Guest Post by Willis Eschenbach
[UPDATE TWO: Rather than trying to cooper up the errors, I have simply removed the incorrect sections and left the calculation of the Planck feedback intact. I think that it is right … however, as events remind me too frequently … I could be wrong … ]
[UPDATE: As Jan Kjetil Andersen has pointed out below, my assumptions about results shown in Figures 3 and 4 are incorrect (although my analysis of Figure 2 may still be correct). SO … I’ll have to put at least the latter part of this post on hold until I think about it some more. To me, this is the beauty of the web, I get to correct my misconceptions immediately rather than following a wrong path for months. I will return to this topic after more thought. At present, in the immortal words of Richard Nixon, my previous statements based on Figs. 3 & 4 are inoperative … it’s a work in progress, I’ll report back.]
I must thank my friend, the irrepressible, irascible, highly improbable, sometimes infuriating but always fascinating Lord Christopher Monckton, for his essay yclept “IPCC has at least doubled true climate sensitivity: a demonstration“. His claims and musings, while not always correct, are invariably interesting and bring up lots of relevant questions and mathematical conundra. They generally make me say either “good, Lord” or “good Lord!”, and they often lead me to interesting research. Here’s what I found out this time.
Lord Monckton says that the IPCC has overestimated climate sensitivity. The crux of his argument revolves around the “Planck feedback” parameter. The Planck feedback is how much the outgoing longwave radiation of the globe increases per degree of increased temperature. It is an important number because the Planck feedback is the negative reciprocal of the pre-feedback climate sensitivity, which Lord Monckton calls lambda_0 (λ0) in Figure 1.
ORIGINAL CAPTION IN LORD MONCKTON’S POST: Fig. 1 The official climate-sensitivity equation. Equilibrium or post-feedback sensitivity ΔTeq is the product of pre-feedback sensitivity ΔT0 and the post-feedback gain factor G.
The pre-feedback sensitivity λ0 is given in Fig. 1 as 0.312 degrees C (or K) per watt per metre squared (W/m2). This is the same as saying that the Planck feedback is -3.2 W/m2 per degree C. In other words, the Planck feedback says that when the globe warms by 1°C, it radiates (and thus cools) by an additional 3.2 W/m2. This is a negative feedback, as indicated by the minus sign.
I was able to verify Christopher’s claim that 0.31°C per W/m2 is indeed the value used by the IPCC by looking at Table 9.5 in the IPCC AR5 WGI Chapter 9 (p. 818, also in spreadsheet form below). This gives the Planck feedback for ten different models, with a mean value of -3.21 ± 0.03 W/m2 (95%CI) per °C. And this is the same as a pre-feedback sensitivity of one over that, or 0.31 W/m2.
Doing some research found lots of back-and-forth about the proper value for the Planck feedback, based on a host of theoretical claims. So rather than entering into those theoretical disputations, “whose thoughts are full of indices and surds” as the poet has it, I figured I would look at the actual data. A radical thought, I know, but I’m that kind of guy. The Planck feedback is the negative of the change in outgoing radiation (∆W) per one degree change in surface temperature ((∆T). The CERES satellite data has that information. I have shown the results for ice-free ocean, for three reasons. The first is that the ocean data is more internally consistent than the land because it is free of obstructions and it all has the same elevation and surface characteristics. The second is that in this particular case, land observations are basically of the same form as the ocean observations but with greater scatter, which obscures underlying patterns. The third is that most of the world is made up of ice-free ocean … in any case, here are those results.
Figure 2. Scatterplot, fifteen-year averages of outgoing top-of-atmosphere longwave versus sea surface temperature. The Planck feedback is the negative of the slope, meaning that on average the Planck feedback is ~ -2.0 W/m2 per °C. All slopes are calculated using area-weighed values.
Dang … can you say “non-linear”? More like “falling off a cliff” … in any case, I’d say that this is a marvelous example of the difficulty with IPCC-style linear mathematical derivations of various values—they often run aground on a reef of non-linear reality. Not only is the reality wildly non-linear, but the average value for the Planck feedback (-2.0 W/m2 per °C) is only about two-thirds that suggested by the models (-3.2 W/m2 per °C). Not sure what I can say about that …
Let me recap the bidding here. I’ve calculated the Planck feedback from observational data as being on the order of 2 W/m2 per degree C of surface warming. This number is about the same whether it is calculated from land or ocean temperatures. This implies a pre-feedback sensitivity of about 0.5°C per W/m2, or about 1.7°C for a doubling of CO2. I note that this observationally based calculation of the Planck feedback is smaller than the IPCC model-determined value of 3.2 W/m2 per degree C.
In turn, this implies a larger pre-feedback sensitivity. As Christopher Monckton pointed out, the IPCC value for the pre-feedback sensitivity is 0.31 °C per W/m2 … however, the observations give a value of 0.50 °C per W/m2.
Hmmm …
Late afternoon here. It was warm earlier, but now the fog is working its way inshore. It hasn’t arrived yet, but what I call the “fog wind” has started blowing. What happens is that the fog is low-lying, in what is called the “marine layer”. As the marine layer works its way inland from the ocean in the afternoon, there’s often a wind blowing over the top of the fog. It outpaces the fog, and up here about six miles (10 km) inland and at 700′ (210 metres) elevation, the fog wind is often the first signal of the approach of the marine layer. The fog wind is easily distinguished in two ways. The first is that despite the day being warm and sunny with clear skies, the fog wind is cold and clammy. At the top surface of the marine layer the fog is constantly evaporating and both cooling and moistening the overlaying air layer. It is this cold moist air layer that blows ashore as the fog wind.
The second way I can tell it’s the fog wind is that it has the green, slightly clammy tidal-flats smell of the northern ocean. If it were wine I’d say it has notes of seaweed and tones of driftwood, with an underlying hint of adventures on the restless sea … what an astounding world it is our privilege to inhabit!
Best to all,
w.
My Usual Request: Misunderstanding is the bane of the internet, but we can minimize it by being specific about our differences. If you disagree with me or anyone, please quote the exact words you disagree with, so we can all understand the exact nature of your objections. I can defend my own words. I cannot defend someone else’s interpretation of some unidentified words of mine.
My Other Request: If you believe that e.g. I’m using the wrong method or the wrong dataset, please educate me and others by demonstrating the proper use of the right method or identifying the right dataset. While demonstrating that I’m wrong about methods or data is valuable, it doesn’t advance the discussion as much as if you can point us to the right way to do it.
Data: I collated the data of the IPCC Table 9.5 regarding the sensitivities of the CMIP5 models here as an Excel spreadsheet. Then I did a variety of analyses on it … although not actively user-aggressive, it’s not user-friendly, but you might glean something from it. Most of the work above is done in R, but the analysis of the Monckton results is in the spreadsheet.
Further Reading: As usual, what I did in this case was to go get the data first, and see if I could duplicate Lord Monckton’s results. After I’d duplicated his calculations, and analyzed and gleaned all that I could from the data, then and only then I went to look at the literature. The two papers I found that were of the most use were by the insightful Nic Lewis, “Briefing Note on Climate Sensitivity“, and a 2011 essay by Lucia Liljegren, who is most always worth reading, entitled Monckton Planck parameter no better than pulling numbers out of a hat … dang, Lucia, don’t hold back, tell us what ya really think …
“… as the poet has it …”: The poet in question is Lewis Carroll of Alice in Wonderland fame, who wrote:
Yet what are all such gaieties to me
Whose thoughts are full of indices and surds?
x2 + 7x + 53
= 11 / 3.
Gotta admire a guy who rhymes “me” with “53” and “surds” with “11/3” … and offers us a formula with only imaginary roots. It’s actually part of a complicated double acrostic, see here for more information.
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Re Greg:
“The Planck term is just the T^4 dependence on surface temp. it needs to be isolated from all the other things between sea level and CERES. ”
The Planck term you refer to is well understood and known with high accurasy as Stefan Boltzman 5.67E-8*T^4.
The important part is how much of that radiaton makes it to the space when you look at it differentially.
One Kelvin higher temperature increases the radiaton from the surface by the SB formula and how much of that is in the end radiatet out to space.
You could model it with some feedback or just model it as some sort of resistance between Earth and space. Both ways has some advantages and some drawbacks, and the reality might be just between.
The big elephant in the room is clouds and associated rain/snow.
Willis wrote: “Not only is the reality wildly non-linear, but the average value for the Planck feedback (-2.0 W/m2 per °C) is only about two-thirds that suggested by the models (-3.2 W/m2 per °C). Not sure what I can say about that …”
In your graph, the change in surface temperature is partially produced by combining data from different locations on the planet, not from raising the temperature everywhere by deltaT. The slopes of the lines on your graph have units of W/m2/K, but that doesn’t mean the slope is Planck feedback.
Planck feedback for a blackbody (dW/dT) is -4oT^3 or -3.8 W/m2/K around 255 K. The consensus gets a Planck feedback from climate models of -3.2 W/m2/K by assuming more warming near the poles than near the equator.
The average LWR photon escaping to space is emitted from an altitude where the temperature is 255 K (the BBeq temp), This produces an average of 240 W/m2 of OLR. If you take the vertical axis of your graph and convert W/m2 to BBeq temps, the vertical axis runs from 200 W/m2 = 243 K to 300 W/m2 = 270 K. So, as the ocean is warming from 0 to 26 degK, the average temperature of the GHGs (or cloud tops) emitting the photons that reach space rises from about 240 K to 265 K and then falls back to about 250 K. There are a lot of clouds and humidity in the tropics that absorb or block thermal infrared emitted lower in the troposphere and prevent it from reaching space. When clouds and humidity change with surface temperature, you are seeing the effect of cloud and water vapor feedback on OLR, not Planck feedback.
Except for some Antarctic winter, the coldest place on the planet is usually the top of the tropopause in the tropics. Tropical oceans are far below where the photons reaching space are emitted.
Yes. And what Miscolczi was mugged and silenced for discovering was that the complex dynamics of radiation balance and emission height adapt to increasing CO2 concentration so that nothing changes in radiative balance. As would be normal to expect in an entropy-exporting dissipative nonlinear thermodynamic system.
Unfortunately, Miscolczi’s analysis depends on humidity data for the upper troposphere from old radiosondes being correct. That data says the humidity in the upper atmosphere has been falling, not rising as the globe warms. Unfortunately, no one trusts the hygrometers on those old radiosondes.
As for Miscolczi’s claim that Aa=Ed exactly, see Roy Spenser:
http://www.drroyspencer.com/2010/08/comments-on-miskolczi’s-2010-controversial-greenhouse-theory/
Fig 2 looks like a cloud/t-storm response to SST.
OK, I’ve lopped off the offending part of the essay and left the calculation of the Planck feedback … I’ve added the following at the top:
I’m sure that folks will let me know if that Planck calculation is also incorrect … like I said, it’s the beauty of the web, where I can depend on the contributions of strangers to keep me on course.
Thanks to all,
w.
Please read my answer to your comment and see if you can add energy reflected from clouds to figure 2.
Reflected short wave radiation would add a great deal to the total picture. As would heat captured creating water vapor.
@Willis – What causes the definite spiral patterns in the chart? These look very similar to the designs I made years ago with a toy called a “Spirograph.” Some phenomena is definitely causing these spiral shapes in the chart. Even the “knee” of the curve has a similar curvature.
Did you notice that on the bottom part of the curve the width of the pattern goes to it’s maximum width around 23C. It is modulated with respect to temperature and temperature sets the frequency of the long wave radiation. The Earth’s atmosphere by some means modulates the long wave radiation.
I was thinking it might be something to do with enthalpy, I have been adding it into my program, but after Willis’s correct comment about it, and when I ran my weather station data that logs every couple minutes that doesn’t seem right, so I’ve started to think it’s the optical properties as air temperatures near dew point. And when rel humidity gets really high, we do end up with fog. Plus the topic of optical properties of really damp air came up with some people while at a star party.
There is definitely something happening. The IR adsorption spectrum is going to change based upon temperature and phase of the WV.
This phenomenon definitely need analysis by someone that knows more than me about this stuff.
Another unstudied aspect of the atmosphere is the effect of the changing height/thickness of the the ionospheric layers. As an amateur radio operator I am aware of how it affects radio waves. IR is in the electromagnetic spectrum. Thus, just as the radio signal is affected, the IR signal is going to be affected. How? I sure have know Idea.
Willis, this seems to be a good way to uncover some real basic things about how the Earth’s weather and climate works. It would be interesting to generate the same figure 2 for a grid pattern over land. It would help separate ocean effects from the basic processes that appear in the figure.
Use temperatures of individual areas in the grid just as you did on the ocean grid.
I have all of the surface station data processed into 1x1grid cell in the reports section of my source forge page, you can get the url from here
https://micro6500blog.wordpress.com/2015/11/18/evidence-against-warming-from-carbon-dioxide/
Monckton of Brenchley August 20, 2016 at 10:13 pm
Christopher, always good to hear from you. To take your objections one by one:
Mmmm … well, perhaps you could specify just how it is “unlike any true feedback”. In addition, whether or not it is a true feedback, it is widely referred to as the “Planck feedback” and I speak English as it is spoken. I note that the term is used as follows:
And where is that quote from? It’s in a paper by some guy named “Christopher Monckton”, and he didn’t seem bothered by the term then … which makes me wonder why it upsets him now. Heck, you’re the same guy that approvingly quoted from a paper called “On the confusion of Planck feedback parameters” … how come you didn’t bust Mr. Kimoto for being so horribly foolish as to call it a “Planck feedback”?
In addition, I fear I don’t understand why it is not a negative feedback. Suppose we add heat to argon, which neither absorbs nor emits thermal radiation. It will end up warmer than an equivalent mass of say water vapor. Why? Well, because the argon doesn’t radiate thermal IR, so when it warms up there is no increase in heat loss. With water vapor, the warmer it gets the more it radiates, which cools it down.
How on earth is that emission of radiation, which reduces the amount of warming, NOT a negative feedback?
You may not have noted up at the top where I said:
I may indeed be doing it incorrectly as you say. But unfortunately, in addition to not demonstrating how to do it right, you haven’t even demonstrated that I’ve done it wrong. Instead, you have merely claimed that I’ve done it wrong, without any attempt to either explain or support your claim, and certainly without any attempt to demonstrate or even explain your preferred method.
So while you may be 100% right, you’ve provided exactly nothing to convince us that you are.
Same objection. It’s not enough just to wave your hands and utter magic words indicating that you are the proud possessor of the truth. You need to bring some citations or sources or logic or math or SOMETHING to the table other than your waving hands and your admittedly silver tongue …
And your claim is that nature always follows the equations that you think it should follow? Really?
Next, as you know, there is not even agreement on which “T” should be used in the formula, since the “T” you refer to is NOT the physical temperature of the planet’s surface. And it is unclear why you think such a formula which does NOT use the real planetary surface temperature would refer to a real planet, despite your adjusting it by 7 / 6 in an attempt to make it fit reality.
Finally, in fact the derivative ∆T/∆F is (F/σ)1/4 / (4F), which is many things but is hardly “linear” as you claim.
I’m sorry, but this is completely unclear … what is a “latitudinal non-linearity” when it is at home?
And I thought you were claiming that the Plank none-dare-call-it-feedback parameter was completely determined as the derivative ∆W/∆T = T / (4F) … but if so, where is the “latitudinal non-linearity” in that equation?
Sorry, my friend, but after you offering us nothing but handwaving and unsubstantiated claims, such a pathetic attempt at a “humorous” insult doesn’t help … you’d love for folks to think that you killed my claims with a single shot a la J. Wilkes Booth, but I fear that your powder was wet and your derringer has misfired.
I’m happy to discuss these matters with you, but simply stating your position as you have done is just an attempt at science by assertion.
w.
Willis,
I’ve had this discussion with C.M. and I understand why he thinks what he does.
1) While he now understands that Bode’s analysis only applies to linear systems, he’s under that false impression that emissions and temperature are linearly related to each other because lambda0 is proportional to T/R (but its also proportional to 1/T^3 and R^-3/4) while Bode conforming linearity requires the input and output to be linearly related to each other and that the open loop gain (lambda0 per Roe) must be independent of both. And while this is approximately true around the reference T of 255K, the actual surface T of 287K is too far from the reference for the approximation of linearity to be approximately true. The example of this is an audio amplifier that once it starts clipping, the gain is no longer independent of the stimulus and decreases as the input exceeds where clipping starts and Bode’s gain equation (Es/E0 = mu/(1 – mu*beta), where mu is the open loop gain, beta is the fraction of output fed back to the input and Es/E0 (he also calls this e^theta) is the closed loop gain and which can also be expressed as 1/mu = E0/Es + beta or in more modern terms, 1/G0 = 1/g + f.
2) Regarding the emitting surface, he’s more or less correct, but doesn’t understand that the zero feedback ‘reference’ is an ideal BB with no atmosphere and the emitting surface of this reference is the hard surface, thus as feedback is increased from the reference value of 0, the surface temperature is what is being increased, even as the new ’emitting’ surface as its defined (which has nothing to do with what surfaces are emitting photons) moves to the boundary between the top of the atmosphere and space.
3) He seems to believe that Bode’s feedback model is being used to model the amplification of the sensitivity by feedback, when in fact, Hansen and Schlesinger who developed the model and more recently, Roe, who restated Schlesinger’s analysis using better variable names, all assert that the model is one of a temperature output representing the surface, T, as its affected by input forcing, R. Bode is also abundantly clear that the model is one of an input being amplified to produce an output and not one of feedback amplifying gain.
4) The incremental nature of the pedantic feedback analysis is only valid if the relationship between the input (R) and output (T) is linear. Bode assumes that if R is the input and T is the output, R/T = dR/dT = closed loop gain. Clearly, the SB LAW tells us that the relationship between R and T is highly non linear, where R is proportional to T^4.
I shall refer you to the first two paragraphs of Bode’s book where he asserts among his assumptions that all elements are linear and that active gain is provided by vacuum tubes with an implicit power supply, Also, refer to page 108 where he asserts that passive systems are unconditionally stable. Many people confuse dynamic behavior with active behavior. In the context of Bode, an active amplifier does not apply COE between its input and output as it assumes that there is an implicit source of energy to provide power gain and power gain is not a property of the climate system.
It’s like the difference between manual steering (a passive system) and power steering (an active system). In the former, COE applies and it takes as much energy to move the steering wheel as it takes to move the tires, although gearing provides force multiplication. In the later case, a hydraulic pump provides energy (as positive feedback) to reinforce the forces applied to the steering wheel and rather than requiring big biceps to park a car, you can use your pinky. Bode is concerned strictly with active systems, of which the climate is not.
Well, there is a power supply if you think about it………..
I will accept if you argue the particulars are not powered though.
micro6500,
The Sun is not an implied power supply, it’s the stimulus and explicitly accounted for by R (the forcing). If I supply a varying stimulus to a passive circuit, the nodes will all wiggle, but this is not an indication of an active system. COE applies to a passive system and no more energy can come out of the system than was put into it in the first place. The apparent warming of the surface is the consequence of past surface emissions being delayed by the atmosphere and returning to the surface in the present. It’s not the consequence of active gain providing additional energy to the system as is implied since everything about Bode’s analysis assumes active gain.
How do you think the consensus can support a sensitivity so much larger than first principles physics will allow? Removing the restrictions imposed by COE on the output as a function of the input of the feedback network is the only way they were able to do this. This was a mistake made by Hansen and reinforced by Schlesinger 3 decades ago and canonized by the IPCC since AR1. This silly mistake has remained broken since, is the only theoretical reason an absurdly high sensitivity can be supported and has been largely responsible for leading climate science down such an absurd path.
Now on this one (I answered these backwards), I can’t yet argue the point articulately yet, but I keep thinking an op amp with some reactive feedback could do everything needed, and it is powered. Now I agree there isn’t a separate stage of gain, but more a fet to the supply, and the gate regulates the source (which I’d do as an op-amp (probably) if I was doing such a circuit). In my analogy the fet is the atm layer, drain the Sun, and ground 🙂 is the ground. Single source of input power.
I’m right with you on this. And it was my modeling background that got me here.
micro6500,
An RC circuit with a delay line can do the same thing and this is a strictly passive circuit. Take some fraction of the output, delay it with a length of transmission line (the portion delayed is no longer available for output) and add this back to the input. Another passive model for the atmosphere is as a mismatched transmission line at the surface/atmosphere boundary whose resulting standing wave ratio reflects power back to its origin (the surface).
The basic issue is impedance. Bode assumes an infinite input impedance and zero output impedance for his basic gain equation. Keep in mind that the open loop gain of an op amp is nearly infinity and even a single FET has an open loop gain on the order of many thousands, thus even in the single FET case (actually you need 2 for the non inverting amplifier required for positive feedback), the closed loop gain is almost completely dependent on the feedback ratio.
The open loop gain of the climate system, while not the unit value assumed, is only a little more than 1, thus both the open loop gain and the feedback fraction contribute equally to the ultimate closed loop gain. In fact, for a passive system with unit open loop gain, the closed loop gain is 1 independent of the feedback fraction. If G is the open loop gain, g is the closed loop gain and f is the feedback fraction, the gain equation becomes, 1/G = 1/g + f, where all of G, g and f are dimensionless ratios. Another flaw in the consensus feedback model is specifying the input and outputs in different units and specifying the gain (sensitivity) in units of degrees per W/m^2, rather than the dimensionless ratio prescribed by Bode.
The climate system input impedance is the same as its output impedance and can be approximated as zero. The difference is that feedback to an OP amp isn’t consumed and is still available for output, while the output of a passive system can either contribute to the system output or be fed back to the input. This is the missing COE constraint.
The real problem is that feedback and gain as defined by Bode has nothing to do with feedback and sensitivity as defined by the IPCC, yet the IPCC cites Bode as the theoretical foundation for its errors. It’s also not just one error, unless you consider it how Bode was mapped to the climate, but a series of small, self consistent and reinforcing errors that has had 3 decades to fester as it spawns error after new error.
micro6500,
To clarify, the equation 1/G = 1/g + f is the gain equation for Bode’s feedback network that assumes active gain (1/G is assumed 0 for op amps). After modifying this for the case of a passive system where COE applies between the input and output of the network, it becomes 1/G = (1/g + f) / (1 + f).
You can derive the first form starting with the initial gain formulation, where g = T/R, R is the input, and T is the output quantified as, T = G*(R + f*T) which is modified to become T = G*(R + f*T) – f*T in order to derive the passive case when COE applies (f*T fed back can not contribute to T).
I’m using R (forcing) and T (temperature) because since everyone on both sides agrees that f is a dimensionless fraction between -1 and 1, it should be unambiguously clear that the methodology mapping forcing in W/m^2 (R) and temperature (T) in degrees K to the Bode feedback model is dimensionally inconsistent with the theoretical foundation claimed to support it. Note that considering the input a change in R and the output a change in T adds another layer of obfuscation that’s even worse considering the T^4 non linearity between T and R and that any change in T is dependent on both the change in R and either its initial value or final absolute value.
Again, the “plank effect” (how surface temperature changes outward radiation using a well known equation) is not feedback as Bode defines it and how it is normally used. Regarding CO2 effects, the reduction in outgoing radiation is an external forcing function. It should be compared to a voltage input to an amplifier from an outside source which creates an output at the amplifier (that may be delayed from the input). Feedback relates to how some of the output is feedback to the input.
More CO2 causes a change in surface temperature (an external force). It is reactions to this change in temperature that are the true feedbacks. The same thing would apply to a change in solar input, where it is easier to see it is an external force. One difference is that shortwave forcing causes more warming per Wm-2 than longwave such as from CO2.