at the upper boundary from IR radiation leads to a super adiabatic lapse rate and vigorous overturn of the troposphere to 8 Km with a 2 Km overshoot. The thermodynamic and radiative properties of water vapor make it self limiting in the troposphere. Adding CO2 will only enhance the overturn and negative attenuation.
This is only one example of many of the founding principles in atmospheric science that those in “climate science” have trashed and abused ad nauseam. It is truly outrageous.
To Nick Stokes:
I think what the standard feedback calculation fails to take into account properly is that a stable temperature is not a “static” thing at all, it is the result of a CONSTANT flow of energy into the system and a CONSTANT flow of energy out, with the resultant temperature amplified CONSTANTLY by a feedback factor, such that the two are in equilibrium. The CO2 in the atmosphere delays the exit of some of that energy and therefore provides a “positive feedback” such that temperature is CONSTANTLY raised (see Stefan Boltzmann Law).
If we take a 255k non-amplified temperature and add CO2 to get an actual temperature of 287k that is an increase of 32k. As Monkton describes in his paper, allowing for 1.04k reference sensitivity, that is “system gain” or feedback multiplier of 1.129.
In other words CO2 feedback is already CONSTANTLY operating on the original incoming energy keeping the temperature CONSTANTLY raised by 32k – so feedback DOES work on the starting state, because it is a feedback to a flow of energy not a feedback to a static number of degrees kelvin.
Sorry Nick, you are often right, but this time I reckon you are majorly wrong!
“it is the result of a CONSTANT flow of energy into the system and a CONSTANT flow of energy out”
But constancy goes right against the very idea of feedback. A feedback loop is where a change to the output is fed back to change the input, which then changes the output etc etc. A constant input can’t be changed, so the whole idea of feedback there makes no sense.
Just poorly defined terminology. What is happening is probably better described as amplification, or as Monkton calls it, system gain. All the input energy from the Sun trying to make its way out of the atmosphere is amplified, not just the increment from the change. You are a bright guy, I am surprised you cannot see that. It even depends on the Greenhouse effect being correct, just maybe not as bad as feared. No need to abandon the Millennial cult of CAGW entirely yet Nick 😉
Mr Stokes must know that he is talking nonsense. Let him build a test rig with a single input/output node and a feedback loop. Let him set a constant input signal, and let him set a non-zero value for the feedback factor. Let him measure the output signal. It will not be the same as the input signal. The difference is attributable entirely to the nonzero feedback.
“Let him build a test rig with a single input/output node and a feedback loop.”
Monckton, why do you assume he hasn’t?
When the man has a mathematics degree and did his Phd thesis in linear system theory.
Do you have a maths degree?
Last time I checked it was in “The Classics” and Journalism.
https://en.wikipedia.org/wiki/Christopher_Monckton,_3rd_Viscount_Monckton_of_Brenchley
And you know better?
Par for the course.
Snake-oil salesman par excellence.
The Monckton modus operandii ….
https://www.youtube.com/results?search_query=potholer54+monckton
(feel free to respond to Potholer Christopher).
The naysayers really ought to chose their advocates such that they dont bring their “cause” into ridicule.
Just try being skeptical of skeptics.
There needs to be a change of flux for there to be an induced feedback to the input.
Blindingly obvious for anyone with a grasp of physics.
Yes, yes much outrage to follow, and more verbiage from the Lord – but sometimes you have to call a “spade” a “bloody shovel”.
Thank you, Antony, for this demonstration of the level of the arguments the alarmists are able to raise against Lord Moncktons results. This is called desparation.
Mr Banton (who, having been outed earlier, now at least posts under his own name) is an activist of little scientific understanding, easily impressed, as totalitarians so often are, by mere credentials. But, like totalitarians everywhere, he has not the slightest interest in the objective truth, and he will carefully ignore facts such as the presence of a professor of control theory among our co-authors, preferring to sneer at me and to recycle the tired arguments of fellow-activists trained by Communists to denigrate the personal reputations of those who have proven effective in questioning the Party Line which, being uneducated, the likes of Mr Banton lack the intellectual capacity to question.
Just this week I received from the United States a personally signed copy of the book “Disinformation” by Ion Mihai Pacepa, formerly the head of the Securitate, the secret police in Ceausescu’s Romania. In that book, Pacepa describes how, in 40 years, his Directorate recruited one million willing, unpaid Western Communists whose sole task was to attack the personal reputations of the likes of me.
Pacepa, in the end, could not possibly handle a million agents directly. So he arranged for them to be trained to recruit their successors. As a result, the propensity to attack the man rather than his argument is now deeply embedded in the Communist Left. Banton is one such hapless tool of Communist ideology.
“Banton is one such hapless tool of Communist ideology.”
Just caught this at the end of what I guess is the expected (unread).
That you presume I am of that political persuasion my Lord, is precisely because that is your motivation.
Not science (of which you are spectacularly unqualified) but of political ideology.
You’re on the right Blog then (the only one left to you)
And did you vote Brexit?….. like I did.
I value the truth and not snake-oil selling my friend.
Have you answered Peter Hadfield’s “Moncktons’ Bunkum” yet? (up to V4.0 I believe) – you have told a lot on the way.
I have no interest whatsoever in the useless Mr Banton’s no-doubt feeble-minded political ideology. It is not in doubt, however, that he is a tool – albeit a pathetically ineffectual one – of Mr Pacepa’s Communists, who trained the West’s leftists and their fellow-travelers to try to silence any challenge to the Party Line not by arguing against the challenge – which Mr Banton lacks the intellectual capacity or moral honesty to do – but against the person. As Mr Banton will see, I give as good as I get.
“Let him build a test rig with a single input/output node and a feedback loop. Let him set a constant input signal, and let him set a non-zero value for the feedback factor.”
No, this is all nonsense. The test rig from the paper is this:
It would be regarded as a simple undergraduate problem to analyse that and get the answer
There is no need to build such a circuit to discover that. So what does it mean? All the circuit components are linear. For the op amps, that is achieved by elaborate manufacture (and lots of internal feedback). The reference state, if you set the input voltage to 0 (Earth), is voltage zero everywhere, and with no curents flowing through the resistors. If you perturb that, by increasing the input to V, then indeed, the output is perturbed to V*μ/(1-μ*β). Just linear feedback. All the voltages and currents in the circuit are proportional to that perturbation. But there is no equivalent of a constant reference temperature somehow feeding in an extra signal to which a response is required.
The difference is that with climate, or even active devices like valves and transistors, there is no such linearity over a wide range including zero. And certainly not, with climate, including 0 K.
Mr Stokes is being disingenuous. The reference signal in Bode’s equation is labeled E0. And it does not matter whether the response of the system is linear over the entire interval from 0 to E0.
To simplify matters, set mu to unity. The feedbacks simply respond to E0 as they find it. If, for instance, E0 is the sum of the emission temperature 243.3 K in the absence of the pre-industrial non-condensing greenhouse gases and the 11.5 K warming from the presence of those gases, then the feedback processes present in the system at that time will respond to that input signal.
“The feedbacks simply respond to E0 as they find it.”
The feedbacks are determined solely by the resistances. This determines the ratio of response to input, which is the perturbation of E0 from zero.
The circuit is just a standard feedback circuit that you could find in any EE textbook. You might expect an undergraduate class to assemble one as an exercise. The fact that a “government laboratory” was persuaded to waste its time in a student exercise proves nothing about climate, and is not going to be accepted as a contribution to any serious research journal.
Mr Stokes has failed and failed and failed again to explain how it is that inanimate feedback processes can “know” that the should not respond to the solar emission temperature that he wishes them not to respond to, and how they can “decide” that they will not respond to the warming from the pre-industrial, non-condensing greenhouse gases, and yet how they can nevertheless respond enthusiastically and solely to the tiny anthropogenic contribution to the input signal.
The fact that a circuit is simple does not make it wrong.
So you never built an analogue feedback test circuit. Banton assured us that you did. Then, again, Banton is making it up as he posts. Such a tedious bad habit by your side. Post hoc rationalizations; but generally irrational.
I have built plenty of feedback circuits. They were to make electronic music, and they worked. But I would not have built a circuit like this. It tells nothing about climate, and not much about feedback, and is anyway pointlessly complicated. It has just the same gain as this:
with S2/S1 = R2*R3*R5/(R1*R3*R5 – R1*R2*R4). And that is the most basic feedback circuit you can get.
Mr Stokes is no expert in feedback systems, and has shown in this thread an unbecoming willingness, over and over again, to state and repeat what he well knows to be false.
We prefer, therefore, to take the advice of politically-neutral and scientifically-competent and, above all, intellectually honest scientists at a government laboratory than from one whom our host suspects of being paid to disrupt threads such as this with plausible-sounding nonsense.
No, I did not ”assure” you of anything – I said ….
“why do you assume he hasn’t?
When the man has a mathematics degree and did his Phd thesis in linear system theory.”
I simply begged the question.
Which seemed to me overwhelmingly likely.
Try harder.
Yes (to within a factor of -1). But it is a d.c. amplifier.
I admit to being a scientific dimwit but even I could see the glaring failure of logic in
“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.”
The words “circular argument” sprang to mind before I had even finished reading it. Was that really supposed to be sensible response by a reviewer?
Newminster is of course right. This is indeed the argumentum ad petitionem principii, excoriated by Aristotle 2500 years ago. Climatologists are insufficiently educated to realize how dumb such remarks are.
If I’m understanding correctly, both Monckton, et. al. and the IPCC are partly wrong.
If I’m understanding this correctly, Temperature = Net energy in + Feedbacks from Net energy in. In the slide above, Tr1 is the Net energy in and Tq1 is the result temperature. I’ll use E for the energy input
Tq1 = E + F(E) where F(E) is the net feedback
If you add ΔE energy to the system you get:
Tq2 = E + ΔE + F(E + ΔE)
IPCC are saying, in effect F(ΔE) = Tq2 – Tq1 – ΔE
This is true only if F() is linear. Otherwise, the correct version is
F(E + ΔE) = Tq2 – Tq1 – ΔE, and F(E + ΔE) F(ΔE)
Monckton, et al. are saying that if you use E = 254.8 and ΔE = 0.7 and Tq1 and Tq2 as above, then
A = Tq1/E = Tq2 / (E + ΔE) -> F(E)/E = F(E + ΔE) / (E + ΔE) and that this proves a linear F() with a small slope.
The problems:
1. Monckton doesn’t include energy from sources other than the sun, which may be ok if those are small
2. F() is not likely linear. So either way, whatever we know about F(E) and F(E + ΔE) doesn’t necessarily apply to F(E + 2ΔE), and we’re only concerned about F(E + 2ΔE)
3. Our ability to measure Tq1 and Tq2 and ΔE are suspect and subject to large errors.
So this discussion is largely moot, until we understand F() much better than we do.
What am I missing?
What Menlo is missing is the fact that, where we can determine the reference temperature and the equilibrium temperature, the feedback system-gain factor is the ratio of the latter to the former, and that, since we are considering only the period from 1850-2011, one would not expect much nonlinearity in the feedback response, and that we have demonstrated that one can, with little error, treat the feedback system-gain factor in the modern era as constant at 1.129, the value we derived both for 1850 and separately for 2010. Case closed.
If I’m understanding correctly, both Monckton, et. al. and the IPCC are partly wrong.
If I’m understanding this correctly, Temperature = Net energy in + Feedbacks from Net energy in. In the slide above, Tr1 is the Net energy in and Tq1 is the result temperature. I’ll use E for the energy input
Tq1 = E + F(E) where F(E) is the net feedback
If you add ΔE energy to the system you get:
Tq2 = E + ΔE + F(E + ΔE)
IPCC are saying, F(ΔE) = Tq2 – Tq1 – ΔE
This is true only if F() is linear. Otherwise, the correct version is
F(E + ΔE) = Tq2 – Tq1 – ΔE, and F(E + ΔE) is not equal to F(ΔE). In fact, F(ΔE) is not meaningful if F() is not linear.
Monckton, et al. are saying that if you use E = 254.8 and ΔE = 0.7 and Tq1 and Tq2 as above, then
A = Tq1/E = Tq2 / (E + ΔE) -> F(E)/E = F(E + ΔE) / (E + ΔE)
and that this proves a linear F() with a small slope.
The problems:
1. Monckton doesn’t include energy from sources other than the sun, which may be ok if those are small
2. F() is not likely linear. So whatever we know about F(E) and F(E + ΔE) doesn’t apply to F(E + 2ΔE), and we’re only concerned about F(E + 2ΔE)
3. Our ability to measure Tq1 and Tq2 and ΔE are suspect and subject to large errors.
So this discussion is largely moot, until we understand F() much better than we do.
What am I missing?
“What am I missing?”
The first equation should be
Tq1 = G(E) + F(Tq1) (1)
First G(E) to get units right, but also feedback is output (Tq1) fed back, not E.
Then comes the calculus, linearizing for small Δ:
Tq1 + ΔTq1 = G(E) + G'(E) ΔE + F(Tq1) + F'(Tq1) ΔTq1 (2)
Subtract (1) from (2)
ΔTq1 = G'(E) ΔE + F'(Tq1) ΔTq1 (3)
That is my point above. All this Bode mystique is just about sorting out this simple linear relation (usually with I and V at input and output – two port networks – more on that here). But it emphasises that the constant terms drop out, because they are common to (1) and (2)
In terms of understanding F (or G), you only need a value of the derivative at the operating point E, Tq1, which you would normally get empirically.
The matter is simpler than Mr Stokes makes it. It is in practice possible to set the mu gain block to unity, whereupon the input and output nodes, being equipotential, become a single node with a feedback-loop attached, as shown in the block diagrams in the head posting.
Then, if one knows the reference temperature and the equilibrium temperature, the ratio of the latter to the former is the feedback system-gain factor. If that factor is the same in 2011 as it is in 1850, one may infer that the climate system has not changed sufficiently in the interim to introduce any significant nonlinearities.
Sorry, I don’t post here much and my post appears twice. I’ll reply here.
Nick Stokes: It’s not clear to me why your (2) is not Tq1 + ΔTq1 = G(E+ΔE) + F(Tq1 + ΔTq1) in which case your (3) becomes ΔTq1 = G(E+ΔE) – G(E) + F(Tq1+ΔTq1) – F(Tq1). And that doesn’t help either. Certainly introducing G’ and F’ is not necessary since we don’t know F and G and since F and F’ are not linear, so the predictive value of your (3) wrt 2ΔE is no greater.
Monckton of Brenchley: the fact that you can draw a straight line between two points on a curve does not flatten the curve, even if the line has a slope of 0.
Both: None of this addresses the non-linearity of the future. Regardless of what the relationship between ΔTq1 and ΔE in the past, this is not going to say much about F(E+2ΔE) or G”(E)2ΔE, or whatever. This is especially true given the large uncertainties in Tq1 and Tq2 which make ΔTq1 highly uncertain. In fact, the system is complex enough and alarmist claim there are inflection points.
Alarmists claim that the slope of the 1850-2011 feedback is large and will grow, and Monckton, et. al. claim that the slope of the 1850-2011 feedback is small and will remain linear. It seems to me that neither assertion is strongly supported by the evidence because the system is not fully understood. So both positions are asserting certainty which is not there.
“Nick Stokes: It’s not clear to me why your (2) “
It is a first order Taylor series expansion, as alluded to by a reviewer, and as is fundamental to any linear feedback theory:
G(E+ΔE) = G(E) + G'(E)ΔE + higher order terms ((ΔE)² etc)
Basic Newton calculus. And it says that there is then a linear relation between the perturbations:
ΔTq1 = g ΔE + f ΔTq1 (3)
where g=G'(E) and f=F'(Tq1). You don’t get g from a whole knowledge of G(E). g and f are just constants to be determined by observation or other analysis.
One may remove the uncertainty as to the magnitude of the open-loop gain factor in the gain block by setting that block to unity and adding any perturbation of the reference temperature Tr to Tr itself before inputting it to the feedback loop. Then, at any time where the thus-augmented Tr and the equilibrium temperature Tq are known, the system-gain factor may be derived at once. It is simply the ratio of Tq to Tr, since the feedback response constitutes the entire difference between Tq and Tr. That is the method we used, both for 1850 and for 2011.
LM of B. My number 1 suggestion to improve understanding would be to formally define the terms delta/total/absolute feedback/forcing.
Reading some of the comments by experienced climate scientists made it apparent that understanding was being hampered by the lack of precision in climate termiterminology.
For example, climate science appears to sometimes leave off “delta” when referring to a changechange. If you do this in a mathematical proof you would not be surprised to get an incorrect answer.
Lack of mathematically precise formal terms is an underlying flaw in climate science.
In the head posting, we have carefully described what we mean by reference and equilibrium temperature and reference and equilibrium sensitivity and the system-gain factor. In the paper, we have been even more meticulous in ensuring that every variable is described at its first mention.
A serious question.
If feedback A is the change in forcing that results from a 1C change in temperature and feedback B is the change in forcing resulresultinging from a further 1C increase in temperature, what do you call the total feedback caused by the combined 2C temperature change. Is this total feedback or feedback. And what do you call the change in feedback between 1C and 2C. Is this feedback or delta feedback.
According to climate science terminology total feedback and delta feedback are both called feedback. Imagine the confusion that would result if we didn’t distinguish between T and delta T.
Our approach in the underlying paper is to use deltas for perturbations, subscripts r for reference and q for equilibrium, and subscripts 1, 2, 3 for 1850, 2011 and 2x CO2 respectively.
We do not consider individual feedbacks at all. Instead, from reference and equilibrium temperatures we derive the system-gain factor as the unitless ratio of the latter to the former, finding that value to be 1.129 both in 1850 and separately in 2011. And that deals with the suggestion by some that feedback may be nonlinear enough to render our equation otiose.
At any given moment, then, the input signal may be incremented by a delta to give a new input signal (i.e., reference temperature). The output signal may be measured. It is then a simple matter to derive the feedback response in Kelvin.