Guest post by Nick Stokes,
People outside climate science seem drawn to feedback analogies for climate behaviour. Climate scientists sometimes make use of them too, although they are not part of GCMs. But it gets tangled. In fact, all that the feedback talk is usually doing is describing the behaviour of variables that satisfy a few linear equations. Feedback talk adds a way of thinking about this, but does not change the mathematics of linear equations.
A couple of articles I’ll refer to are a survey article by Roe, and a frequently cited 2006 article by Soden and Held.
The basic calculus behind feedback and linear signal analysis goes like this. You have a device or system with a number of state variables, which I’ll bundle into a vector x. And the physics requires that they satisfy a set of equations that I’ll write just as
f(x)=0
There is a particular set of values x0 which satisfy those equations that for an amplifier, say, would be called the operating point. Generally it is a state existing prior to perturbation by an amount dx (a vector of state changes). After perturbation it still has to satisfy the equations, so
f(x0)=0 and f(x0+dx)=0
For linear amplifiers, the perturbed state can be well approximated by the derivative expression
f(x0+dx) = f(x0)+f'(x0) dx = 0
and since f(x0) = 0, that leaves the set of linear equations in the perturbation
f'(x0) dx = 0
We don’t have to worry too much about the form of f'(x0), or indeed f(x0). The point is that it is linear, so all terms are proportional to perturbation. We can just take it that f'(x0) is a matrix operating on the vector of perturbations dx. Roe (p 99) has a section headed “Feedbacks Are Just Taylor Series in Disguise”. Actually “Taylor Series” overstates it, since only first order terms are used. But it is getting close to the correct treatment as linear equations of perturbations.
Usually we think of one of the components of dx as the input, or forcing, and another as the output. Then the equations can be shaken down to make output proportional to input, or gain. This is just a property of a linear system of n equations in n+1 variables, and the feedback algebra just expresses it. But you don’t have to think of it that way. I’ll give some examples leading up to climate.
One thing that is important is that you keep the sets of variables separate. The components of x0 satisfy a state equation. The perturbation components satisfy equations, but are proportional to the perturbation. You can’t mix them. This is the basic flaw in Lord Monckton’s recent paper.
Example 1 – the abstract feedback system
The Wiki description is as good as any. It’s labelled negative feedback, but applies generally. The diagram is:
with the accompanying text
Note that it starts with two equations in three unknown voltages. Two are overall input and output, and the third, V’, is the voltage at the input to the amplifier (triangle). V’ is eliminated, leading to an equation relating input and output (red star). This is then manipulated to a gain ratio. But all these steps are just standard high-school manipulations; they don’t add anything. A computer (or a student?) could have solved them at any stage.
Example 2 – a junction transistor
Here is a very simplified AC circuit, with bias arrangements and capacitors omitted. The voltages are the perturbations (AC). Simplified transistor properties are assumed – zero input impedance, infinite output, and a current amplification β=100. So the AC voltage at the base (V’) is held to zero. There are 3 unmarked currents, denoted by the suffices of the resistors I0, I1, If. Directions are I0 right, I1 down, If right. 5 variables in all.
So we write down linear relations. There are 3 Ohm’s Law
| Vin=I0*R0 | Vout=-I1*R1 | Vout= -If*Rf |
and one current gain relation:
β*(I0 – If) = I1 + If
Again, anything further done with these equations is just high school manipulation. But it can be shaken down to a voltage gain by eliminating currents, written in gain/feedback style:
V1 = -β (R1/R0) V0 / ( 1 + f) where f=(β+1)R1/Rf
Note that it is an inverting amplifier, and the feedback is negative.
Example 3 – Climate feedbacks
Again, it’s just a matter of writing down linear equations, resulting here from equilibrium flux balance. I’ll follow this 2006 article of Soden and Held. Unfortunately, they don’t actually quite write the flux equations, but I’ll do it for them. They write:
ΔR is the change in flux at TOA, which is the GHG forcing. ΔT is the surface temperature response. The feedback factors are T for temperature,w water vapor, C clouds and α (=a) for albedo. What they are actually doing (multiply by λ) is writing a flux balance
ΔR = λTΔT + λwΔT + λCΔT + λaΔT
Each term on the right represents a flux due to that factor. They do a bit extra, which I won’t go into, to deal with the fact that flux is at TOA and response is at surface. Their T flux is what people often call the Planck feedback; they roll into it other kinds of temperature dependent cooling, but it is mainly radiation (Stefan-Boltzmann etc).
This hopefully demystifies all the stuff about positive, negative feedback and runaway. The first is a big term that determines what is thought of as feedback-free (open-loop) gain. It is the 3.2 W/m^2/K figure that is often quoted, and turns into the 1.05K/doubling which forms the basis for Lord Monckton’s ECS. That comes from this paper. The other terms are mostly negative, so they diminish the coefficient of ΔT and so increase the amount ΔT must respond to stay in balance. That is interpreted as positive feedback.
It actually gives a perhaps less scary picture of thermal runaway. If these negative fluxes increase, there will come a point where the coefficient of ΔT is zero. That doesn’t mean instant flames. It just means there is nothing to counter heat accumulation from the forcing flux. So the temperature will indeed rise without limit (until some nonlinearity intervenes), but only as forced by the few W/m2 of ΔR. Not good, but not perhaps as dramatic as imagined. If the coefficient became negative, then there could be exponential rise, which might get more dramatic.
So did climatology make a startling error in omitting “reference temperature”.
I may have given away the answer, but anyway, it is, no! Soden and Held is a typical exposition. They correctly gather the perturbation terms – that is, the forcing, in terms of GHG heat flux, and the proportional responses. It is wrong to include variables from the original state equation. One reason is that the have been accounted for already in the balance of the state before perturbation. They don’t need to be balanced again. The other is that they aren’t proportional to the perturbation, so the results would make no sense. In the limit of small perturbation, you still have a big reference temperature term that won’t go away. No balance could be achieved.
So are all sets of linear equations to be regarded as amplification/feedback?
Well, nothing really hangs on it except the way you talk about them; the algebra is the same. But what characterises amplification is that one of the coefficients is large relative to the others. That means that changing that variable induces a large response in others (hence amplified). What is characterised as feedback is where this variable appears in at least one other term, and is also multiplied by the big coefficient. That makes a big proportional change in the output variables. That modifies the apparent performance in ways described as feedback.
So what is the outcome here? Mainly that you can talk about feedback, signals, Bode etc if you find it helps. But the underlying maths is just linear algebra, and the key thing is to write down correct perturbation equations, and manipulate them algebraically if you really want to. Or just solve them as they are.
Sorry, if the feedback was positive, we would have fried millions of years ago.
Exactly Robert, there _must_ be negative feedback int he climate system or it would have hit an extreme and stayed there.
If the climate ‘models’ don’t take this into account they’re worse then useless (because some people believe them).
Climate models are written to reproduce the recent past history of two (tenuously) connected variables and, when they reproduce the recent past, are assumed to be correct and are then used to create hobgoblins for political, ideological and commercial reasons. The “scientific community” goes along with this fraud as long as the funds for “further research” continue to flow. Nostradamus would be proud.
It was called massaging the numbers in slide-rule days.
Hi Robert of Ottawa (I must be only a few kms away at most from where you are). Indeed, the preoccupation with positive feedbacks in climate science is surprising if they are truly scientists in this field. Your comment should be considered axiomatic.
We’ve had 20 times the present level of CO2 in the earth’s atmosphere and, infact at present, we aren’t far above the CO2 starvation point for all life on the planet. If we ended up calling the Holocene the Anthropocene, it would be for the “Great Greening” that’s taking place and for possibly extending life on the planet for perhaps 100s of millions of years more than was destined the way things were going before fossil fuel burning.
Nick: Except for mentioning runaway warming as something we might worry about, I salute your contribution here and admit I had similar misgivings about the “state” temperature of 1850’s without getting my teeth into it. It seemed to me the 1850 temperature would have arrived at itself as a product of existing conditions of GHG and whatever other effects (not necessarily in equilibrium, though). You make a fair case for Lord M’s “error” claim being wrong.
Having said this, I still have grave problems with the “Principal Component” applicability to climate. It probably operates in climate, but with so much else going on m, it historically has regularly been overpowered by natural drivers. You brushed Tom Halla off in early comments on the thread related to the MWP. How did we get from the MWP, when, apparently CO2 was about the same as in 1850 and it was as Warm as 2000s by this ‘control knob’ mechanism? Clearly, something much bigger than GHG forcings can swing average temperatures by several degrees -say from the Holocene Optimum to the coldest depths of the LIA. This should not be subject to much argument.
The fact that molten salt nuclear reactors will usher in low carbon energy worldwide and will do so cheaper than fossil fuels or anything else makes discussions about atmospheric CO2 rather academic oe even irrelevant. We KNOW very well the effects of molten salt nuclear power – and it doesn’t require knowledge of climate feedbacks, etc.
The evil of global warming hysteria is that its adherents are so ignorant about “solutions.” But THAT is the most important issue. Therefore I look upon articles like this as mostly a waste of time and energy and
avoiding what’s important. Nuclear engineers have the knowledge we need. Neither Nick Stokes nor anyone else is in possession of anything that can trump technology.
In this article posted on Neutron Bytes on June 4th, 2019, Dan Yurman interviews Dr. Jose Reyes, a co-founder of NuScale and chief designer of their small modular reactor:
https://neutronbytes.com/2019/06/04/interview-with-nuscale-ceo-jose-reyes/
Molten salt SMR’s are some years away from being commercialized. On the other hand, NuScale’s SMR design uses half-height conventional fuel rods. The targeted capital cost for their first 12 module facility, about 700 Mw total after the 12th NuScale SMR module is installed, is $4,200 per kWe.
NuScale is a decade ahead of the pack in getting an SMR into commercial production. Their current schedule calls for the first US-manufactured SMR to be in operation in eastern Idaho by the end of 2026.
I still have to disagree Nick.
If you took an opamp, wired for unity gain, inverting output.
Feed in 1.0v, you will measure -1.0V on the output, of which we can all agree.
Do we move to the are of disagreement.
Increase the input voltage by 0.0V to 1.1V
The output will change by 0.1V becoming -1.1V.
I say you always need to refer the input as 1.1V, you appear to say (and your fellow climate friends) that you only use the 0.1V input change, delta V if you wish.
We both understand the the two output voltages will not exist at their current values of either -1.0V or -1.1V WITHOUT the WHOLE of the input voltage being present ie 1.0V or 1.1V.
The output voltages only exist at the levels they do, is because of the whole of the input, not just the delta.
I am all for reducing equations to their simplest form, however, equations only work in the real world, if they map to physical reality.
As Lord Monckton has discovered, the formal equation use, is wrong.
Sir,
Increase the input voltage by 0.0V to 1.1V
Did you mean increase input by 0.0V or 0.1V? That:
The output will change by 0.1V becoming -1.1V.
suggests that it should be 0.1V?
Nick,
Well good luck with this, although looking at the comments so far, you have an uphill battle.
I would have preferred in a way that you just presented the derivation of the climate energy balance equation without any mention whatsoever of control theory – to show that it can be done. One of the most frustrating things about Lord Monckton’s ideosyncratic view is that he insists that climate science has used control theory to estimate climate sensitivity, that it did so in a flawed manner, and hence that such estimation can be improved on by using an improved model supported by his “world experts in control theory”. Although he seems to have backed off somewhat from the first erroneous claim, he is resolutely sticking to the last claim. To judge from the comments he has received, this misrepresentation has seriously damaged the understanding of many people and left them in a snark-hunt for the perfect control box analogue.
The catastrophists require much more warming than can be honestly ascribed to CO2; this is where the talk of +ve feedback comes from and they do prescribe control theory; the controlling variable being CO2.
You lost me at f(x)=0. No matter. The feedback analysis, while interesting, doesn’t provide much help in explaining the earth’s climate that we can piece together from the data. The problem I have with the GCM’s is that they can not explain the cyclic pattern we have observed through time since the end of the last interglacial. It is clear that CO2 changes can not explain the Little Ice age, the Medieval Warm Period, the Dark Ages, the Roman Warm Period, etc. How do you explain the 3-5 degree higher temperatures during the Holocene Optimum? Current GCMs are one-trick ponies. Increase CO2 increase temperatures. There is a reason that the temperature decline from the late 1940s through the 1970s has been adjusted away. The GCMs cannot explain the cooling.
I can not reconcile the predictions of significant warming from a doubling of CO2 with the Ideal Gas Laws. The pressure changes required for a 3 degree increase in temperature from adding .04% of CO2 to the atmosphere make no sense to me.
To say that Hansen’s prediction from the late 1980s proved correct is not accurate. Nothing that he predicted has come to pass. When you compare his temperature predictions for “business as usual” CO2 emissions growth to actual temperatures since his prediction, he wasn’t even in the ballpark.
I find the entire discussion silly. The assumed linearity makes the discussion moot. There is no evidence of linearity in the climate. There are also too many unknown variable, and certainly some unknown unknowns including the future insolation. So we don’t know X0, much less f(x) or f'(x). This is what makes climate models just so much nonsense.
Adding a different equation that purportedly takes into account something “they” forgot, is just as nonsensical as the original and for the same reasons. The point is we don’t know enough to predict, and don’t have near enough data to model the black box which is the climate system. Picking a starting point and drawing a linear equation to today and making a prediction based on that is exactly the complaint.
Even if you have an accurate picture of past feedback, in this case future, non linear feedback doesn’t depend on past feedback and it could be exponential or it could be exponentially negative. We just don’t know. So the discussion is speculative and political about “what if” with both sides invoking “science” disingenuously.
The problem with IPCC is not that they’re wrong about feedback — it’s that they significantly overstate their certainty for political purposes which include ongoing funding for their research.
A “linear” feedback is simply one which is proportional to the output that drives it.
Real feedback systems are rarely perfectly linear. But an “approximately linear” feedback is one which, though perhaps not linear over the full range of theoretical values, is nearly linear over the range of values of interest, and most of the interesting climate feedbacks are approximately linear, for practical purposes, over the ranges of interest, simply because the ranges of interest are small. Consequently, most feedbacks do not introduce substantial nonlinearity into a system, and a simple linear analysis is not far from the mark.
For example, although Planck heat loss (Planck negative feedback, a/k/a Stefan-Boltzmann response) is proportional to the 4th power of the temperature, the increase in radiative heat loss going from 300K to 301K is just 1% greater than the increase in radiative heat loss going from 299K to 300K. For practical purposes, that’s linear, even though the 4th power of T is obviously not a linear function. It “works” to approximate it as linear because the anthropogenic perturbation of temperature is on the order of only about 0.3% (on the Kelvin scale).
Most climate feedbacks are like that: although not fundamentally linear, they are approximately linear, over the (small) ranges of interest.
An exception is CO2 forcing, because the range of interest for CO2 level is not small. Mankind has raised the atmospheric CO2 level by about 46%. That large change means the logarithmically diminishing effect of additional CO2 becomes significant.
Here’s a graph showing what I mean by an “approximately linear” function:
I suppose the real question is this: Which set of assumptions produces results that reflect observed behavior? Those used by the bulk of the modeling community, at least those associated with the IPCC, do not seem to operate reliably.
To avoid positive feedback in climate models, you have to deny that atmospheric CO2 concentration is sensitive to surface temperature.
To be more explicit, you have to deny that decomposition of damp organic residue does not increase with temperature or, perhaps, that the surface of the earth is not coated with damp organic residue.
What is the CO2-sensitivity-to-temperature incorporated in climate models? If it is less than that indicated clearly by the Antarctic ice-cores, the models are anti-scientific.
Let me correct:
… you have to deny that decomposition of damp organic residue does not increase with temperature or, perhaps, assert that the surface of the earth is not coated with damp organic residue.
For those that want to stay within the radiation domain, what validity has an analysis that does not consider a boundary that interacts profoundly with the radiation? You know better.
To avoid positive feedback in climate models, you have to deny that atmospheric CO2 concentration is sensitive to surface temperature in a positive way.
Obviously the warmer is is and the more CO2 is in the air the more plants turn it into carbohydrates and other organic material.
Giving overall negative feedback.
Overall photosynthesis might increase with more CO2, but it doesn’t keep up with geometrically increasing bacterial activity on accumulated residue. Compare the carbon contained in temperate and tropical soils.
… and seas.
Here’s a simpler description of how feedback works, and a simpler analysis of a linear feedback system (followed by a list of all the significant climate feedback mechanisms of which I am aware):
https://sealevel.info/feedbacks.html
Nick,
I’d be curious to hear your response to my post here regarding all of this:
https://wattsupwiththat.com/2019/06/05/the-moral-case-for-honest-and-competent-climate-science/#comment-2717580
RW,
I didn’t much agree about the 3 decades delay. The main slow process is diffusion into the ocean. But worse is this:
“Do you agree that in order to ‘amplify’ +3.7 W/m^2 of ‘forcing’ from 2xCO2 into +3.3C at the surface it requires +18 W/m^2 of net gain at the surface/atmosphere boundary (287K = 385 W/m^2;”
That makes no sense at all. No-one suggests that whatever relates these small increments can be said to be a rate that applies throughout a notional process of warming from 0K.
Lord M does something like that too when he postulates an E(R) function that must pass through 0K.
Why not consider the base state in the feedback system to be the earthy with no greenhouse gases? The addition of such gases makes for a relatively small perturbation (is it 15 degrees?) from the hypothetical steady state. In that case, I think Lord M’s approach seems correct. One could then calculate the effect from different perturbations with differing compositions of greenhouse gases. Is that right?
When engineers want to predict the physical behavior of an amplification circuit design operating inside a larger electronic system, they have the option of building a prototype of the design in the laboratory to see if its actual behavior matches theoretical calculations.
The benefit of this approach is that if they have a physical prototype in front of them, the engineers have easy access to the amplification circuitry itself; and just as important, they have easy access to the measurement and test equipment needed to observe and precisely quantify how a physical implementation of the proposed circuitry design actually behaves relative to theoretical predictions.
First question: Is it not true that the Soden & Held paper from 2006 obtains most of its ‘observational data’ from general circulation models (GCMs) of the earth’s atmosphere, not from the earth’s climate system itself as it physically exists in nature?
Second question: Is it possible to verify the existence of the Soden & Held water vapor feedback process through observations made directly within the atmosphere itself — in other words, inside the earth’s real climate system as it physically exists in nature — using instrumentation systems and data collection systems designed specifically for that purpose?
Mmmm, … in this equation:
ΔR = λTΔT + λwΔT + λCΔT + λaΔT
… I think I see fluxes-represented-as-temperatures being added together. Is that even allowable in physics?
I thought that we could not add temperatures. So, how can we add fluxes derived from temperatures?
Maybe I’m an idiot.
“So, how can we add fluxes derived from temperatures?”
Fluxes are very often derived from temperature differences. This goes way back to Fourier, and even, less clearly, to Newton. The coefficients are heat transfer coefficients. And you can add fluxes because heat is conserved.
CAGW depends on implied and assumed positive feedback.
To say that climate models do not use them is to lie.
“To say that climate models do not use them is to lie.”
They don’t.
And it’s therefore not.
A GCM is run from a set of initial conditions using the physics of the atmosphere (such that can be modelled on current computational economies) in play, and integrated forward in time.
Feed-backs then emerge within the model atmosphere, and in turn integrated forward.
They are an emergent feature and are NOT used per see as in being part of the modelling.
Well let’s ask the IPCC… http://www.ipcc-data.org/guidelines/pages/gcm_guide.html
“… many physical processes, such as those related to clouds, also occur at smaller scales and cannot be properly modelled. Instead, their known properties must be averaged over the larger scale in a technique known as parameterization. This is one source of uncertainty in GCM-based simulations of future climate. Others relate to the simulation of various feedback mechanisms in models concerning, for example, water vapour and warming, clouds and radiation, ocean circulation and ice and snow albedo. For this reason, GCMs may simulate quite different responses to the same forcing, simply because of the way certain processes and feedbacks are modelled…”
Hmmm…seems to explicitly-state that certain feedbacks are modeled.
GCM’s basically only give positive feedback signals. They can only come from a set of initial conditions using the physics of the atmosphere that has such conditions built into them.
If they did not have positive feedbacks built in, via misuse of the science assumptions, they could not and would not give positive feedbacks out.
“To say that climate models do not use them is to lie.” Is spot on.
During the past 800,000 years there have been eight alternating glacial and interglacial periods and atmospheric CO2 concentrations varied in a range of 200 to 300 ppm. When CO2 was at its peak Earth entered into glacial periods; when CO2 was at its lowest, brief interglacials began that reached higher temperatures and sea levels than we experience now. All this discussion of CO2 forcing and feedback mechanism are like discussions of the number of angels that can dance on the head of a pin, without first establishing the existence of angels. CAGW, human-caused climate change and/or extreme weather has been falsified by observations. Mother Nature has told us what has happened but we can’t stop counting the angels.
CO2 is no longer at its peak when interglacials end, but it is still high. But you are right that CO2 is just about at a minimum when the rather abrupt “terminations” start, and temperatures rise to interglacial levels in a few thousand years.
“… Climate scientists sometimes make use of them too, although they are not part of GCMs…”
Lol
Show me the GHG effect or the equilibrium in this system.
No GHE there (at least visible) …. it’s lost in the overall signal.
There is no equilibrium because it is a small part of the climate system and is bounded by it.
The climate system of Earth has energy in = energy out.
Or at least it should.
IN EQUILIBRIUM.
(less solar cycles and orbital eccentricity)
“…The climate system of Earth has energy in = energy out.
Or at least it should.
IN EQUILIBRIUM…”
Should? Try harder.
“Should? Try harder.”
As in – it now ISN’T.
Try harder.
You said it “it should. IN EQUILIBRIUM.”
It MUST in equilibrium.
Nick ==> Unfortunately, neither the climate or the mathematical equations need to describe it are linear.
Thus “Again, it’s just a matter of writing down linear equations, resulting here from equilibrium flux balance.”
Quoting the new paper from Zhang and Kirtman:
“The Earth’s climate can be generally regarded as a chaotic system that is highly sensitive to initial conditions (Lorenz, 1963; Shukla, 1998). In chaotic systems, the error, defined as the distance between two initially close trajectories, evolves exponentially with time and become saturated (Dalcher & Kalnay, 1987). Hence, if there exist initial errors in the climate system (as is always the case), then beyond a period the system becomes random and unpredictable.”
Feedbacks (as defined in this essay) change the “initial” conditions of each computational iteration . . . . and since the equations ruling the various component systems are in fact known to be nonlinear, we can not know what effect, or even the sign of the effect, of these initial condition changes.
There is no reason to believe that the climate system behaves like an electronic feedback system or a junction transistor feedback system. Logically it seems that it must — but in actual fact, no such feedbacks have been proven to operate except in trivial, short-term examples.
Nothing wrong with the concept of feedbacks — but a great deal wrong with the idea that they operate in a linear manner in the Earth’s actual climate system or that we can predict or project changes caused by such “feedbacks”.
…..the mathematical equations needed to describe it…..
Kip,
“There is no reason to believe that the climate system behaves like an electronic feedback system”
Well, my contention here is that you don’t need to believe that. The key thing is that forcing changes produce proportional responses in long-time global averages. There are reasons for believing that to be true, some based on the general conservation principles that apply, and the effects of diffusion. If you put a kettle full of hot water in the bath, the temperature will go up proportionally to the heat added. That’s true even if you have chaos like a couple of wriggling infants. It’s because heat is conserved and diffuses, so evens out.
All I’m really saying is that it comes back to the linear analysis of small perturbations. You can follow the math of control or electronic amplifiers if you find that helpful. Or do your own. It is elementary maths.
Nick ==> The major point is that small perturbations do not remain, neccessarily, small nor even of predictable sign in the real climate system or in climate models, for that matter. See mine @ur momisugly Judith Carey’s https://judithcurry.com/2016/10/05/lorenz-validated/
These linearized equations all look so nice but they do not reflect the real climate nor the true physics of the climate.
Nick writes “It’s because heat is conserved and diffuses, so evens out.”
This is bathtub thinking. Literally. The earth is much larger than our intuitions let us understand. Using that argument one might believe there is no way a 1m difference in sea levels across the Pacific ocean could persist. But consider that the 1m rise across the 15,500 km is about a thousandth of the width of a human hair per meter when averaged.
So sure that cant persist forever but over what timescale can it? And yes time matters a great deal to any thoughts of “evening out” and considerations of what it means that the climate is chaotic.
I dont have the answers either…but I can sure see that bathtub thinking is fundamentally flawed.
The argument is that diffusion smooths out non-linearity, so that a linear approximation is more useful. I can’t see that you are contradicting that. The difference you describe may persist, but the variation is very smooth.
Non-linear diffusion smooths-out non-linearity?
“ And the physics requires that they satisfy a set of equations that I’ll write just as f(x)= 0”.
Translated into simple language, this means that if the value under consideration depends on several factors, then one can ignore the change in all factors except one. It was on the basis of this assumption that the notorious formula for the logarithmic relationship between the temperature of the atmosphere and the concentration of CO2 was obtained. This relationship is accepted by IPCC and majority of climatologists.
http://donaitkin.com/the-relationship-between-co2-and-temperature/
The problem is that under real conditions the influence of various factors on the temperature of the atmosphere cannot be excluded, and, therefore, the relationship between CO2 concentration and temperature is not substantively proven. In fact, Arrhenius, who was mentioned in this discussion, also knew this. Arrhenius believed that it was in a laboratory experiment that one could determine how the concentration of CO2 influences temperature. In 1896 he wrote: “In order to get an idea of how strongly the radiation of the earth (or any other body at temperature 15oC) is absorbed by quantities of water vapour or carbonic acid in the proportions in which these gases are present in our atmosphere, one should, strictly speaking, arrange experiments on the absorption of heat from a body at 15oC by means of appropriate quantities of both gases. But such experiments have not been made as yet, and, as they would require very expensive apparatus beyond that at my disposal, I have not been in a position to execute them”.
https://www.rsc.org/images/Arrhenius1896_tcm18-173546.pdf
I apologize for the long quotation, but it is clear from it that Arrhenius, unlike those who now call him the founder of the theory of the greenhouse effect, understood the need for experimental proof of this effect. Moreover, we know that such an experiment was not carried out till now, more than 120 years later, although modern scientific laboratories have highly sensitive and expensive equipment.
In essence, there is no physical justification for the mentioned logarithmic dependence of temperature on the concentration of CO2, or for the theory of the greenhouse effect as a whole. The question is: what is the point of discussing mathematical equations if we do not know whether they describe the physical processes correctly and do they take into account all factors?
The modellers always try to say that the climate computer code simply calculates the physics for any increase of CO2 and then spews out the new temperature. This is wrong for the main reason that all along, for the last 30 years ever since the 1st generation (we are now up to the 6th generation) Al Gore’s Church of Climatology has supplied special code to the modellers for each new successive generation.
The 6th generation was supposed to have many solar forcing variables in it but when the simulations showed that these new solar variables were causing all of the warming for past years, there was no warming left to do for the 413ppm CO2. So the 6th generation code was held up and delayed until they could work out some way to include some of the solar variables (there are many) and still have Mr. CO2 do his thing of warming. The 6th generation code was then released again and now it shows even more warming than the 5th generation. I suspect that the reason is, that some of the solar variables were incorporated and that Mr.CO2 was allowed to increase the temperature in the same manner as the 5th generation.
Some of the climate modellers themselves have expressed surprise to certain reporters that the 6th generation models are running so hot. If the climate modellers were in complete control of every last line of their code, then there wouldn’t be this surprise from more than 1 modeller in more than 1 supercomputer GCM , that the 6th generation is running so hot. Indeed there wouldn’t even be a need to have generations of models at all. The generation numbers haven’t changed from 1 to 6 because of computer hardware. It is the software changes that define the generations. So in the end there is some computer code that is common to all the models. This code i suspect is the actual forcing code for CO2 increase. Since Tapio Schneider admitted that they will never have enough computing power to solve the Navier Stokes equations for cloud turbulence on a global basis, the actual physics in the models is just a glorified video game. I contend that the code that is passed to each climate computer reresenting the next generation is the actual forcing code represented by a simple forcing formula. If this wasnt the case, then the modellers would not have expressed surprise to the reporters that their simulations are running so hot. The other proof of this is that simple 1 dimensional programs duplicate the GCM’s projections of future temperatures for doubling of CO2.
“Since Tapio Schneider admitted that they will never have enough computing power to solve the Navier Stokes equations for cloud turbulence on a global basis, the actual physics in the models is just a glorified video game. ”
It’s much worse than that. We do not know how to solve the Navier-Stokes equations even with unlimited computer power except in a few simple cases. We don’t even know if there is a globally defined solution, and if there is, whether it is smooth or has singularities.
IIRC, there was an interview of Dr. Wil Happer here on WUWT earlier this year, where he basically praised the Arrhenius GHG ideas, so I would suppose that might indicate he is mostly a conventional ‘Lukewarmer’, where basic theory is concerned?
Point is, if my recollection is correct, Happer also mentioned CO2 as the one gas where the log scale limited response is supposed to apply?
So, in these modern times, is this point corroborated, or isn’t it?
Things were not constant in 1850, because, to the extent that one can rely upon the thermometer record, temperatures significantly increased through to 1880 even though the change in CO2 was only a few ppm.
Indeed, as from 1850 to about 1853 there was about 1 degF of warming and a change of just about 1 ppm of CO2.
Clearly the system was not in equilibrium at that date, or these significant changes would not have occurred. something drove those changes, but it was not CO2.
Climate is never at equilibrium. It can’t be because different parts of the climate system such as the atmosphere and the ocean change at vastly different rates.
Reading this thread took me back to 2009 when I read ALL of the comments in the Harry_read_me file from Climategate. Lots of ‘correction factors’ and guesstimates.
I am still trying to get my head around this. This is where I get lost.
We have an initial temperature, say 10c. Something happens, say CO2 rises, and this, absent any other changes, would raise the temp by 1C to 11C.
But, says IPCC, something else does happen. When the temp goes up 1C, water vapor rises, and the amount of water vapor rise which 1C increase produces is 3C, so we end up with a total warming of 4C, to 14C total.
Whether this is right or wrong, it makes sense to me. I can see that CO2 can have a warming effect, and I can see that a warming could indeed increase water vapor and that would indeed add to the CO2 warming effect.
So I whether we call this feedback or whatever, I can see how it could work, how a modest warming could, if the system works that way, produce a much larger warming in consequence of the effects of the smaller warming that triggered the whole thing.
Can someone explain to me what the IPCC is saying as a description of this, and what CM is saying? I have some incoherent impression that CM is saying that the additional warming must in some way multiply the 10C we started with. That makes no sense to me, so I am probably failing to understand his point.
I know this is a really simple thing, and probably I am missing the obvious, but there it is, I am, and would be very grateful for an explanation in these simple terms. Who is saying what about this situation and what is the disagreement exactly?
Michel ==> You are being confused because the basic presumptions are simply not true. That is a Totally Linear version of a system that has been known for over 50 years to be NONLINEAR.
There are several good essay series on “Chaos” and climate — one my myself here at WUWT: Chaos and Climate – Part 1: Linearity ; Chaos & Climate – Part 2: Chaos = Stability ; Chaos & Climate – Part 3: Chaos & Models and Chaos & Climate – Part 4: An Attractive Idea.
“Chaos theory is a branch of mathematics focusing on the behavior of dynamical systems that are highly sensitive to initial conditions. “Chaos” is an interdisciplinary theory stating that within the apparent randomness of chaotic complex systems, there are underlying patterns, constant feedback loops, repetition, self-similarity, fractals, self-organization, and reliance on programming at the initial point known as sensitive dependence on initial conditions” — wiki
Simplistic linear approaches to climate systems are doomed to failure — chaos is the major factor preventing climate models from being able to accurately project further than just a few weeks or months — and at that they are only projecting major climate features, not any real useful details. They are improving but not much.
I cite a recent paper from Zhang and Kirtman in a prior comment on this thread that directly discusses this problem.
““The climate system is a coupled non-linear chaotic system, and therefore the long-term prediction of future climate states is not possible.”
– IPCC TAR WG1, Working Group I: The Scientific Basis
Anytime you see SIMPLE explanations of anything climate related, know that is has been dumbed-down and is probably totally useless.
Yes, that is a good summary. To put it into the linear algebra
F + .75*ΔT = ΔT
where F is the forcing, your 1°C, and the second term is the effect of water vapor. That goes back to Arrhenius.
And yes, in effect Lord M is saying that 10°C is part of the signal (change) and has to be included somehow. In fact he would include it as 283 K, which really swamps the arithmetic.
If that is what he is saying, it seems like its obviously wrong. Its like a category mistake of a very basic sort. I can’t even get my head around how to phrase what this coherently.
We have, according to the theory, a steady state of some level, say 10C. We then apply heat to it, or stop it losing heat, and the temperature starts to rise. As it does so, it increases water vapor. When this whole process gets through we get a rise of 4C, which is 1C due to the initial warming of our heat application, and an additional 3C caused by the rise in water vapor’s heating effects.
This makes sense, whether its right or wrong, and can be stated coherently as a description of what is supposed to happen to the climate when a heating impulse is applied.
I don’t understand how to phrase what CM is saying that is different from this.
Curry and Lewis made an argument which also makes sense, whether its right or wrong, namely that if you look observationally at the effects of applied warming, the actual rise in temperature is lower than some estimates of the consequenntial changes imply.
This too makes sense. Whether the total effects of the initial warming trigger events which lead to a further one, two or three degrees – or even none – is an empirical matter.
In the example of the 10C, 1C and 3C above, what is CM saying the relationship is? He is saying something different from my crude summary. But what exactly? In my crude example the fact that we start with 10C is immaterial, the account would be identical if it were 100C. Why does he think the initial temperature plays any role in the calculation, and if so, what role is it supposed to play?
Or is he just saying in a roundabout way that the 3C number is too high and should in fact be something lower, like 0.5C?
What he’s saying boils down to his slide at https://wattsupwiththat.com/2018/08/15/climatologys-startling-error-of-physics-answers-to-comments/, which he calls “the end of the global warming scam in a single slide.”
There
is the (with-feedback) ECS value he calculates from 
, which is the temperature increase that doubling CO2 would cause without feedback. He calculates it, as Mr. Stokes does in his analogy at https://wattsupwiththat.com/2019/06/06/demystifying-feedback/#comment-2718602, by in essence extrapolating the with-feedback equilibrium temperature 
as a function of without-feedback equilibrium temperature 
.
The difference lies in the extrapolation coefficient
. For that quantity Mr. Stokes uses, as any high-school algebra student would know to do, the function’s local slope, which in Lord Monckton’s slide would be 
. As the slide shows, however, Lord Monckton instead uses the average slope 
or 
. He has somehow convinced himself that feedback theory dictates this. It doesn’t (and that the near equality between his alternative 
values indicates that the function is nearly linear).
Quite some time after he started shopping this theory around (he started at least by the time of this talk: https://www.youtube.com/watch?v=Ebokc6z82cg) he hit upon a second rationale, which is that local-slope “measurements” are too noisy to rely upon, whereas the constituents of average slope are large values that tend to swamp the noise out. If we were sure that
as a function of 
is nearly linear, that would make some sense. But, of course, that begs the question; the IPCC’s ECS estimates imply that it isn’t linear at all.
Occasionally, therefore, Lord Monckton backs up to telling us why that function can’t be much different from linear. He goes into Clausius-Clapeyron, logarithmic forcing functions, and a lot of hand-waving that not everyone would find compelling. (I’m not saying that he and his “eminent” co-authors haven’t got a compelling near-linearity demonstration squirreled away somewhere. But there’s no reason to believe that the paper he keeps mentioning is any more coherent than he’s shown himself to be so far.)
In other words, what we get is a motte-and-bailey argument in which the bailey is the impression he gave in the YouTube video: that he’s mathematically demonstrated a fundamental feedback-theory error on “climatology’s” part. The motte is the much-less-attractive physical argument that the function can’t be very nonlinear.
(All this, of course, ignores Mr. Hansen’s point that all these equilibrium quantities are unicorns anyway.)
Unfortunately, Mr Born knows less math than a high-school student. For the secant slope that he asserts (without evidence) to be the system-gain factor (which he calls the “extrapolation coefficient”) is nothing of the kind. It is merely a secant slope. To the extent that the function E(R) is a growth function, the system-gain factor E/R will always be less than the secant slope.
As to the alleged nonlinearity of E(R), I have already explained to Mr Born that official climatology considers the climate-sensitivity parameter, which encompasses the influence on temperature of the sensitivity-altering temperature feedbacks, to be “typically near-invariant”.
Thus, official climatology would take the ratio of the equilibrium sensitivity 32.5 K in 1850 to the 10 K reference sensitivity to the naturally-occurring, noncondensing greenhouse gases and derive therefrom a system-gain factor of about 3.2. It would then extrapolate to the warming from a CO2 doubling by taking Charney sensitivity as the product of 3.2 and the 1.05 K reference sensitivity, giving 3.4 K, which is indeed approximately the midrange estimate of Charney sensitivity in the models. In official climatology’s world, this is indeed – within the margin of uncertainty – a linear extrapolation, consistent with the statement in IPCC (2001, ch.6.1) that the climate-sensitivity parameter is “typically near-invariant”.
It is only when one remembers to take account of the fact that the feedbacks present in 1850 are feedbacks not only to the naturally-occurring perturbation of the input signal (emission temperature) but also to the entire reference signal, which is the sum of that perturbation and of emission temperature, that one can see that, contrary to the assertion that the climate-sensitivity parameter is typically near-invariant, official climatology’s Charney-sensitivity estimates imply a strong nonlinearity in E(R) that has no physical justification and, therefore, always leads to a contradiction.
Mr Born himself discovered this when he tried to set up a power-law function E(R) and found that the ratio of the feedback fraction in response to greenhouse-gas warming would be 11 times greater than the feedback fraction in response to emission temperature, which is self-evidently impossible, and is certainly in conflict with the statement that the climate-sensitivity parameter is “typically near-invariant”.
Somehow the LaTeX didn’t work. The average-slope values I was referring to were E_1/R_1 and E_2/R_2.
I’ll try the LaTeX again:
The difference lies in the extrapolation coefficient
. For that quantity Mr. Stokes uses, as any high-school algebra student would know to do, the function’s local slope, which in Lord Monckton’s slide would be 
. As the slide shows, however, Lord Monckton instead uses the average slope 
or 
. He has somehow convinced himself that feedback theory dictates this. It doesn’t.
Note how Lord Monckton buries his bald assertions in nomenclature to frighten the natives. His fanboys love it.
But if you work through his slide–that is, if you plot the two points
he extrapolated from and the third point 
, which he extrapolated to–you’ll see his theory boils down to bad extrapolation.
As to whether the relationship in question actually is very nonlinear, I have no real opinion, although my guess is that it’s not. But his bald assertions and tortured readings of the literature don’t prove it’s not.
As to the 11 times he mentions, that’s from the example at https://wattsupwiththat.com/2019/06/05/the-moral-case-for-honest-and-competent-climate-science/#comment-2717128 by which I showed that even a highly nonlinear function could, contrary to what Lord Monckton’s reasoning (“
“) at about 17:50 in his talk at https://www.youtube.com/watch?v=kcxcZ8LEm2A, implies, result in very little average-slope change over a small interval.
By the way, if you think of E as a DC amplifier’s response to a stimulus R, the average slope I’ve been referring to would be the large-signal gain, while the local slope would be the small-signal gain. An engineer who relied on the former rather than the latter to assess stability could encounter a nasty surprise.
Your understanding is qualitatively correct, michel, but not quantitatively. It’s not nearly that large.
It is generally expected that warmer temperatures should increase the amount of water vapor in the atmosphere, because warmer air holds more moisture (roughly 7% more for each 1°C of warming). That’s is called water vapor feedback. This effect is usually approximated in climate calculations by assuming stable relative humidity as temperatures change. Under that assumption, warmer temperatures cause greater amounts of water vapor in the atmosphere, and since water vapor is a greenhouse gas, increased water vapor in the atmosphere should increase greenhouse warming: a positive feedback.
This is generally believed to be the most important positive climate feedback mechanism, by far.
I ran MODTRAN (Tropical Atmosphere), using the U. Chicago web interface, and found that with an older version (circa 2012), an increase in CO2 level produced a 65% greater increase in temperature with constant relative humidity (i.e., with water vapor feedback) than with constant absolute humidity (i.e., without water vapor feedback). However, they must have updated their MODTRAN version, because when I did the same exercise in 2015 it showed just over 8% amplification, rather than 65%.
The earlier value (+65%) is not far from AR5’s estimate of the combined effects of positive water vapor feedback and negative lapse rate feedback. AR5 considers Water Vapor and Lapse Rate feedbacks together (section 7.2.5, p.587) and gives an estimated range of +0.96 to +1.22 W/m² per 1°C of warming, for the net effect of the two feedbacks, combined. If we also assume that it takes 2.8 to 3.4 W/m² forcing to cause °C of global warming, that would imply a 0.96/3.4=28% to 1.22/2.8=43% positive net combined feedback from water vapor & lapse rate feedbacks, which, with “compounding,” would result in a net amplification of 1/(1-ƒ) = 1/(1-(0.96/3.4)) to 1/(1-(1.22/2.8)) = 1.39× to 1.77×, adding 39% to 77% (best estimate 54%) to the original warming.
The highest estimate (by far!) that I’ve ever seen for the effect of water vapor feedback is the +300% figure you mentioned, from a 2013 “control knob” paper by Lacis, Hansen, et al, which claims (without support) that the “feedback contribution to the greenhouse effect by water vapour and clouds” effectively quadruples (adds 3× to) the warming effect of CO2 and other GHGs. That is certainly a fringe viewpoint.
Ah Dave, you are a wonderful man. I take back everything I have ever said about you.
“water vapor feedback is the +300% figure you mentioned, from a 2013 “control knob” paper by Lacis, Hansen, et al, which claims (without support)”
Such a wonderful take down of it might even be +600% Andy I have not seen before.
Even the name of the paper.
Pure magic.
I have a question, then. On a calm day, locally, the air temperature drops until it gets near the dew point, then it stops. You can even get a temperature inversion, where the air is ‘warmer’ than the ground. The dew point has a diurnal variation, too. It drops in the morning about an hour or so after sunrise to its low point and rises in the afternoon to its high point about an hour or so after sunset. That suggests that ‘warming’ does not, directly, change the absolute humidity much. If daytime sunshine doesn’t do it, how could ‘greenhouse’ gases do it?
Hi Griff
I don’t mind the non-linearity question. If small perturbations are considered (and 3K out of 280k might well be considered small), perhaps the linearity approximation is good enough. This wouldn’t hold for the claimed “tipping points”, but that’s an entirely separate question I don’t want to get into here.
On the question of amplification of small perturbations, if A and ‘beta’ represent passive components, their values will both be less than 1.0. That means the closed loop gain A/(1+A.beta) is absolutely less than 1.0. Therefore if the climate response to increased CO2 is a passive system, the closed loop response cannot amplify the input.
A passive component is energy dissipative. The output cannot contain more energy than its input and therefore amplification is not possible.
In other words, climate sensitivity cannot be increased by amplifying processes. Is that how you see things Griff?
Or if it is not how you see things, can you explain the climate system components that are not passive (relevant to climate sensitivity) and give a reasoned suggestion of their numerical values to fit into the feedback model you describe.
Thanks
The most important aspect of any climate feedback that is pretty much never considered let alone discussed is the feedback on the change in flux at the TOA, itself. That is what determines future climate.
The irony, Tim, is that the feedback to TOA net flux is the ONLY feedback considered by energy balance models, which is what Lord Monckton is actually challenging. There is never any direct feedback to temperature. A change in temperature changes state variables which change the TOA net flux balance. Any impact of a temperature change on further temperature change is always via net TOA flux since (normally by fundamental assumption) that it the only way that the climate system can heat or cool in a zero-dimensional model. This is one of several reasons why trying to partition an absolute temperature in 1850 which is assumed to be in equilibrium is a fool’s errand.
It’s curious the often mentioned 1850 as some kind of stable equilibrium state given it is near the juncture of LIA to present climate “optimum”. Almost as though it was latently primed at that point. While using the global mean to search for the greenhouse/feedback fingerprint likely the only way to prove the point, it can only come from knowing shift from baseline profile. In a few decades we’ll have the temporal range of real global observation to confirm longer term trends empirically. But the undisturbed baseline will still be elusive. A bit of a fools game. Must say from the input here and elsewhere, the likelihood of stepping from glaciated to interglacial into a 3rd state unknown hot state seems exceedingly unlikely in the ice age we are currently in. Much more likely and intuitive that buffering by water with its various states, mobility and other properties and will keep our climate quite liveable. The same can’t be said for our impact on prime land that we also depend on heavily, nor ballooning population and inequity that exacerbate it.