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.
Mr Stokes, why, pray tell, it the estimated temperature in 1850 the base state one is measuring peturbations from? Why not 1200, still in the MWP, as the “normal” temperature?
Some physical factors produced the temperature in 1850, and the same factors are still presumably operating now. Was there any feedback effects operating in a description of what produced the climate in 1850? If not, why?
“Mr Stokes, why, pray tell, it the estimated temperature in 1850 the base state one is measuring peturbations from?”
Can you quote what you are talking about, so we know exactly what they say? As said above, the basis for the analysis is that there is an operating point and linear fluctuations about it. You don’t need complete knowledge of what the operating point actually is, or how it got to be that way. The coefficients of the linear perturbation variations are likely obtained from observation or model outcomes. An analogy is the internet. Signals that you receive have passed through all sorts of amplifiers with many different operating points. You don’t need to know about that to process the signal.
They are looking at forcing from GHG and its consequences, including feedback, that are proportional to it at equilibrium. So 1850 is representative of a state when forcing from GHG was stable.
Your post is a reply to Lord Monckton, I presume, so it is on point to ask why the state in 1850 is the chosen base state, rather than some other date not during the LIA. You are also falling into a cliche CAGW trope that the LIA was normal, rather than the coldest period since the last outright glaciation.
What my question is, was the ~300 ppm level of CO2 in 1850 not contributing to any feedback that resulted in that climatic state? Discounting miracles, that invoking some special factor that did not exist in 1850, but exists now, rather goes contrary to my understanding of the basic rules of science.
So Christopher Brenchley pointed out a really obvious error in the established model? Can you explain why he is wrong, without handwaving?
“state in 1850 is the chosen base state”
Well, chosen by Lord M. It seems a reasonable choice to me, because it represents a state with stable GHG, so the fluctuation from that level is the forcing. The change in T from that time is the response, not the change from 1200 or whatever. The existing 280 ppm and its effects on T, with feedbacks, are part of the chosen operating point.
I’ve tried to explain why he is wrong in the later part of the post. A key point is this. You have perturbations that result from the forcing of GHG since 1850 (or whatever time chosen). You have n relations in n+1 unknowns, which boil down to a proportional relation between forcing perturbation and T response. That passes through zero (no perturbation, no response). If you add in a term that is not proportional to perturbation, like reference temperature, then it can’t pass through zero, with constant coefficients. Zero perturbation does not return to the operating point. Something has to give.
Mr Stokes, you are still not explaining what you presume caused temperatures in your chosen baseline period. Was CO2 having an effect, or not? If it was, Monckton was basically correct.
“you are still not explaining what you presume caused temperatures in your chosen baseline period”
No, and I’m explaining why you don’t have to. It’s just a state that happened, and was in balance. It’s my equation (f(x₀)=0. You don’t have to know what caused what. All you need to analyse are variations about that point, and their proportionality.
It’s the same if you buy an amplifier. If you are curious you can poke around and measure the operating point (voltages etc). You don’t need to analyse to find what made it that way. If you want to figure the gain, you only need to analyse the AC part of the circuit. But you’ll probably just measure input and output.
I do believe your approach resembles homeopathy, or other mystical worldviews. Consistency in natural laws should be a reasonable presumption, so anthropogenic CO2 shouldn’t know it has a different effect than “natural” CO2.
Mr Stokes, how do you model the effects that produced temperature in your chosen baseline period?
Thus far, you have been handwaving.
“anthropogenic CO2 shouldn’t know it has a different effect than “natural” CO2”
It doesn’t. The linear equations I refer to just relate total quantities. If the driving perturbation consists of a mix of anthro and natural (say a burst of volcanoes), then it’s up to you to fractionate the result accordingly.
Y’all are still trying to not admit the Established Model has an obvious mathematical error.
To me the basic flaw in your explanation (which i thank you for) is the assumption of zero perturbation and equilibrium at any given point before changing a variable like CO2. i don;t see that in the climate at any point. It appears to be constantly perturbed by changing variables and constantly changing on every scale. Starting a linear equation from an assumed static position that is not static will always give you the wrong answer, which is pretty much what we see with every climate model. They start off reasonably close then diverge more an more because the starting position was only approximate and was actually in flux rather than in equilibrium.
At least some complex, chaotic, non-linear systems appear to never reach equilibrium because the input variables never stop changing – the economy for example, which is why economic models never forecast accurately over anything other than the short term. The other problem those models exhibit is that appear to be right(ish) for a period until they are suddenly very wrong.
To look at our actual climate, it is very difficult to show that when we first started to produce significant amounts of CO2, the climate was stable and in equilibrium. The Little Ice Age suggests that it was not (and never is). I would also note that the non-climate events that are often removed from climate, like volcanoes, are still variables in climate and could cause climate trends (if they exist) to reverse or amplify.
If you start from the wrong position and assume things are not changing when they are, even the best model will end up simply wrong quite quickly.
Phoenix44 says:
To me the basic flaw in your explanation (which i thank you for) is the assumption of zero perturbation and equilibrium at any given point before changing a variable like CO2.
Agree. Stokes is assuming a “balance” in 1850 because CO2 was constant, but forgets/ignores the most important GHG — water vapor. Plenty of evidence that increasing/decreasing water vapor effects persist for many yrs (perhaps a major cause of the LIA & MWP) and is never really in balance.
Pheonix44,
“Starting a linear equation from an assumed static position that is not static will always give you the wrong answer, which is pretty much what we see with every climate model. “
Perfectly stated!
‘Mr Stokes, why, pray tell, it the estimated temperature in 1850 the base state one is measuring peturbations from? Why not 1200, still in the MWP, as the “normal” temperature?’
I have seen your answer Nick, but why not use a warmer period as the reference point that also did not have a co2 influence? The 1730’s were the warmest period until the 1990’s according to Phil Jones. Why not use this? Or the even warmer 1540 period?
Personally I do not think there is anything that can be termed ‘normal’. the temperatures goes up and it goes down and is rarely static for too long. It varies due to a number of factors, some of which are key at any one time which might then be replaced by others.
When looking at the 1730 decade Phil jones was actually most interested in what happened in 1740-just about the most severe winter ever. after that he confirmed that the climate was much more variable than he had previously believed.
Beng135
You said, “Plenty of evidence that increasing/decreasing water vapor effects persist for many yrs (perhaps a major cause of the LIA & MWP) and is never really in balance.”
Indeed, both of the links provided by Stokes at the beginning of his article admit that water vapor is the most important forcing agent, and that clouds are the most uncertain. And, the article by Roe states that the effects will be most persistent for those the system is most sensitive to!
Tony
“Why not use this? Or the even warmer 1540 period?”
You don’t need a period embodying some target characteristic. It’s just a question of choosing two states that you can measure and see what the difference is that could be interpreted as a response to something operating over that period. So it needs to be fairly recent, so we know more about it. And it really should not include too much time in which the forcing wasn’t operating, since that just confuses the issue. So I think 1850 is a reasonable choice, although again, it was Lord M’s choice, not mine.
In terms of working out a rate from an interval difference, the lack of equilibrium at present is far more of a problem than the lack of equilibrium in 1850. It’s why ECS is such a hard problem.
As there are equations that should produce a certain temperature from a certain insolation, why does a magic state somehow occur? The formula should work equally well for 1200, 1650, or 1850, if it actually works now.
“So 1850 is representative of a state when forcing from GHG was stable.”
I think you need to clarify that this refers to anthropogenic GHG’s from burning fossil fuels. Who knows what natural changes in GHG concentrations (including water vapor) were occurring in pre-industrial times. But, as you noted above, feedback on perturbations is a linear combination of all of them, so there’s nothing analytically wrong with focusing only on the feedback due to anthropogenic emissions to get a theoretical calculation of the net effect of those emissions, though I think there’s a huge issue on the reliability of those theoretical calculations.
“I think you need to clarify that this refers to anthropogenic GHG’s from burning fossil fuels.”
It actually refers to the forcing. Volcanic CO2, say would be included too. And usually solar variations and volcanic aerosols are included too. The reason is that you are going to measure response variables, and for this purpose you can’t do attribution (that may come later). Of course, there will be noise – fluctuations that would have happened without forcing.
The linear equations that I wrote express required relations in the variables, regardless of cause. And there is one extra variable, or degree of freedom. It is when you prescribe that extra variable to get a numerical answer that you inject the notion of cause. Whatever you prescribe is the forcing. For an amplifier, it would be the input signal.
Climate is never at equilibrium, and can never be, because the very different time constants in different parts of the system, particularly between the ocean and the atmosphere. This is why ECS for example has no physical meaning.
Nick Stokes – June 6, 2019 at 6:41 pm
Enough is more than enough.
Excerpt: The “title” and the 1st two sentences from the very 1st paragraph of Nick Stokes’ above posted article, to wit:
Now I have always assumed that Nick S was a passionately committed believer and supporter of …. CO2 causing Anthropogenic Global Warming (CAGW) climate change ….. which is 100% based in/on LWIR “heat energy” feedbacks between all the per se “greenhouse gases” (except H2O vapor of course) and the earth’s surface.
So, given the fact, ….. that CAGW climate change is rooted in the belief that there is a “mystifying feedback” that exists between atmospheric CO2 and surface entities, ….. then why in the world would an avid believer want to be “demystifying” that which must remain “mythical” to be of any value to/for their “claims of fame” and future employment?
And just why would people “outside climate science” give-a-hoot about said “feedback analogies” other than to disprove and criticize the silly, per se, climate scientists whose livelihood is dependent upon said “feedbacks”.
And anyone that believes the following ……. would take things back that they never took in the 1st place, to wit:
Of course the “feedback analogies” are a part of the Global Computer Models (GCMs) ….. a BIG, BIG, BIG part of them, ……. and that is pretty much exactly why those Models have failed miserably at “forecasting the future” climate ……… as well as “hindcasting the past” climate.
Sam C, ….. yea ole Devil’s advocate just doing his thingy. 🙂
Joe Bastardi has seen that even for a 2-week forecast, the US models cannot “see” any cold air, and only see it when the forecast is for a mere couple days in the future. The “climate” models are essentially the same as the forecast models. I have no doubt both types of models are bovine excrement because they (purposely) vastly overestimate CO2 effects among other issue. Watch his 2 free public videos here:
http://www.weatherbell.com/premium
Surely the starting point is the very earliest days of the solar system, say the time when the planet first acquired an atmosphere, and when the sun had illuminosity far less than today.
Everything is a perturbation from that time onwards.
If one does not want to go that far back, surely it must be the start of the Holocene.
If we cannot explain the temperature profile of the Holocene, we have no chance of reasonably estimating how temperatures will progress and develop throughout the remainder of the Holocene, and eventually back into the deep throes of the ice age that the planet is presently in.
Richard V
You are on the right track with the call for looking farther into the past.
Basically Nick (and others as well) are saying that if the CO2 concentration was stable, GHG forcing was stable (unchanging) at the time. To me, this is a fatal flaw in Nick’s argument. Let’s take his assumption that (because CO2 was stable at 280 ppm in 1850) the temperature was therefore stable because the GHG forcing was stable. All that is implied in the his starting assumptions.
I don’t think I am misrepresenting it in any way. See Nick’s words for confirmation. Stable CO2 means stable total GHG forcing means stable temperature, which prevailed in 1850.
Logically, if applied to previous times, it means that if the CO2 concentration was unchanging going back in time, the temperature was also unchanging cause there was no perturbation from 280 ppm. I am ignoring any cause-effect arguments, just observing.
Essentially the premise about 1850 is that CO2 concentration represents temperature. If there are feedbacks at play, Nick has it that they are in any case wrapped in the linear equations that gave us the equilibrium temperature in 1850. I am not claiming that CO2 was the only cause of the temperature rise from some zero-GHG state, only that Nick is using the CO2 concentration as a proxy for all contributions via a set of equations that we do not need to know about in detail.
I agree we don’t need to know the details, but we should not accept the premise that the temperature in 1850 was tied to the CO2 concentration that happened to prevail at the time without first testing it.
If the premise, upon which Nick’s explanation is based, is correct, they we can check for some f(x) function of global temperature and how it varies, compared with the CO2 concentration at the time. Looking back from 1850 to 8000 BC we find numerous proxy temperature profiles indicating that the temperature is far from stable and that the CO2 is almost invariant. This bodes poorly for the assumption.
The temperature, presumed to be strongly dependent on the total GHG forcing, itself indicated by the CO2 concentration as proxy, is all over the place. It is obvious that the “GHG forcing” that supposedly dominates the temperature, nay, produces it, is itself dominated by non-GHG factors because reality contradicts the assumption.
The “assumption” about 1850 is overly-simplistic. The tightly constrained CO2 level over millennia and the wandering temperature (several degrees C) indicate that either the temperature response is very strong for tiny variations in CO2 (disproved by recent observations), or there are other larger factors controlling the global temperature. Stable CO2 as a proxy for all GHG’s, was unable to stabilize the global temperature.
How then will the IPCC’s goal of a stable CO2 concentration bring about a stable temperature? It never had that effect before. Why should it work now?
On the flip side, how do we know that a stable temperature or a varying one was not produced by non-GHG factors? Obviously they dominate, in terms of temperature result. We have millennia of confirming observations and proxies.
On the basis of evidence available, there is no reason to accept that in 1850 there was an equilibrium temperature state for all climate forcing factors. The CO2 concentration increased very little from anthropogenic sources during the subsequent 100 years, yet the temperature rose rapidly until 1940 – rapidly compared with the net rise since then when GHG concentrations increased markedly.
I conclude by observing that strong positive feedbacks are nowhere in evidence in the historical record over the past 10,000 years, while there is ample evidence that CO2 is not a convincing proxy candidate for total forcing nor for temperature. There is no historical evidence that, going forward, stabilizing the CO2 concentration will stabilize the global temperature.
Richard V
“Everything is a perturbation from that time onwards.”
There is no one designated reference state. You can compare any two states not too far apart. For convenience one is designated reference, and relative to that you calculate the perturbation terms. In the tyre example I gave before, the reference state is what you presently have, not a tyre in a vacuum. If you had to pump it up again later, that would be the new reference state.
Crispin.
“If there are feedbacks at play, Nick has it that they are in any case wrapped in the linear equations that gave us the equilibrium temperature in 1850.”
Again I must protest that 1850 was Lord M’s choice, not mine, although I don’t criticise it. It’s true that you can’t get perfect stability at the start of the range. You certainly don’t have it at the end either, and that is a much greater deviation. That doesn’t seem to bother folks who like to forget about the E in ECS.
“How then will the IPCC’s goal of a stable CO2 concentration bring about a stable temperature?”
It won’t. The goal is to remove a cause that is forcing a continuing temperature rise. Well still have to live with variations.
Nick wrote
“The goal is to remove a cause that is forcing a continuing temperature rise.”
There is some correlation of AG emissions of CO2 with temperature some of the time in the past 70 years, but not much and the correlation coefficient is dreadful.
Humanity is utterly wasting its time and money attempting to control the global temperature. The ECS is low, though still unknown. There is no strong, positive water vapor feedback in evidence, and plenty of evidence that its existence is dubious.
There is also ample evidence that having a stable CO2 concentration does not stabilize the temperature, and further that increasing it 50% has nearly no effect, much against expectation. All the climate modelling and hype it produces looks like crap. It’s ridiculous.
Yes, but “The Narrative” must be propagated! Oh, the HUMANITY!!
So Nick, are you going to let the embarrassing uninformed speak for you?
Honest question: why do we know (or assume) that all components of x are linear?
It is small perturbation (linear) theory. It’s the general calculus proposition that locally, the tangent line, plane or whatever is a good approximation to the function. The electronic amplifier creators go to a lot of trouble to make sure this works even for quite large perturbations. For something like climate, one relies mainly on the fact that underlying laws have smooth variation. Heat fluxes are generally proportional to temperature difference etc.
Except all that is only partially true and only for convection. It isn’t correct when you get near any phase change on many solids and on radiative transfers. Wonder how many of those other situations are involved in climate science …. oh all of them. So using that theory is less than useless.
You make a good point here LdB.
Water is a good example as at phase change the temperature remains constant, thus the Planck equation coefficient (sensitivity) is zero.
And there is an awful lot of this phase change going on in the atmosphere.
And the phase changes from liquid to gas to solid and back to liquid happen at different altitudes. The release of latent heat near the tropopause, at the tops of cumulonimbus clouds in thunderstorms, and in tropical storms, completely bypasses the “greenhouse” effects of CO2 and H2O (vapor) that the models say “trap” heat near the surface. Even before this happens, water vapor condenses into droplets to form clouds, which block insolation at higher altitudes. Both of these negative feedbacks from water vapor are absent from the naive “greenhouse gas forcing” linear arithmetic.
Monster,
The phase changes at different altitudes and the associated energy/heat transformations IS an elephant in the room. Further consideration needs to be that these rapidly developing storms are not static or stationary but actually moving and developing ahead of the highest altitude shown on radar. The highest altitude is likely where the storm is beginning to collapse and dump rain/H2O. It’s a very dynamic process and a tremendous amount of energy involved.
I am very relieved that others are seeing what I see.
eyesonu – June 7, 2019 at 2:00 pm
Eyesonu, fear not, because lots of others are seeing the same.
It is the CAGW shouters and believers who intentionally avert their eyes and their mind to what some of us freely admit to seeing.
And some people won’t say anything due to their misguided respect for “authority”.
Heat fluxes in the atmosphere are greatly effected by water phase change, which is as non-linear (actually, you could call it catastrophic in the mathematical sense) as you can imagine.
Obfuscation.
I got into the conversation a bit late, but, come on, guys. Any of you who have attempted to model complicated systems know that the first thing you do is linearize the heck out of the defining equations, solve, and see how the results compare to observations. If they compare well, then you can use the results to interpolate with confidence between data points, but extrapolate (predict) with extreme care. Mr. Stokes’ comments about linearity and perturbation theory are imho right on; the argument then becomes is the baseline analysis (equation set) correct…
Climate sensitivity is given as K per doubling of CO2. In other words, temperature is proportional to the log of CO2. By definition, that is not linear.
You can treat the problem as linear over a certain range but to get away with that, you should really have a solid understanding of the system’s response. That’s not the case for the climate.
For sure the climate sensitivity approximation to reality doesn’t work for very low levels of CO2. Going from zero molecules of CO2 to one molecule would produce an infinite temperature rise because going from zero to one molecule is an infinite number of doublings. Similarly, for very high levels such as on Venus, the temperature is more determined by the density of the atmosphere than by the radiation properties of CO2.
So, where is the climate sensitivity concept valid? We don’t actually know that for sure.
“Climate sensitivity is given as K per doubling of CO2.”
It’s often given as K per unit forcing in W/m2. Then you can make a conversion from W/m2 to log(CO2). But anyway, K per doubling is linear. Doubling means a unit increase in log_2(CO2).
It’s true that the linear relation between K/(W/m2) and log(CO2) has a limited range. It was originally worked out empirically by Arrhenius in 1896 and has held good since then. It’s possible we’ll get to a stage where it has to be refined. Or better, measure a new operating point.
I don’t want to jump the gun here, but I can already see what I suspect the issue is. This is an empirical claim:
“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.”
I don’t think it is possible to assert axiomatically. Just off the top of my head I can think of a number of systems that falsify the claim, notably in this case temperature at the melting point of water. The perturbation by itself won’t satisfy the same equations independently of the initial conditions at all.
These are globally averaged quantities, and at equilibrium, so there is time averaging as well. On the fine scale, there is always ice melting somewhere, and it’s all added up. The main point is that there might be discontinuity at melting in specific heat, and so rate of temperature change, but what mainly affects the averages are conserved quantities, ie total heat.
Again, this seems to be a flawed assumption. Why are you assuming equilibrium? Weather is essentially evidence of disequilibrium and there has always been weather as far as we know.
Heat is also not a conserved quantity in thermodynamics, energy is. Heat can raise the temperature by some amount or vaporize some water at the ocean surface. That work is then done and cannot be done again without violating conservation of energy.
In other words: If you are considering only radiant energy in energy and energy out you are completely ignoring the fact that heat is *any *transfer of energy, including chemical, mechanical and so forth. If you see a energy imbalance in the thermal spectrum you have no way of knowing just from that whether it is a result of increased temperature or increased mechanical work (say extra hurricanes or whatever).
Sure, it may be possible that the system behaves that way, but again, that is a very strong empirical claim that must be subjected to extremely rigorous empirical tests. It cannot just be barely asserted like what you are doing.
I hate to say it, but the very fact that the wind blows falsifies the notion. Disequilibrium exists at every level you care to look at, and”average temperature” of a non-equilibrium system was a coherent concept to begin with. Even if it was the case though, equilibrium in atmospheric temperature is less than a rounding error in the total climate system.
Pardon, but did a typeristing error preclude you from saying, “…’average temperature’ of a non-equilibrium system was not a coherent concept to begin with”?
If so, then you’ll get no raised eyebrows from me.
“Pardon, but did a typeristing error preclude you from saying, “…’average temperature’ of a non-equilibrium system was not a coherent concept to begin with”?”
Yes, sorry, I completely messed that sentence up. The average temperature of a system not at equilibrium is not a sensible concept.
>>
Heat is also not a conserved quantity in thermodynamics, energy is.
<<
The first law of thermodynamics in differential form (using the Clausius standard) is:
This is also called the law of conservation of energy. U is the internal energy of the system, Q is the heat transferred to or from the system (positive heat is heat transferred to the system), and W is the work performed on or by the system (positive work is work done by the system). Although the units of heat used to be BTUs or calories (still is in some disciplines), the SI unit for heat is the joule–a unit of energy. Both BTUs and calories can be converted to joules. Heat is therefore energy and is conserved.
Jim
Just think about it for a second. Heat is the change in energy: “Let the amount of heat which must be imparted during the transition of the gas in a definite manner from any given state to another, in which its volume is v and its temperature t, be called Q”…
If heat, the flow of energy between systems, was conserved, equilibrium would be impossible. Temperature is defined as a local thermodynamic equilibrium. You see how this could be a problem.
Heat is not the same as energy.
The form of the equation you gave is for a closed system, which obviously makes sense. Still it is the energy that is conserved, not the heat, since the system will move from disequilibrium to equilibrium over time (second law). So as the system does work to reach equilibrium the heat flow will necessarily decrease to zero.
>>
Heat is not the same as energy.
<<
I’m sorry. but heat is energy. The definition of heat is a transfer of energy across a system boundary due to a temperature difference. Heat is measured in joules, BTUs, and calories. It can also be converted to foot-pounds, newton-meters, pascal-cubic meters, watt-hours, or any other unit of energy.
Jim
Heat is energy that flows spontaneously from warmer to cooler. So all heat is energy.
However, all energy is not heat … potential energy, chemical energy, radiational energy, etc.
… and therefore, Beeze’s claim that “Heat is not the same as energy” is 100% true.
w.
>I’m sorry. but heat is energy. The definition of heat is a transfer of energy across a system boundary
A thing and the transfer of a thing are not the same. Besides, heat only refers to thermal energy, not all the other forms. The formula you provided *only* applies in a closed system when you ignore all other forms of energy. But obviously that doesn’t describe the climate.
The total energy is all the different types of energy added together, so heat in the sense of temperature, kinetic, chemical potential etc. When you add all of these together you get the total energy and that is what is conserved. Thermal energy is not a conserved quantity.
It’s interesting how we are living in a bizarre world–where people make contradicting statements and think both are true.
>>
Willis Eschenbach
June 7, 2019 at 5:17 pm
Heat is energy that flows spontaneously from warmer to cooler.
<<
That’s not exactly the definition of heat. This is from my text on Classical Thermodynamics:
“Heat is defined as the form of energy that is transferred across the boundary of a system at a given temperature to another system (or the surroundings) at a lower temperature by virtue of the temperature difference between the two systems. That is, heat is transferred from the system at the higher temperature to the system at the lower temperature, and the heat transfer occurs solely because of the temperature difference between the two systems. Another aspect of this definition of heat is that a body never contains heat. Rather heat can be identified only as it crosses the boundary. Thus, heat is a transient phenomenon.”
Notice that energy transferred from a colder region to a warmer region is not heat by this definition. Also, the atmosphere can’t trap heat or heat can’t hide in the ocean.
>>
So all heat is energy.
<<
True. That’s what I’ve been saying–I thought.
>>
However, all energy is not heat … potential energy, chemical energy, radiational energy, etc.
<<
No, but you can change heat into other forms of energy. Heat, like work, is a boundary phenomenon. Heat is energy; work is energy; both only exist at the boundary of a system, but the energy they represent must be accounted for. Either the internal energy changes, or work, heat, or other forms of energy appear to balance the equation. Energy is conserved.
>>
… and therefore, Beeze’s claim that “Heat is not the same as energy” is 100% true.
<<
As I said, this is very bizarre. If ALL heat is energy, then how can you say that heat is not the same as energy? One of the definitions of energy is the ability to do work. In thermodynamics, work, like heat, is a transient phenomenon. Are you now saying that work isn’t energy either? I’ve taken a lot of physics courses, and work is always considered to be the same as energy–always.
Jim
>>
Beeze
June 7, 2019 at 5:32 pm
A thing and the transfer of a thing are not the same.
<<
You’re arguing definitions? Look up the definition of heat. Heat is the transfer of energy, so your statement is wrong.
>>
Besides, heat only refers to thermal energy, not all the other forms.
<<
I’m not sure why you think this is important. I agree–heat is heat.
>>
The formula you provided *only* applies in a closed system when you ignore all other forms of energy.
<<
I can add additional terms to that formula. I didn’t want to confuse the issue with lots of terms. Chemists add a term for chemical potential. You can add a term for surface tension to explain the workings of those little boats that run on surface tension. There’s the work term of course, and the term for internal energy. If a term is zero, then it doesn’t need to be included. For example, heat is zero for an adiabatic system.
>>
But obviously that doesn’t describe the climate.
<<
It depends on what you want to describe. The first law of thermodynamics won’t entirely explain the climate, but it does play a role.
>>
The total energy is all the different types of energy added together, so heat in the sense of temperature, kinetic, chemical potential etc. When you add all of these together you get the total energy and that is what is conserved. Thermal energy is not a conserved quantity.
<<
Well, temperature isn’t a form of energy, so it won’t add into your total. You need to add heat into that total to make the numbers come out right.
It’s not often to see someone (two someones actually) argue “x is y” and then “x is not y” in the same statement.
Jim
Your texbook definition causes the confusion. It uses the word “heat” in two senses, first as a flow of thermal energy and then as thermal energy itself, in the sense of temperature as a measurement of local equilibrium of thermal energy. So you have two bodies with different equilibria, and the “heat” in the equation is the additional thermal energy of the “hotter” supplied to the equilibrium of the “cooler”.
It is clear that the distinction is made from the final sentences: “Another aspect of this definition of heat is that a body never contains heat. Rather heat can be identified only as it crosses the boundary. Thus, heat is a transient phenomenon.”
A transient phenomenon cannot, by that fact alone, be a conserved quantity. Again, your equation only applies to a closed where thermal energy is the only form under consideration. The FLOW of energy is not conserved and is distinct from the TOTAL energy, which is.
If the flow of thermal energy was conserved the second law would be violated.
“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.”
I don’t see the logic here. Can a control expert chip in? In the meantime, I’ll check my college text books from a couple of courses “Process Systems Analysis and Control” and “Process Modeling, Simulations and Control for Chemical Engineers”. It’s been awhile.
Too much hand waving and smoking mathematical mirrors in the replies so it seems.
Mental mathturbation.
Math Heads think if the math is right, then they do not need to understand the mechanisms. For them, False Premise + Good Math = Settled Science.
That is an inconvenient truth.
Beans beans the musical fruit
The more you eat the more you toot
The more you toot the better you feel
So let’s have been for every meal.
Beans gives positive feedback to gas emissions. 😉
Over my head.
But today I drove through a region that was 15 degrees C for 100 kms, then it rose to 18 degrees C for the last 100 kms. And there it’s remained.
So far I haven’t experienced any deleterious effects.
But just in case, I’m going to spend tonight in the waiting room at the emergency ward at our local hospital.
One can’t be too careful about being exposed to extreme weather.
The President has something to say about extreme weather.
Having waded through all that, I am way more mystified than I was before. Nothing at all has been clarified, so either I am denser than a sack of hammers, or your first few words, “People outside of climate science”, (of whom I am one) are a classic case of misdirection.
Hi Nick,
the maths aside, I’m sure you have it correct, how did you come to the conclusion that the posted long-winded spiel ‘demystified’ anything? I would assume the electronics part of the math is quite well known as the variables are controlled for in the design, how are you applying/controlling for unknown variables? From what I understand this is the crux of the matter.
You state above, as a reference to a baseline period, “They are looking at forcing from GHG and its consequences, including feedback, that are proportional to it at equilibrium. So 1850 is representative of a state when forcing from GHG was stable”. Excuse my haste I’ve just stripped this from Wikipedia (nothing wrong there … ) and the primary greenhouse gases in the Earth’s atmosphere are water vapor, carbon dioxide, methane, nitrous oxide and ozone.
My dodgy reference describes carbon dioxide as a trace gas whereas water vapor (and I got caught in an awful lot of it in Adelaide the other day) could be described as significant. Your post refers to GHG’s (total) but your post alludes to only one of the variables being affected by the multiplication of a large coefficient. Why in the literature is this assumed to be carbon dioxide? The reason I ask is in your post you mention thermal runaway and that is when you lost me. IF this happens and IF that happens, you turned a reasonable attempt at demystifying feedback into mush. Somewhere in your explanation you have mention how the feedback formula accounts for the feedback that controls the imagined ‘thermal runaway’.
Cheers,
Andy
“how did you come to the conclusion that the posted long-winded spiel ‘demystified’ anything”
Well, I think Lord M is way ahead of me in verbosity, or even mass of math. I think it demystifies because of what is not there. It describes simple linear algebra that you can do without the blessing of the venerable Bode. You don’t even need a tenured professor of control theory. You don’t need to argue about what the EE books say about what is a signal.
Feedback is an analogy used for thinking about climate. That’s fine, but you need to make sure the analogy doesn’t take over. I’ve shown that it is just a way of talking about the underlying linear equations. And that is the place to return to if you want to resolve anything about climate.
“but your post alludes to only one of the variables being affected by the multiplication of a large coefficient. “
Yes, and I was inexact there. It’s true for say a voltage amplifier, but in the climate example, the coefficients have different units, so it doesn’t make sense to describe one as large. As I said above, in the equations for perturbations, there is one variable too many to get numbers out. You have to put in more information. You have to describe something that would induce the perturbation, and so quantify it. If you know that a certain amount of GHG was added, that will fix the perturbed state.
Re Nick Jun 6 9.30
“Feedback is an analogy used for thinking about climate. That’s fine, but you need to make sure the analogy doesn’t take over. I’ve shown that it is just a way of talking about the underlying linear equations. And that is the place to return to if you want to resolve anything about climate.”
Without direct evidence to prove or disprove climate hypotheses, which will take decades to emerge, the climate people resort to computer models, or more properly mathematical analogies , of which linear approximations are one of many techniques. So your statement contains the very truth that the analogies HAVE taken over. Then you say that if you want to resolve anything in climate science you have to use analogies!
Clearly, you are uttering a paradox, and for your statement to make any sense you must resolve it.
Anyway, with regard to these mathematical analogies, aka computer models, here is a question for you; how do you verify and validate these models? If you can’t, then they remain hypothetical.
“how do you verify and validate these models?”
There are lots of internal things done. How well to they conserve energy, mass etc. They actually solve differential equations; the main test of any equation solver is to substitute the answer back in the equation and see if it satisfies.
But on a practical level, the main validation of the fluids aspect is that they double as weather forecasting programs. And they get that right, in huge detail, for some days into the future.
Of course, when used as climate programs, after a week or two they get to a stage where the phasing of events is lost. They keep forecasting weather, but it is no longer the weather that happens. But it is weather that is consistent with the forcings, which can then change. There is every reason to expect that in the long term that response to forcings will continue to be shown by the earth also, even if the weather doesn’t follow the same sequence.
With weather forecasting, you can check the results. It’s true that with GCM’s you have to wait a long time. We are starting to get suitably longterm validation of the very early efforts like Hansen’s. The warming they forecast has been showing up.
>>The warming they forecast has been showing up.<<
Say what? The models are all running way hotter than reality.
“The warming they forecast has been showing up.”
What, all of it?
I thought temperatures peaked 2-3 years ago?
I still maintain late 80s were warmer and we still have lots of record highs from the 30s. It must be extremely warm elsewhere 😉
“It’s true that with GCM’s you have to wait a long time.”
Nick, thanks for admitting that GCMs are just hypotheses … and must remain so for decades at least.
In other words, they are literally not true.
TonyN
If you compare the average of the many model forecasts, they speak for themselves that they are not only untrue but laughable.
Anyone saying otherwise is not of sound mind and still living in the 1970,s LSD era.
Climate models = Imagineering.
Nick,
The warming they forecast? Come on!
Most of what they ‘forecast’ was known history…. not really a forecast, and easy to match with ‘creative’ forcing history (including very creative aerosol history). I stipulate that rising GHG levels have to cause some warming. But that isn’t even interesting, much less important. How much warming, where, how much rain, where, etc. are the things that matter, and the models are not very good at those predictions. Even more important are the down-stream consequences (especially sea level rise), and those consequences are even less certain than the models. As we have discussed on other threads (at other blogs), empirical estimates consistently disagree with the models. What’s more, the models disagree with *each other* by substantial amounts, which ought to make rational people question their validity, their underlying assumptions, and of course, their accuracy… if they were all somewhere near correct, then they would all agree with each other. They don’t; and even such agreement, if it existed, would not prove accuracy… but the substantial disagreement definitely proves *inaccuracy*.
Your post is at best tangential to what actually matters. Monckton’s posts are orthogonal to anything that matters, and I am puzzled you would bother to reply.
Stokes,
You said, “And they get that right, in huge detail, for some days into the future.”
Not where I live in the Mid-West USA. The rate of false-positives for precipitation is very high. They seem to do fairly well for temperatures, but I suspect that they could do almost as well with historical records.
Clyde Spencer says:
They seem to do fairly well for temperatures
They definitely do NOT do well — they are pathetic. Watch Joe Bastardi’s public videos for a while — they ALWAYS overestimate future temps, especially the further they go into the future (like 2 weeks):
http://www.weatherbell.com/premium
I think Nick you are missing a point. The simple model you show is an elementary analysis of an amplifier. The feedback is not even necessary, since a basic amplifier can be controlled by the input voltage. More voltage-more gain, more noise. Feedback is an attempt to control a runaway condition.
The climate is not simple, not elementary, and doesn’t function via linear algebra. Virtually all the processes go from laminar to turbulent- wind, water, heat, radiation(very complicated with absorption, emission, conversion to atomic vibrations, conversion to thermal motion), etc.
That is the problem using averages to model the system. Nothing in the system responds linearly through average inputs. There may be a range where the response appears linear, but outside that range it is not.
I think the best example most people are at least aware of is an airplane stalling- it can happen at any airspeed, altitude and temperature, humidity etc. At a particular point attempting to make a plane lift more, even thought the lift response has been a nice smooth curve, the plane will stall and possible crash. The air flowing over the wing responds to the exact temperature, pressure, and velocity at particular points. Go one tiny step too far and the flow breaks down into turbulence.
The designers go to great lengths to understand where and under what conditions the air at any point on the airplane can go from laminar to turbulent flow because it is so important.
Lord M. I quack, kook and crank.
” … how are you applying/controlling for unknown variables? ”
>>
fudge factors come in handy
What I cant work out is why you would have a feedback on temperature at all it’s a minor byproduct of the process. It is a bit like putting feedback on the wind resistance on a heavy loaded train and pretending the speed of the train is controlled by the wind resistance.
The train example works pretty much the same, you can convince yourself the wind speed has an effect all you like, until the driver really opens the throttle or breaks and shatters your illusion.
Temperature is nothing more that the speed of molecules it isn’t a major player in the electromagnetic radiative balance at all and it isn’t valid to treat it like that.
“Temperature is nothing more that the speed of molecules it isn’t a major player in the electromagnetic radiative balance at all and it isn’t valid to treat it like that.”
WEll, there is Stefan-Boltzmann. εσT⁴. But the issue here is flux at the surface. Down IR is a big part of that, and wv is a big source. And we know wv concentration varies with temperature.
The thing is to work out the governing equations, and then see what matters. Not before.
Wind resistance is pretty important for trains.
Only you would believe any of that, because you are pretty much illiterate to real science. This is all just part of your trolling and misdirection where you try to pretend you understand it, sorry you aren’t fooling anyone.
Nice ad hom.
Actually that demonstrates perfectly the poisonous attitude of the “hard-line” denizens here.
That makes any engagement so dispiriting.
Even with the likes of the ever patient/polite and patently knowledgeable Nick.
It’s as if you wear your bias/and hatred of the science (as some metaphor for the opposite stance to your ideological bias) as a badge, unable to move past it.
Yes, yes. The world’s Earth scientists are all incompetent and/or corrupt and a silver tongued classics scholar knows more than them sufficient to reveal the “startling” error of climate science.
Takes a massive bias to buy that bizarre illogic.
How about you become a true sceptic and be sceptical of the snake-oil salesmen in your own camp.
The idea that anyone presenting the science is a “Troll”, if it fails to comply with the “its not happening”. It’s natural. It’s a scam. Lefty take-over, etc meme.
No, someone who explains/links to the science does not become a troll for that.
And the biggest “fools” are those that are so wedded to their bias that they come on here and say worthless things like the above.
PS: This is why I turned down the invitation of Charles to contribute here.
And why I expect ad homs to come my way below.
To which I will not respond.
So feel free.
“Nice ad hom.
Actually that demonstrates perfectly the poisonous attitude of the “hard-line” denizens here.
That makes any engagement so dispiriting.
Even with the likes of the ever patient/polite and patently knowledgeable Nick.”
Do you consider everyone here a hard-line denizen?
Yes, Nick has the patience of Job.
So 300ppm of CO2 is the baseline in 1850. That’s logical. I saw the other day where the CO2 in the atmosphere has increased to almost 415ppm. Yet the temperatures have been cooling since Feb. 2016. Disconnect?
Here’s some science, since we are referencing circuit analysis:
atmospheric CO2 acts on LWIR radiation to space, as a variable time delay circuit, on the time scale from ns to ms. Some might point out that the delay can be in the ps range.
Ps This post is neither trolling, nor an ad hom.
Pps Might some here consider your post to be a trolling ad hom screed?
I have no issue discussing things but when you can’t even get a sensible discussion going because one party decides to rewrite definitions and basic norms it is clear they are trolling. Nick is a troll, a very polite one but a troll none the less. How you would have been received I can not say, can you construct something using normal science?
LdB
Years ago I taught a class on System Dynamics computer modeling. For the benefit of the students, I was demonstrating how to build a model to simulate the performance of a car, which included the acceleration, gas mileage, and top speed, as a function of the depression of the accelerator pedal.
Wind resistance was something I had to take into account because it varies with the 3rd power of the speed. To ignore it would give unrealistic performance.
Nick
Re: “Stefan-Boltzmann. εσT⁴”
To clarify, please use the full absolute temperature to the first two Taylor terms.
When simplifying please keep the full absolute temperature terms as well as the Del T.
That would help show how important is the absolute temperature vs assuming just Del T.
David
Nick, dear lad, the ‘equations’ govern nothing. They are, supposedly, in the real world, a mathematical explanation of an observed phenomena. Have a nice day!
For LdB re: “wind resistance”
https://www.quora.com/Why-is-air-resistance-roughly-proportional-to-the-cube-of-speed
As speed rises the dominant controlling force on an object becomes wind resistance.
Look up terminal velocity too.
OK, the change in the output of a system is the perturbation times the gain of the system. That’s fine.
The gain of the system is a function of the forward gain of the system and the feedback. There should be no argument about that.
There is an input signal for which the output is zero plus some offset. That is our input reference.
Suppose we have a black box for which we don’t know the gain. We find the gain by perturbing the input, measuring the change in the output, and taking the ratio.
What’s the value of the offset? If we know the value of the reference, we set the input signal to that and the output signal will be the offset.
So, we’ve got the climate. We’ve got an average global temperature and we’ve got the atmospheric CO2 level. Based on physics, we postulate a forward gain without feedback as something like 1C per doubling of CO2. With no other information, could we calculate the gain of the system with feedback? If we know the reference level and the output offset, the answer is yes. The gain will be:
where:
So, given a CO2 level and a global temperature and a reasonable figure for forward gain, we can calculate the system gain and thus the feedback as long as we know the system offset and the input reference. The bigger the difference between the input signal and the reference, for a given output (as compared with the offset), the smaller the gain and therefore the less positive the feedback.
So, Nick is right, it’s just linear algebra. Yes, all we need is the change in the input and the gain and we can calculate the change in the output. The trouble is that we don’t actually know the system gain. To figure out the system gain, we need to know the input reference. That is basically Monckton’s point.
So, you ask, could we get the system gain if we have a time series of data. Yes indeed. Lewis and Curry get something like 1.66 K per doubling for ECS (Equilibrium Climate Sensitivity). That puts Monckton’s result in the ball park.
“What’s the value of the offset? If we know the value of the reference, we set the input signal to that and the output signal will be the offset.”
No, you don’t. Valve audio amplifiers often had a transformer at the output stage. What is the offset there?
If it’s linear, you can work out gain by just graphing input vs output for a few signal levels, and the gain is the slope of the graph. The offset will be the intercept, but you don’t need to know that a priori. But you could measure it; it is just the no-signal state. You could do the same with climate.
“That puts Monckton’s result in the ball park.”
Well, it puts L&C out of Monckton’s ball park. See the width of his histogram. That’s one thing about these low ECS claims. They are very inconsistent, but their fans don’t seem to mind. They just cheer when it gets lower.
But can they be turned up to 11, Nick?
That is the hard question.
Valve audio amplifiers often had a transformer at the output stage. What is the offset there?
That transformer is usually there to (passively) shift the (AC) impedance — the ratio of voltage to current — from what the amplifier would like to deliver to what the speakers would like to see. Conceptually, I suspect that your feedback analysis probably should be based on power (voltage times current) rather than voltage, but it’d take some work, and I doubt it’d change anything. And this whole feedback business wasn’t your idea in the first place.
I’m not sure that you’ve demystified anything except possibly for yourself. But thanks for trying.
I’m also not sure that you’ve really answered Lord Monckton’s paper. To the extent I can follow the paper, he seems to be arguing that one or more of the feedback terms used in climate science are in the wrong reference system (“local” relative to current state) rather than absolute. I’m pretty sure that one can do feedback analysis in either reference system, but one presumably does have to be consistent.
Don,
“I’m pretty sure that one can do feedback analysis in either reference system”
What I was trying to say with the first bit of calculus is that the analysis does compare a reference system with a local (perturbed) system. The feedback talk is applied to the difference (local-reference) system, where everything is linearised first order to the perturbations. He’s trying to transfer a reference variable (emission temp) to that first order system, but it is zero order. You just can’t do it.
Yes. That’s called AC coupling. For an electronic amplifier, a change in the DC level at the input produces a transient at the output and then the output returns to zero. Presumably for the climate such a characteristic would produce an ECS of zero.
Hi Nick,
Good to see your post. I have a question about treating the temperature record as a signal to be processed. I hope I’msexpressing that properly.
It seems to thar in ordinary signal processing, you start with a clear signal and then it gets degraded as it travels — by interference, jamming, what have you — by outside forces. In the case of the temperature record, what is the noise, and from where does it come?
James,
It’s a bit O/T. Noise is a problem locally, due to various measurement lapses. But that gets damped hugely it taking an average over time and space. For global averages, the main issue is sampling error; what other answer might you have got if you had sampled in different places. Bigger samples reduce this, so GHCN V4 is an improvement.
Commiebob – “the less positive the feedback”? In my electronics experience it is impossible to have a stable system which has net positive feedback. Negative feedback makes systems progressively more stable. I know this is true for simple, linear systems like amplifiers. However, the earths climate is composed of multiple nonlinear interconnected systems, so IMO it is probably naive to assume that what works for a linear amplifier will work with our vast and complex global climate system. And even more naive to use the simple amplifier analogy to ‘prove’ anything about climate science. I usually know when I am out of my depth, but apparently some here don’t.
The poster child for positive feedback is the regenerative receiver.
Usually, positive feedback is poison, unless you want to create an oscillator. Then, the Barkhausen stability criterion is the rule. The product of the forward and feedback gains has to be unity.
Joke:
There must be a bajillion kinds of stability analysis, depending on the design practices of the kind of system under consideration. The bottom line in any of them is to avoid having enough positive feedback to cause problems.
Good 1.
“As far as I can tell, Nick studiously ignored that part”
Not deliberately. But let me make amends. You wrote
G = (T – offset) / (ip – ref)
G being the gain. ip is the input signal, suggested as log(CO2). I am not sure why the denominator is written as a standard state difference with ref, which the corresponding term for T is described as offset. But the comment says that the offset is determined from the reference state, so it seems to be the same thing.
Now I agree with that; it defines G as a rate, in a standard calculus way. Gain and feedback factors belong in the world of rates. Now what happens of you try to add something, reference temperature or whatever, into the numerator? It isn’t a difference, but will be treated as one. IOW, the gain will be calculated as if part of the change was a shift to the reference temperature from zero. And of course that is not true, but worse, it happens regardless of the smallness of the actual changes. The rate G is not a stable limit that you can put a number on, but goes to infinity.
Since pre-industrial times, we have had half of a doubling of atmospheric carbon dioxide concentration. In this period we have had about 0.8C global average temperature increase, but we have no way of knowing what part of that was caused by the increase of atmospheric greenhouse gases due to humans. UN IPCC suggests that at least half is anthropogenic. Considering that all of the various feedback mechanisms have been active during this whole time, why is there any reason to expect a larger temperature increase while the next half of the doubling is completed?
All of the feedback mechanisms that are responsible for driving the climate to some quasi-equilibrium state, such as our present interglacial period are active in producing that quasi-stable state. When it is disturbed, the climate responds. We have seen that response. It is not particularly frightening.
“The UN IPCC suggests that at least half is anthropogenic” So does Roy Spencer: ” I’m willing to admit over half of it could well be due to increasing CO2.” http://www.drroyspencer.com/2019/06/uah-global-temperature-update-for-may-2019-0-32-deg-c/
In other words there is the undeniable possibility it is mostly or even entirely due to GHG emissions.
“the climate responds. We have seen that response.” We have seen the start of that response. 0.8C is the average, some places see less, some a lot more, 3-4C around the Arctic for example. There is more baked in https://iopscience.iop.org/article/10.1088/1748-9326/10/3/031001
another 1C masked by aerosols and GHG concentrations are still rising exponentially.
Maybe a dark blue Arctic ocean won’t make too much difference or maybe the ice has helped stabilise the climatic. One more August Arctic cyclone like 2012’s and we’re going to find out.
Well we will find out if you are right because we are definitely going to go there because world emissions are still increasing and they won’t be stopping any time soon. That is because emission control is the dumbest idea you could use to tackle the problem even if you assume it is correct.
That is what you get for letting a group of social science graduates lose on an engineering and physics problem .. it is a little more challenging than asking “would you like fries with that”.
“but we have no way of knowing what part of that was caused by the increase of atmospheric greenhouse gases due to humans” – here is a serious bid:
“Simulations including an increased solar activity over the last century give a CO2 initiated warming of 0.2 °C and a solar influence of 0.54 °C over this period, corresponding to a CO2 climate sensitivity of 0.6 °C (doubling of CO2) and a solar sensitivity of 0.5 °C (0.1 % increase of the solar constant)”
https://www.researchgate.net/publication/268981652_Advanced_Two-Layer_Climate_Model_for_the_Assessment_of_Global_Warming_by_CO2
What amazes me here is not Nick’s clear explanation of feedback in artificial (electronics) systems, but his apparent belief that nature never figured that out too.
We burn fatty hydrophobic long-chain fatty hydrocarbons (parafins) in our jets and trucks and act like we humans invented something amazing. Yet nature figured out how to store and and very carefully “burn” long chain hydrocarbons in beta oxidation reactions billions of years ago to fuel life.
Those greasy bug splatters smashed onto your windscreen is exactly that — greasy oil that the now dead insect was to use to fuel its flying around for days or weeks doing whatever it was going to do before it met your car’s windshield at highway speed. Fatty fuels = dense energy. The point here is, we humans pretend we invented something that nature figured out billions of years ago.
Earth’s climate system is clearly ruled by feedbacks. We didn’t invent that. It just happened.
A many on many setup. Positive and Negative feedbacks. On all time scales – from hours to millennia. Water of course, in its 3 phase changes is the biggest of these internal feedbacks. Sea ice modulation of high latitude heat venting from the oceans. Latent heat transport to the tropopause via bulk transport of convection. Evaporation increasing salinity and driving dense water sinking to push the ThermoHaline overturning Circulation to cool the tropics and warm the high latitudes. Feedbacks cooling and regulating the Earth’s climate heat energy budget by transporting energy along thousands of different paths and forms, which only a few of which models tackle.
And climate models, while decent on radiative energy transports, are hopeless to emulate most (if not all) of water phase changes on first principle. So the modellers fudge them. They fudge H2O physics to make it look like they are doing science. They call it parameterization. But it is feedbacks, feedbacks of which they are mostly guessing at the numbers. And educated guess is still just a guess. And the guessing allows them to make the models do what they want, like a Hollywood CGI animation scene.
Climatology has no hard quantitative clues on clouds adjusting albedo or limiting upwelling IR radiation as a fedback to an energy input… the modellers just fudge it.
Convection transport physics transporting heat above the effective radiation level… they just fudge it.
Precipitation as a phase change releasing heat and microphysics of water droplet formation… they fudge that too.
Then they call it all “science.” Hold big meetings. Publish lofty sounding papers. And push their fake science on an unwitting public.
They produce models with predictions of positive feedbacks of water vapor in the tropics with mid-troposphere hot spots to get 2X to 4X amplification by positive feedback … amplification never to be found in observational data. Yet they trundle onward, claiming it is “largely resolved.” Far from it. The only feedback response the modellers are hoping for with a “correctly tuned” output is the grant paycheck from the climate gravy train, like a trained seal getting its fish reward for a stupid trick.
Clearly, Earth’s climate is highly regulated with strong negative feedback from the immense oceans. Oceans of salt water. Convection physics processes that are substantial players along with radiative physics.
Mainstream climatology is just playing the Useful Idiot role for the Global Socialists and the Green Blob that wants our freedoms and our money, respectively.
You’ve provided a surefire setup for a new cottage industry in Florida; that being a bunch o’ YouTube preppers, rendering Love bug scrapings into tallow candles.
Waste not, want not. Or something.
100% Joel O’Bryan,
Very well stated .
The theory of CAGW relies on positive water vapour feed backs to multiply CO2s effect on temperature ,as the doubling of CO2 in the atmosphere can only raise the temperature of the planet by .6 degree Celsius.
Only by adding in positive feed backs and deducting negative feed backs can the planet warm more than .6 Celcius with a doubling of CO2.
The theory of CAGW depends on the tropical hot spot which has not been found .
IT is plain to see that the GCMs run far too hot and with the computing power that is thrown at them they should be accurate .
Therefore it is a reasonable conclusion to assume that the parameters that the climate models are based on are faulty .
The climate models have used the input of positive feed backs to push up temperature and are not entering correctly the negative feed back role which in the case of water vapour ( the main GHG ) works as both a negative and a positive feed back .
This deception is the what the whole Global warming scam is based on .
Nick, thanks for an interesting post.
The big feedbacks that I see in the climate system are temperature threshold based.
For example, take the late-morning typical development of the tropical cumulus field. Below a certain threshold temperature, there are no cumulus clouds at all. However, after the temperature passes a certain threshold, we very quickly see a fully-developed cumulus field covering the entire sky. And this, of course, cuts way back on the incoming solar energy.
The same thing is true of the next step in the tropical daily cycle. If the temperatures continue to rise after the establishment of the cumulus field, when it passes a second threshold we see cumulonimbus, the great thunderstorms that are so efficient ar removing energy from the surface.
These temperature threshold-based systems are quite similar to the way say house thermostat operating a furnace works. When you are above a certain temperature, the furnace is off. When the temperature goes below the set-point, the furnace kicks in.
Note that in none of these cases is the response linear …
Would you be willing to talk a bit about the mathematics of this type of setup?
Best regards,
w.
Thanks, Willis.
The first thing to say is that Soden and Held do have an important term for feedback from clouds. Quantification is with models, so probably doesn’t get as fine-grained as this. The modelling is based as far as possible on observation.
Another point is that the feedback here is on equilibrium global average temperature and averaged forcing. So what counts isn’t the non-linearity of the individual events, but whether statistically, after the climate has shifted, the overall flux when averaged responds linearly with the climate variables. If it were non-linear, what do you think it might look like? It could be, of course. But it’s hard to see why adding say 2° would depart radically from double the effect of adding 1°. If it did, it would be interesting to understand why. One of the factors favoring a smoothed average response is the geographic inhomogeneity. Even if there is something special happening when you go from 28°C to 29°, say, at any point of warming only a fraction of places are in that zone. And they pass through it.
That was actually the point about the transition from 1D models to GCM’s. 1D had the criticism that it was averaging a lot of things that were very non-linear if you drilled down far enough. In fact, just about everything in turbulent fluid flow, and the same is true in engineering CFD. But the GCM idea is that you can emulate the non-linear events (still only down to a rather coarse scale) and then add them all up to see what the average in space and time amounts to. And of course the average does behave a lot more smoothly, which means a linear approximation is much more reasonable.
I’ve been saying that you don’t have to know in detail how the operating point (reference etc) state works. It might include processes like you describe that are hard to quantify. But the perturbation analysis only needs to know that the state exists and is sustainable in the absence of forcing. It doesn’t need to know why. The problem would come if there are kinks in the response curve with change. But the kink won’t affect all regions at the same time.
Hi Nick,
actually enjoying the technical discussion and I appreciate the effort (and your response earlier). However, generalities about this and that are one thing (although I do like Willis’s input) but now you have made another statement that I can take out of context.
The statement “but its hard to see why adding say 2 degrees would depart radically from double the effect of adding 1 degree”. I almost had kittens when I read that.
In an alternate universe 2 degrees is the tipping point (re: thermal runaway) ergo if I have understood you correctly and nothing happens at 1 degree then mathematically twice as much will happen at 2 degrees (linearly speaking of course).
I do not understand why you spend so much time defending CAGW when, in this post, you have virtually explained why it shouldn’t be?
Cheers,
Andy
Andy,
“In an alternate universe 2 degrees is the tipping point”
Well, there are many possible universes. But in the scientific one 2 degrees isn’t a tipping point for thermal runaway. It’s a reasonable target, saying that we don’t have very good control of the process, and if we can’t agree to aim for that, the chances of getting control are bleak. I don’t think you’ll find scientists, or even IPCC etc, saying thermal runaway starts at +2C.
I was, though, talking about how a specific phenomenon (Willis’ thermostat) might respond.
Nick;
when does thermal runaway happen? you know as well as anyone here that the answer is never, stop playing and just say it.
Thanks, Nick. Let me see if I can explain my issue. This shows the correlation between absorbed energy at the surface and the surface temperature.
As you can see, not only is the correlation different, even the SIGN of the correlation is different. Note that on the land the correlation is almost always strongly positive, so that is what we assume the world to be like … but it ain’t, because over large areas of the ocean, the correlation is negative.
And that means that unless we are to believe that more energy cools things down, we have to assume that in those areas the incoming energy is NOT regulating the surface temperature, it’s the other way around—the surface temperature is regulating the incoming energy.
Nor is that a simple linear negative feedback, which could only reduce the amount but could not change the sign of the correlation.
Let me add a couple of graphs to further illustrate the temperature threshold-based nature of the game. First, here is cloud top height versus surface temperature:
Linear? Not even remotely. Here is the same thing, but for cloud area fraction vs SST:
Note the breaks at about 26°C in both of those. Finally, here is Pacific equatorial rainfall amount and SSTs from several sources:
Again, note the break at around 26°C.
I bring all of this up to show the threshold-based nature of the systems. For example, the cloud area decreases from an SST of zero up to about 26°C … and above that, it increases.
Now, you can average that all you want, but “linear”?
I don’t think so.
Your comments on this kind of threshold-based feedback greatly appreciated, thanks again for the post.
w.
Willis,
Thanks again
“the incoming energy is NOT regulating the surface temperature, it’s the other way around—the surface temperature is regulating the incoming energy”
One reason I recommend the linear equations formulation is that it doesn’t care about what caused what. It just says there is an association. And you can solve for that.
“because over large areas of the ocean, the correlation is negative”
The ECS issues concern a global average. That effect may be quite different for land and sea, but the amount of land and sea doesn’t change. There is no reason why the summed global response shouldn’t varying linearly with some forcing even if locally it is going different ways.
“Linear? Not even remotely.”
But again, we’re looking for a linear response of a global average to a global forcing. If this effect has a sharp cut-off at 26°C, that doesn’t negate a linear response globally. The area below 26°C would diminish smoothly with warming, and so the spatial integral of the cloud top effect would still vary linearly.
It’s the same with sea-ice albedo. There is a discontinuous ice front. But if the front recedes proportional to warming, then the averaged albedo diminishes smoothly.
Willis,
I have long been impressed by your insight. And I think you are on to something.
I agree with you that the earth’s temperature is stable at least partly because it includes a governor system.
By observation, the set point of the governor appears to be about 26 C. What could change the governor setting would be some change in the atmosphere such that there is a shift in the 26 C threshold. I’m guessing here, but would a change in atmosphere density do it? A shift in gas ratios? A shift in ionoshperic electrical potential? Change in cloud nucleation rate?…
-BillR
Mr. Stokes analysis has one over-simplification: it ignores the reference state. In the amplifier example, at zero input, the amplification stage would have zero output. In an audio amplifier, that would lead to noise when the amplifer is in “idle” or zero input. Consequently, audio amplifier circuits have a bias added to the design to prevent it from returning to zero output.
Mathematically, there are a few ways to address this need: one could add a base signal to the input such that it never returns to zero. One could also add something to the feedback transfer function Beta to prevent it from returning to the zero state. (Please don’t get hung-up on the signs of the math, one can move negatives around at whim minding positive vs. negative feedback.) A third choice would be to have the transfer equations additive (V1+V2) on which I’ll comment later (vida infra).
Thus, I would argue that Lord Monckton’s approach is the former approach and Mr. Stokes is the latter. From the point of view of the model, either can be made to work. In the case of thermal forcing feeback models, it must be able to predict the 1800’s temperatures at the base CO2 conditions. If one calibrates the model bias (reference condtion) from that point in time, then the model will predict changes from that reference condtion based on changes to input.
The rub arises in determine the thermal forcing transfer function. Lord Monckton is arguing that the forcing function calibration was performed incorrectly creating a reference point error. This might be true unless the bias signal to the reference state is buried in a feedback transfer fuction Beta such that the net transfer gain is additive to the reference condition (temperature in this case). Not having examined the models myself, I do not have an informed opinion.
Building on this ignorance futher, I would be very dubious of the model if that the forcing function calibration is used to calculate a temperature gain and then simplying adding that to the reference temperature. Such a construct is basically the V1+V2 approach and either calibration assumes a decoupling of the transfer functions such that the mechanisms responsible for reference condtion are unaffected by the additional heating/CO2. That error could be addressed by considering additional mechanisms to the incremental temperature feedback that are present in the reference temperature function. Mr. Eschenbach has been actively exploring such possibilities via water evaporation and cloud formation.
As the devil is in the details, this reader will await the constestants to clarify how they implement the reference condtion and account for all the mechanistic effects relative to that reference condition.
One of many flaws in the climate fundamental flaw is the assumption that W/m^2 of feedback are linear to temperature, when the only relation in all of physics demands that W/m^2 are proportional to T^4 and that feedback is linear to W/m^2 of emissions. The climate system assumption of approximate linearity is the problem since for feedback analysis to be relevant, the system must be linear across the entire range of forcing, which is from 0 W/m^2 at night to over 1000 W/m^2 at high noon at the equator. Approximately linear over a small range around the average just doesn’t cut it. Of course, another flaw is the implicit and infinite power supply powering the gain, which the climate system lacks.
It all boils down to the same old flaw of ignoring COE, which must be honored between the input and output (forcing and temperature), but is not. This is ignored because the simplifying assumption of an external power supply precludes the need to conserve energy between the input and output. This is also why runaway seems plausible, when it’s absolutely impossible without the implicit power supply. Venus is not runaway GHG, but runaway clouds where the ‘surface’ in direct equilibrium with the Sun has become the cloud tops and the temperature of the solid surface below is dictated by the PVT profile of its atmosphere.
Without ignoring COE, there’s no way that the next W/m^2 can be differentiated from the average W/m^2 so that it can increase surface emissions by 4.4 W/m^2 (a temperature increase of 0.8C) while the average W/m^2 only contributes 1.62 W/m^2 to the surface emissions. There’s no way that feedback can apply only to the last W/m^2 when it must apply to all W/m^2 equally, which based on the claimed amount of feedback would result in a surface temperature close to the boiling point of water. The bottom line is that there’s nothing to demystify since the climate feedback model has absolutely no correspondence to either the laws of physics or the ground truth.
BTW, the analytical error in Schlesinger’s paper and Roe’s rehash of Schlesinger’s work is assuming that the feedback factor and the feedback fraction are the same thing, but since the feedback factor is an archaic attribute calculated as the feedback fraction times the open loop gain, the two are the same only when the open loop gain is unity. Meanwhile, both Schlesinger and Roe assume a non unit open loop gain that ‘amplifies’ W/m^2 of forcing into a temperature.
“One of many flaws in the climate fundamental flaw is the assumption that W/m^2 of feedback are linear to temperature”
Nothing special about feedback; as shown, it’s just a linear relation between flux and temperature. It isn’t a clisci invention – one version is called Fourier’s Law. More generally it is widespread in engineering as the heat transfer coefficient.
” to be relevant, the system must be linear across the entire range of forcing which is from 0 W/m^2 at night to over 1000 W/m^2 at high noon at the equator”
No, the relations are between global averages of equilibrium temperature. They vary within a narrow range.
“It all boils down to the same old flaw of ignoring COE”
No, as I showed with S&H, their expression is flux balance, which is COE.
And as I said, the linearity required is not being honored by the climate model. You agree that it’s a linear model, but stubbornly refuse to acknowledge that T and W/m^2 are not linearly related.
You can’t just declare that linearity over a small range is all that’s required when the model requires otherwise, moreover; the equilibrium temperature varies over a whole range across the planet. The actual average temperature only represents the average W/m^2 of emission, the system must operate over a wide range of emissions (and forcing), not just one value.
Heat transfer has nothing to do with the sensitivity and only affects the redistribution of existing energy. Relative to Fourrier’s Law, dQ/dt has the units of Watts, not W/m^2. One is a flux and the other is a flux density. You need to understand the difference between these two.
You still haven’t explained how the climate can tell the difference of the next W/m^2 from all the others so that it can be amplified by so much more. Unless you can explain this, nothing else you say will matter.
Once again you demonstrate an ability to pierce through to the heart of the issue. My understanding of Nick’s argument also leads me to your conclusion. I would note also, the fact that one can construct a tidy mathematical argument does not indicate actual relevance to the physical reality one is attempting to describe.
rip
co2isnotevil
Yes, Stokes is claiming that linear approximations are adequate, but I’m sure that there is a restricted range for that to be approximately true. Nowhere does he state over what range the linear assumption is valid.
Yes, that restricted range is the entire range of forcing, which for Earth is from 0 W/m^2 at night to more than 1 kw per m^2 at noon on the equator. This entire range of forcing defines the ‘small signal’ and the requirement is for linearity spanning the operating range which must span the dynamic range of the small signal inputs and outputs. If the behavior is non linear outside of the operating range, which is always the case for real amplifiers when they start to distort and can no longer be quantified using linear feedback analysis, approximate linearity is OK as long as linearity is strictly maintained for all possible inputs and outputs both as averages across time and as instantaneous functions of time.
George,
“refuse to acknowledge that T and W/m^2 are not linearly related”
Makes no sense
“Relative to Fourrier’s Law, dQ/dt has the units of Watts, not W/m^2.”
No, it isn’t. Here’s Wiki
q = -k∇T
where (including the SI units)
q is the local heat flux density, W·m−2
k is the material’s conductivity, W·m−1·K−1,
∇T is the temperature gradient, K·m−1.
Nick,
Thermal conduction has to do with the heat flow through matter and is relating a delta T to absolute W/m^2 and not a delta T to a delta W/m^2 or T to W/m^2 and has nothing to do with feedback or the climate sensitivity. The point you’re missing is that W/m^2 of solar forcing are linear to W/m^2 of surface emissions and W/m^2 of emissions are proportional to T^4. W/m^2 of forcing are not linear to temperature as is being assumed, not even incrementally.
The only feedback model that makes sense is to have all W/m^2 of solar input as the forcing input and W/m^2 of emissions equivalent to a temperature as the output, where the gain is 1.62, where each W/m^2 of forcing results 1.62 W/m^2 of surface emissions which is 620 mw per m^2 more than an ideal BB which emits 1 W/m^2 per W/m^2 of forcing.
You still haven’t answered the question about how can the climate system tell the difference between the next W/m^2 and the W/m^2 of solar power, so that the next W/m^2 of forcing can increase surface emissions by 4.4 W/m^2 (0.8C) while 1 W/m^2 more solar forcing will only increase surface emissions by 1.62 W/m^2.
Another serious flaw is considering CO2 to be a forcing influence. The only actual forcing is from the Sun and changes to the system, for example CO2 concentrations, are more properly considered as equivalent to W/m^2 of solar forcing, keeping the system, i.e. CO2 concentrations, constant.
Nick,
BTW, there is one place where heat transfer matters, but again, it has nothing to do with the radiant balance. This establishes the thickness of the thermocline as it acts to insulate deep cold waters from warm surface waters.
The only linear relationship related to energy and temperature is that T is linearly proportional to stored energy (i.e. 1 calorie, 1 gram of water, 1C). However; energy is measured in Joules while Watts are a rate of Joules. A higher heat capacity just means that equilibrium is approached slower, but has no effect on what that equilibrium will be. The same is true with conductivity, which also affects the rate of heating or cooling, but not what the equilibrium temperature will be.
The ONLY thing that effects the equilibrium temperature is the availability of W/m^2 to offset the emissions consequential to that temperature and the relationship between W/m^2 and the equilibrium T is the SB Law dictating the T^4 dependence of W/m^2, thus the sensitivity has an unavoidable 1/T^3 dependence that can not be ‘linearized’.
To be absolutely clear, the Earth is not an ideal BB, but is a non ideal radiating body whose macroscopic behavior can be fully characterized by the SB Law with a non unit emissivity. Try again if you think that there’s another laws of physics that can quantify the macroscopic behavior of the planet relative to incremental forcing, but it’s not Fourriers Law whose only possible effect would be on the time constants which have nothing to do with what the equilibrium state will be.
The data confirming what I’m saying is unambiguous and the analysis is readily repeatable. If you don’t believe me, do the analysis yourself. Here’s a scatter plot of 3 decades of monthly averages of the surface temperature vs. the emissions of the planet for each 2.5 degree slice of latitude from pole to pole.
http://www.palisad.com/co2/tp/fig1.png
The green line is the prediction of a gray body whose emissivity is 1/1.62 (0.62) and conformance to the T^4 dependence is unambiguous. The blue line represents the IPCC nominal sensitivity drawn to the same scale as the data. Notice how when plotted to intersect with the current surface state, this passes through zero, rather than being tangent to the actual response? This is a direct result of the inappropriate assumption of approximate linearity. In other words, the 1/T^3 dependence of the derivative of the planets response to solar energy (the sensitivity) is ignored.
Even more interesting is that the magenta line represents 1 W/m^2 of surface emissions per W/m^2 of forcing at the current surface temperature and that when you plot the average solar power vs. the surface temperature for the same slices of latitude, the slope of this is also 1 W/m^2 of emissions per W/m^2 of incremental forcing.
http://www.palisad.com/co2/tp/fig2.png
In this plot. the yellow dots represent the relationship between the surface temperature and planet emissions while the red dots show the relationship between average solar input and the surface temperature, where the magenta line is what my analysis predicts. Where these two curves intersect defines the steady state average response. Any model of the climate system must be able to reproduce this measured response.
Feedback loops in electrical/electronics systems, which are very well understood and with my electronics/electrical background, I have never understood why these are used in relation to the climate system. To me, its an excuse to justify the BS (The Bad Science of climate science).
Complex systems are by definition not linear. They can be described by linear equations over a short range of observable inputs, but so can ANY non-linear plotting of values.
We can observe a population of coyotes and rabbits and see that an increase in rabbits results in an increase in coyotes. We could even describe that trend linearly. However, once you reach a certain population of rabbits (e.g. the point where there is not enough grass to support the rabbits) the curve changes rapidly and a linear equation quickly loses predictive accuracy.
Trying to analogize a complex system such as the earth’s climate to a non-complex system such as an amplifier is not appropriate. Amplifiers are closed systems specifically constructed (through insulators and conductors) so that electromagnetic forces are consistently dominant through the expected operating range.[1] Complex systems have far more variants at play, and they are notable precisely because those inputs are dominated by other inputs until they reach a leverage point, when they suddenly become dominant.
[1] One of the reasons people often analogize complex systems to more static systems is that there is an element of complexity inherent in any material science. It all comes down to the range of inputs you wish to define. Define inputs for an amplifier or rocket engine narrowly, and you do not have to deal with complexity. But increase energy input past the point where materials can handle entropy and suddenly you have a VERY complex system where it is almost impossible to predict outputs. (c.f flight profile of a rocket where output energy exceeds the material strength of the engine)
I don’t see how your comparison works, too many variables. The thread topic is very specific with clearly known variables. In a natural environment, with unknown variables, where does the extra energy come from to “amplify” the, “feedback”, effect?
Simple and obvious answer is there is none. If CO2 was the “driver” of that amplification and feedback, Venus would have a run-away warming effect if we believe the theory. Simple observation, since the 50’s, it simply isn’t the case. CAGW via emissions of CO2 from human activities causing a “run-away” warming effect which then leads to catastrophic weather events is completely bogus. Only people on that funding gravy train “believe” that.
“Complex systems are by definition not linear.”
Then the climate system is not a complex system since W/m^2 of solar energy are quite linear to W/m^2 of surface emissions corresponding to its temperature. The constant ratio of about 1.62 W/m^2 of surface emissions per W/m^2 of forcing is independent of the temperature or total fluxes. This constant ratio is the reciprocal of the equivalent emissivity of a gray body model of the Earth’s emissions relative to the surface temperature and connects the dots between the behavior of an ideal BB and the Earth, which is not an ideal BB. None the less, non ideal BB’s can be accurately modeled with a non unit emissivity and there’s no other law of physics that can quantify the emissions of matter consequential to its temperature.
The climate system is only made to look more complex than it is by ‘linearizing’ the non linear relationship between emissions and temperature in order to provide the wiggle room to fudge support for what the physics can not.
Why? Because that’s all they can come up with.
Op amp inverters do sums nicely, but when faced with lag times, it’s best to go digital. By the time the system approaches a new equilibrium, the inputs have changed.
Same applies to digital! If you are modeling a system digitally and time is involved, then when you apply the inputs to each part of your model and calculate the outputs, you then have to reapply the outputs to any changed inputs until all change has settled. That is the first step of your simulation.
This is digital simulation 101.
Yes, there’s a better solution in the Z domain considering that the 620 mw per W/m^2 of feedback power returned to the surface from the atmosphere is energy emitted by the surface in the past, temporarily stored in the atmosphere which delays it before being returned to the surface.
BTW, the IPCC incorrectly considers the 1.62 W/m^2 of surface emissions per W/m^2 of forcing as the before feedback sensitivity. The only valid pre feedback emissions sensitivity is 1 W/m^2 of surface emissions per W/m^2 of forcing which corresponds to about 0.2C per W/m^2. Not only is the climate feedback model incompatible with Bode’s linear feedback amplifier analysis, feedback is effectively applied twice. Once to multiply 1 W/m^2 of emissions per W/m^2 of forcing up to 1.62 W/m^2 (about 0.3C) and then once more to arrive at 4.4 W/m^2 (about 0.8C).
So the whole feedback effect is wholly dependent on input temperature change and this temperature change can be the result of many factors. So how do you determine what the factors are and their magnitudes?
The article I cited by Soden and Held is the most frequently cited source for that.
Please see my comment here concerning what the 2006 Soden and Held paper uses as its primary source of observational data supporting their postulated water vapor feedback mechanism:
https://wattsupwiththat.com/2019/06/06/demystifying-feedback/#comment-2718240
As I read their 2006 paper, Soden and Held’s primary source of ‘observational data’ comes from the climate models, not directly from the water vapor feedback mechanism itself as it theoretically operates within the earth’s climate system as a whole.
If this is indeed where most of the observational evidence comes from, the obvious question arises as to the validity of that ‘observational evidence’ and its applicability to verifying the actual presence of the water vapor feedback mechanism in nature.
Nick, very many thanks for this.
And many thanks too to Anthony. Its the acceptance of posts from people who take different views which marks this site as being a worthwhile read.
Keep it up. There are some of your readers who’ll detest it. But there are many more who will appreciate it enormously. It makes WUWT significantly different from Ars, Real Climate etc, where the entire aim is to should down dissent and never allow an opposing point of view to be heard.
As JS Mill remarked, the quickest way to refute a fallacy is to allow it to be published and exposed to argument. Free debate, not censorship and abuse, are the answer. Thank you for realizing this and for implementing it in practice.
Stokes should post more on how to make the complex become simple, and then consequentially transform the simple into the impossible.
all to prove the point that Stoke’s own original version of impossible was a much superior product because it is based on the consensus of what is apparently … much more simpler?
I don’t think that you even tried to explain anything and tried to hide it behind condescending claptrap.
All you did was say that there are many feedbacks and they negated a stronger sensitivity to CO2 in 1850 but not now or in the future. It might be simple high school algebra but many assertions written as if it were like 1+1 = 2, even though stretching plausibility a bit. I’ll give you that Monckton doesn’t destroy the argument but he does highlight that a far from likely scenario is needed for high sensitivities to be considered robust calculations.
To me Earth’s climate resembles a Schmitt trigger more than a system with linear feedback. The system has switched between glaciation and interglacial periods for quite a while now. As it’s a natural system each steady state has quite a bit of noise. Looking at the noise only is interesting but basically a waste of time and money looking for the next switch of state would make more sense
Great comment Ben. The two steady states are very interesting – each some sort of equilibrium that keeps repeating at generally the same point over time.
In the glacial steady state, global sea levels are approx 100m lower, global temperatures are about 10degC lower, global ice cover is about 5 x current, and global atmospheric water content (=cloud cover) is not well known.
But it seems reasonably stable for long periods of time – before it switches back.
Firstly, thanks to Nick Stokes for a very clear and concise explanation. ( In stark contrast to Monckton’s mumbo jumbo )
The non-linearity is already there: the Planck (negative) feedback is T^4. Now if anyone wants to “linearise” that for small perturbations and then ‘forget’ they did that to pretend that the climate could reach a tipping point dominated by the small positive feedbacks is either does not understand feedbacks or is misleading you.
The climate has not reached a ‘tipping point’ and turned us into Venus in the last 3.5 billions years and has gone through much larger changes in “forcing” than our pathetic reintegration of 80ppmv of natural CO2 that was sequestered in the ground. It is alarmist political BS so suggest otherwise.
Thanks again to Nick for laying this out so clearly. It is quite possible Monckton is trying blind everyone with science in his cryptic arcane presentation, expecting everyone to say: wow, I can’t follow that but he sure seems to know what he’s talking about. That would be typical of his character. He is cynical and manipulative.
Maybe opposition to CAGW needs some “cynical and manipulative” players . It has been noted before that arguing facts and science in the climate debate is like bringing a knife to a gun fight.
Thanks, Greg
For tipping points, I don’t think T^4 would be the saviour, but I agree with Ben Vorlich above that we have in the past seen an apparent alternation between two quasi-stable states (my thought was an unsymmetric multivibrator). I think a tipping point would take us to a warmer one stabilised by some other nonlinearity. Still, it might turn out too warm for comfort.
Greg,
Using a linear approximation of S-B introduces negligible error in flux calculation for small perturbations around a given (brightness) temperature, provided of course that the gradient at that brightness temperature is used for the approximation. You can easily test this for yourself. The same is not true of using a secant gradient drawn from an origin at absolute zero to the S-B emission evaluated at 255K, say. The local gradient is exactly 4 times this secant gradient – a relationship which is always true for whatever brightness temperature you wish to start at. Using this secant gradient for extrapolation yields massive error in estimation of projected DeltaT. Nor is it appropriate to apply the linearised form to some temperature when the gradient has been calculated from a very different temperature. Lord Monckton actually uses a mix of non-linear form and linearised form in his calculations unless he has changed them since the last time I looked at his basis. The oft-quoted Planck response of 3.3 W/m2/K yielding 1.1deg K per doubling of CO2 under the assumption of no other feedbacks is already based on the linearised form for perturbations around a brightness temperature of ca 255K (corresponding to a surface temperature of ca 288K).
“It is quite possible Monckton is trying blind everyone with science in his cryptic arcane presentation … He is cynical and manipulative.”
Gee, that’s quite an “ad hom” sounding comment against Christopher M., especially coming from someone who seems to be presenting himself as a climate skeptic? If I didn’t know any better, I’d almost guess that the writer has had his toes stepped on by ‘M.’ somewhere before! Note that I’m not trying to cast any sort of aspersion onto Christopher M. here myself .. I just know that he has been a more or less outspoken right winger at times, and maybe this is really the source of the ‘ad hom’ I quoted above?
As far as the basic problem with Nick Stokes version of how control theory might work for these purposes, I think Stokes himself pretty much nailed it (in the negative sense of *defeating his own idea*), when he said;
“So 1850 is representative of a state when forcing from GHG was stable.”
(this was in response to Tom Halla’s questions).
So, it would appear that Moncton’s approach is at least more consistent in an ideal sense, as compared to magical thinking about a special “pre-industrial” age! That would be that special time in history, 1850, when all forcings were stable and there was no pressure toward climate change at all?
To put this a different way, if you don’t want to concede that traditional climate theorists have “made a mistake” on feedback, that’s more or less defensible, I guess, despite Moncton’s tendency to put it that way. Surely by now though, the Stokes’s of the world should at least be willing to concede that Lord M.’s model is a *possibility*, i.e., it *might* be better, as an ideal model, than a lot of what’s come before, better than what you might call the “conventional” idealized theories?
Hey Nick,
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.
Nice to hear that! But what is actually a main message of your text? I thought that previously you were saying that Lord Monckton’ objections are wrong because feedback responds to perturbations only, not on a whole reference signal. Now looks like you’re happily saying: ‘of course feedback acts on the entire reference signal! Climate science knows that and that always was the case!’. Well, to me looks like you happily aligned your position with His Lordness. There still may be discussion around exact numbers but at least conceptually we’re all in the same boat.
Paramenter,
“Now looks like you’re happily saying…”
No, I’m certainly not saying that. The main message is that the language of feedback is just a way of talking about linear relations, and if you get tangled, go back to those relations. The relations give you n equations in n+1 unknowns, which you can reduce to a convenient proportionality. That describes the system. You need one more variable to define your instance. The gain formulation makes this easy. You provide the input; they system says, multiply by gain to get the output. But if you do provide that information, you could just as well have got the answer from the original equations.
What Lord M has wrong comes from the original equations. They follow from linearising. You have a set of equations which may be nonlinear, and which describe a reference state, which is sustainable without signal. The perturbation equations describe what happens if some forcing is applied. Some variables change in a way proportional to the forcing. So you can work out a set of coefficients that are true for any perturbation. The reduced form after algebra has just one coefficient, the gain.
You can’t put a state variable like reference temperature into this first order system, for two reasons:
1. It was part of the reference system, which was in balance. You don’t need to change it, and it would disturb that balance to do so.
2. It isn’t proportional to the perturbation, so would completely mess up the first order system. If the equations worked for one level of perturbation (or signal), then with constant coefficients, they would fail for any other.
I have little patience with Lord Monckton’s obfuscations, but Mr. Stokes has contributed by persisting in what is a mere semantic disagreement about how to describe a system in which a stimulus causes a response. There’s nothing wrong with saying as Lord Monckton does that feedback acts throughout the stimulus domain, although he’s obviously wrong in thereby implying near linearity.
Let’s call the stimulus R analogously to Lord-Monckton’s before-feedback equilibrium temperature, with the response E analogous to his after-feedback equilibrium temperature. We’ll avert our eyes from the fact that by making both variables temperatures he is finessing forcings problematically away.
In physical systems it is often instructive to describe the relationship implicitly: the dependent variable depends on, among other things, itself:
When it does there’s no reason not to call that a feedback system and say, as Lord does, that feedback applies to the whole stimulus.
This can be expressed more restrictively in the case of feedback amplifiers, which are so designed that feedback is additive:
And, despite what a lot of engineers have been saying, we see by inspection that feedback may in fact operate throughout the domain.
But in climate the feedback may not be inherently additive. So the additive relationship not appear until the equation is differentiated:
where the derivatives are evaluated at some reference state
Isolating yields:
In the with-/without-feedback relationship,
and 
, so we get Lord Monckton’s relationship
So the perturbation relationship on which Mr. Stokes insists is entirely consistent with what Lord Monckton calls feedback over the whole domain. It’s just that Lord Monckton argues as though
nearly uniformly equals 
, which, of course, he hasn’t proved.
There’s plenty to argue about in Lord Monckton’s theory without getting bogged down in semantics.
And even if there wasn’t you would still argue because of your personal feelings, Joe please just let it go, you are better than this.
When it does there’s no reason not to call that a feedback system and say, as Lord does, that feedback applies to the whole stimulus.
Mr Stokes explicitly says otherwise.
Well, that’s just an error on his part.
Seriously, it doesn’t matter whether he’s right or not about that nomenclature. Imagine that at some point in the past there were no greenhouse gases and the sun was dimmer than now so that the earth’s surface temperature was lower than its current emission temperature. A brightening of the sun would add forcing and increase temperature, which in turn might decrease albedo and therefore cause additional forcing and a further temperature increase: the temperature increase would be reinforced by what I’d call temperature feedback, in the form of albedo-reduction-caused forcing increase.
Lord Monckton also characterizes reinforcement like that as feedback: feedback “to the emission temperature” since it’s part of what got the earth’s surface to the current emission temperature and beyond. He argues that the reason for the IPCC’s high ECS estimates is that “climatology” made the “grave error” of failing to take such below-emission-temperature reinforcement into account.
The issue is whether it did fail to—or whether that even matters to “climatology’s” ECS estimate. In the head post Mr. Stokes properly addresses this issue’s substance by explaining why indeed it does not matter. And that’s good.
But over the years Mr. Stokes and others have muddied the waters by arguing about whether mechanisms such as that reinforcement are properly called feedback. And scores of readers consequently seem to think it matters.
It doesn’t.
“Mr. Stokes has contributed by persisting in what is a mere semantic disagreement “
It’s not semantic. It’s a matter of what you put into the equation. Change that, and you get a different answer. In Lord M’s case, a very wrong one.
Here is a homespun example. You have a tyre at 26psi. That is the reference state. It will stay there unless you do something. You don’t know much else about it; could even be full of CO2. But it works. You have a hand pump and want to get it to 28 psi. How hard will that be?
So you send a signal – one pump-load. The accurate gauge says it’s now 26.1 psi. So, you imagine, that is the response. Gain is .1 psi/pumping, and 20 pushes in total should suffice.
But no, they say, you haven’t taken into account the whole signal. What about the original volume of gas? What about the tyre thickness? Surely you have to add those in.
Fortunately, you’re a climate scientist, and don’t listen. It takes 20 pumps.
A closed non chaotic system, meaniless
An excellent and irrefutable example of the error in Lord Monckton’s analysis … thanks.
w.
OMG, you guys can’t be serious! A homespun analogy, I wonder how good those are usually? The pressure in the tire being a static condition to start with, nothing like the presumed steady state flow situation you were talking about as applying in year 1850. Maybe a better analogy would be flipping a running garden hose into a flowing river, or something?
Anyway, if you really wanted the ‘tire’ analogy to apply to the atmosphere, first you would have to put a roof on the atmosphere, then you would have to pump some air into it. Didn’t I see something like that on the movie ‘Spaceballs’?
Good analogy for how Lord Monckton goes wrong. For the extrapolation coefficient he doesn’t use local slope (your .1 psi/pumping) of response as a function of stimulus. His error is to use average slope (in your example current pressure ÷ number of pump strokes to achieve current pressure) instead.
That he does so can clearly be seen in his “end of the global warming scam in a single slide” at https://wattsupwiththat.com/2018/08/15/climatologys-startling-error-of-physics-answers-to-comments/, where he uses average slope
rather than local slope 
as the extrapolation coefficient 
, i.e., as what 
is multiplied by to calculate the ECS value 
.
But which coefficient he uses has nothing to do with whether he does or does not employ the term feedback or something else to describe the mechanism by which the current pressure was achieved. So whether that nomenclature is correct or not is a red herring; it’s just semantics and an unnecessary distraction.
But where is the feedback in your example? With feedback in addition to the perturbation the one pump would give you some pressure more than 26.1 psi.. So, when you figure the gain from the feedback you have to consider that the feedback component represents a response to the original signal as well as to the perturbation because, as you have acknowledged in your previous comments, the feedback can’t distinguish between the original signal and the perturbation. It appears to me you comments support Lord Monckton’s argument. Maybe you could propose a more complete analogy, i.e. one that involves a feedback?
“But where is the feedback in your example? “
Lord M’s main error is in the partition between state variables and perturbation. With the tyre the states are easy to visualise – tyre at 26psi, and tyre at 28psi. The first is reference, and the one used for reasoning is the perturbation – how much response per pumping. It is the linearised version of the difference between the states. The same partitioning applies to feedback, since this is in fact just a way of describing terms in the linear equation for perturbations.
Hey Nick,
So you send a signal – one pump-load. The accurate gauge says it’s now 26.1 psi. So, you imagine, that is the response. Gain is .1 psi/pumping, and 20 pushes in total should suffice.
But no, they say, you haven’t taken into account the whole signal.
And, I reckon, they’re right. What pressure our hand pump has to apply during pump-load to overcome the existing tyre pressure and top-up the tyre pressure from 26 to 26.1 psi? 0.1 psi or more than 26 psi? Methinks latter is true. This is hardly a feedback system but, if anything, suggest our Lord is right: each iteration of pump-load has to include existing in the tyre pressure plus additional value.
Fortunately, you’re a climate scientist, and don’t listen. It takes 20 pumps.
Accordingly, climate science builds a hand pump with the output pressure 0.1 psi and successfully inflates the tyre with the initial pressure 26 psi. Feedback mechanism is clever enough to figure out that we want only difference and takes care about the rest. Easy life, except that does not work like that.
That is precisely the reason I said earlier we need something more than such ‘thought experiments’. Our Lord and his co-authors build test rigs to prove their point, what is a good start. When their article is published it should contain design and all details so the process can be replicated and validated.
Paramenter:
Actually, it’s only according to Lord Monckton that their “test rig” proves their point; we haven’t seen that test rig. Just as we haven’t seen his “eminent” co-authors entering into the rough and tumble of defending what Lord Monckton says is their belief.
And I’m pretty sure the “test rig” merely proves that using average rather than local slope works if the system is linear—but also that local slope, whose use Lord Monckton tells us is the “grave error” that “climatology” makes, works, too. Moreover, it’s straightforward to design a feedback circuit that shows local slope to be superior to average slope if the system is nonlinear.
Unfortunately, Mr. Watts stopped running my posts when I exhibited insufficient deference to Lord Monckton’s (exceedingly questionable) expertise, so you won’t see my test-circuit design.
Hey Nick,
No, I’m certainly not saying that.
It sound like. Look at that:
In the limit of small perturbation, you still have a big reference temperature term that won’t go away. No balance could be achieved.
For me you’re referring here that reference input is still here, as it should be – exactly what Lord Monckton is saying.
You can’t put a state variable like reference temperature into this first order system, for two reasons:
1. It was part of the reference system, which was in balance. You don’t need to change it, and it would disturb that balance to do so.
I cannot see that in the justification you have provided. In Wiki formulas input always contains output which in turn contains input plus deltas. Under the previous post I’ve linked this textbook diagram, bit expanded compared to Wiki. Full output of the iteration (original input plus disturbances) comes back as new input – here denoted as Ym: measured value of the output (Y). That makes sense to me. Lord Monckton and his co-authors built a test rig to prove this behaviour. Methinks that’s the way forward. I’ve suggested alternative and cheaper approach: build a virtual feedback control loop using decent quality simulation control software as MATLAB Control System Toolbox or Python Control Systems Toolbox. Otherwise we’re risking running only gedankenexperiments and everyone will simply imagine different outcomes. My imagination vs yours!
2. It isn’t proportional to the perturbation, so would completely mess up the first order system.
That’s unclear for me. Of course reference temperature is not proportional to perturbations and why it should be? Still it is included in the output and henceforth in the input for next iteration of the feedback loop.
“For me you’re referring here that reference input is still here”
No, I’m saying that if you wrongly put the zero order term among the first order terms, it won’t go to zero as they do, and you can’t get a solution which acts as a proportional perturbation.
You should keep the term with the other zero order terms, which were in balance before perturbation.
BTW, no-one seems to have asked, why pick out just this one “emission temperature” component of the reference state? Why not put them all in? Which would actually work, because they would cancel. But why do it?
“1. It was part of the reference system, which was in balance.”
But it wasn’t and never is. It’s perpetually unbalanced, i.e. perpetually dynamically oscillating around an approximate average.
Stokes,
You said, “You have a set of equations which may be nonlinear, and which describe a reference state, which is sustainable without signal.” Well now, if the forcing were to decrease, then I would expect the temperature to drop, demonstrating that the “reference state” is being maintained by the sum of an even earlier temperature and the temperature increase caused by an increase in the forcing. That is, one has to take into consideration the total signal and not just a delta, particularly if the response is highly-nonlinear over the total possible domain.
“Well now, if the forcing were to decrease, then I would expect the temperature to drop”
Yes. That is just the Planck feedback term in operation. It doesn’t say anything about accumulated history.
If you have a heater in a room maintaining a steady temperature, then you turn down the current, then the room will cool. This isn’t a result of any “total signal”. It just reflects that fact that the temperature difference from ambient was being maintained by an outgoing flux (Fourier’s law, maybe with an overlay of S-B). Lower the flux and the temperature difference drops.
“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.”
Something just does not pass the smell test.
https://wattsupwiththat.com/2018/08/15/climatologys-startling-error-of-physics-answers-to-comments/
IPCC (2013) mentions feedback more than 1000 times.
…
Will feedback now be erased from the IPCC reports? Easy after erasing previous warm spells, I guess.
Let’s see –
The Hole in the Ozone Scare,
Acid Rain Forests,
Global Cooling,
Blowball Warming,
and finally Climate Change.
But oops – feedback must go.
How about Climate Linearity As A Goal by 2025!
$Trillions for Linearity!
Save the Algebra!
Fridays for Algebra!
Green New Algebra Curriculum!
Sounds more sciency than just good ol’ Climate Chaos.
Just sayin’.