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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“this would imply an overall climate sensitivity on the order of 0.4°C to 0.7°C per doubling of CO2.”
Which is a net positive carbon cost, i.e. beneficial without any enviro-climate downside, unless you are a dishonest Liberal looking for a scare-the-public story at every opportunity.
But whatever, let’s just tax the crap out of CO2 emissions anyway because the money buys votes for more socialism. And socialism is where the Millenial generation, raised on liberal-think and common core, is headed. Millenials are thinking someone else is always going to buy their free stuff.
My friend the irrepressible, irascible, highly improbable but always fascinating Willis Eschenbach was infelicitous in referring to the Planck parameter as a “feedback”, for it is unlike any true feedback; he was incorrect (as I had once been) in attempting to determine it at the hard-deck surface rather than the emission surface of the Earth, at a mean pressure altitude ~300 mb; he was accordingly incorrect (as I had once been) in determining its value to be of order 0.2 Kelvin per Watt per square meter, when it is in fact 0.312 Kelvin per Watt per square meter or thereby; he was incorrect in imagining the Planck parameter to be non-linear, for the first derivative of the fundamental equation of radiative transfer with respect to temperature and radiative flux density may be expressed in the form delta-T / delta-F = T / (4F); and he was incorrect in imagining that the value of lambda-zero had been determined without regard to latitudinal non-linearities.
Apart from that, Mrs Lincoln, how did you enjoy the play?
Yes, calling the “Planck effect” feedback is incorrect, as IPCC and many others do. True feedback is how a rise in surface temperature will cause a further change in temperature (up if positive feedback or down if negative) caused by some physical process responding to the temperature change. Positive feedback examples are warmer air holds more water vapor (a greenhouse gas); it also absorbs more incoming solar energy, a negative feedback now being ignored. Warmer oceans cause more evaporation cooling and cloud cover, both of which are negative feedbacks, major cooling factors now being ignored or under estimated. In fact IPCC must assume clouds are a positive feedback so the simple energy balance models match the complex computer models estimates of climate sensitivity.
The so called “Planck feedback” is merely how the surface radiation responds to a temperature change. It is simply radiation physics. Perhaps they want to call it a feedback because it produces a negative value so they can say “See, all of our feedbacks are not positive.”
The so called ‘Planck feedback’ is not related to feedback at all and is a math error crafted to provide the illusion of open loop gain (Bode’s mu). If lambda0 is the open loop gain, then according to Bode, the sensitivity equation should be,
deltaT = deltaR * lamabda0/(1 – lambda0*f)
where the sensitivity is deltaT/deltaR
Of course, since f is defined as a dimensionless fraction between -1 and 1 (by both the consensus climate model and Bode), and lambda0 has units of degreesK per W/m^2, the open loop gain term multiplying the feedback term is dimensionally incorrect, so what Bode calls the open loop gain (mu) can only be assumed to be 1, thus the lambda0 term becomes an obfuscating scale factor that’s outside the influence of f (the feedback system). This is also evident by the consideration that f = ci*lambda0, where ci is a feedback coefficient expressed as W/m^2 of feedback per degree. Written another way, c = f/lambda0, which says that all a feedback coefficient does is undo lambda0 and apply f, which is Bodes quantification of feedback (beta) to the input which implies unit open loop gain.
The climate science feedback model is invalid at its core and in fact, models nothing of any significance relative to how the climate actually operates. It’s nothing more than a bastardization of Bode where the feedback network is considered to amplify gain, when Bode’s analysis models a stimulus amplified by a constant gain to produce an output. Constant gain for all W/m^2 of input is the indicator of input to output linearity which is another prerequisite of Bode. Between violating the linearity requirement and the climate system being passive (i.e no internal sources of heat/energy), how this ever got through peer review 3 decades ago is an embarrassment to science.
Moreover; Bode’s amplifier removes the requirement for conservation of Energy between the input (forcing) and output (temperature). Climate science also chose to quantify the gain (sensitivity) with a metric that you can’t trivially apply conservation of energy to unless you know the T that the delta T started from, which of course is cancelled out of their formulation!
Error on top of error on top of error. It’s all consistent, but consistently wrong.
Planck Feedback is the most basic climate feedback mechanism. It is simply that when the Earth’s
surface gets warmer, it loses heat faster by radiative emission, thereby reducing the increase in temperature:
Rise in temperature => increased energy loss via radiative emission => reduced temperature
Reduced temperature => reduced radiative energy emission => increased temperature
Radiative emissions from a warm body are
proportional to
the 4th power of the body’s absolute temperature (temperature in in Kelvin).
It is easy to calculate that a uniform global temperature increase of
1°C would increase average radiative heat loss from the surface by roughly 1.4% (variously estimated to be
3.2 to 3.6 W/m²):
(2884) / (2874) = 1.014 = 101.4%
Coincidentally, 3.6 W/m² is also the approximate amount of additional energy calculated
to be retained (i.e., the “forcing”) due to a doubling of atmospheric CO2 levels
(though Prof. Wm Happer has found evidence that CO2’s forcing is
overestimated by about 40%)
Ouch. I really botched that formatting. Let’s try again…
Planck Feedback is the most basic climate feedback mechanism. It is simply that when the Earth’s surface gets warmer, it loses heat faster by radiative emission, thereby reducing the increase in temperature:
Rise in temperature => increased energy loss via radiative emission => reduced temperature
Reduced temperature => reduced radiative energy emission => increased temperature
Radiative emissions from a warm body are proportional to the 4th power of the body’s absolute temperature (temperature in in Kelvin). It is easy to calculate that a uniform global temperature increase of 1°C would increase average radiative heat loss from the surface by roughly 1.4% (variously estimated to be 3.2 to 3.6 W/m²):
288^4 / 287^4 = 1.014 = 101.4%
Coincidentally, 3.6 W/m² is also the approximate amount of additional energy calculated to be retained (i.e., the “forcing”) due to a doubling of atmospheric CO2 levels (though Prof. Wm Happer has found evidence that CO2’s forcing is overestimated by about 40%).
daveburton,
What you are call Planck feedback does not conform to what Bode called feedback and Bode is the foundation analysis that climate related feedback is based on.
The specific error is considering it feedback in any sense. It does nothing more than quantify the required behavior based on first principles physics describing the relationship between temperature and W/m^2 (forcing or emissions since in LTE they are the same) according to the Stefan-Boltzmann LAW.
If you look at how this is derived, they start with the slope of SB at 255K, multiply this by an empirical constant and then call it the open loop gain claiming that it is valid across all forcing and temperature. They do this by asserting that its approximately linear, which it is, but only around the reference temperature of 255K. The average surface temperature of 287K is too far from the reference for the assumption of approximate linearity to be approximately true.
co2isnotevil, we’re quibbling about word definitions. I don’t know what Bode called feedback, but if it doesn’t simply mean a mechanism through which the output feeds back to influence the input to the same system, then it wouldn’t be a conventional definition, these days.
Negative feedback is an opposite-direction response to a perturbation in a system, which reduces the magnitude of the change (or, if there are delays in the feedback path, it can cause oscillations).
Positive feedback is a same-direction response, which tends to increase/amplify the magnitude of a perturbation.
Example: Higher CO2 level causes more plant growth, which causes more CO2 -> O2 conversion, reducing the CO2 level: a negative feedback.
Example: Warmer air temperature increases the amount of water vapor in the atmosphere, because warmer air more readily holds moisture. (This effect is usually approximated in climate calculations by assuming stable relative humidity.) When warmer temperatures increase the amount of of water vapor in the atmosphere, because water vapor is a greenhouse gas it increases greenhouse warming: a positive feedback.
Example: Higher water temperature causes increased evaporation, accelerating the water cycle, and increasing the rate at which heat is transported away from the surface, thereby cooling the water: a negative feedback.
Example: Higher surface temperature increases the rate of radiative energy emission, cooling the surface: a negative feedback (Planck feedback). Where the surface temperature is 287K (≈57°F or 14°C), a 1°C increase in temperature results in a 1.40% increase in radiative emission. Where the surface temperature is 255K (≈-1°F or -18°C) a 1°C increase in temperature results in a (256/255)⁴ – 1 = 1.58% increase in radiative emission.
You are correct that Planck feedback is due to first principles of physics, but the fact that Planck feedback is due to first principles of physics doesn’t mean that it is incorrect to call it “feedback.”
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First thank you for some really interesting posts. Remember the series of Argo float graphs you posted several years ago that showed the ocean is limited to about 31C. You have connected that temperature to thunderstorm activity as a thermostat in several posts since then. When I look at figure 2 and see the negative sloop above 26.5C I interpret that as meaning something other than thunderstorms is causing the cooling since higher ocean temperatures between 26.5C and 31C means the heat should be carried to the top of the atmosphere and radiated to space; but it is not. There is an inorganic chemical reaction in the ocean that produces calcium carbonate and removes considerable heat from the ocean. This reaction has been know for many years; but is not understood. The reaction is inhibited by magnesium and fulvic acid. I suspect that the missing heat is going into calcium carbonate compounds.
Another thought; this reaction or a release of either CO2 or O2, I don’t remember which gas is released, could change the transmission of heat from the surface to space.
Retired Engineer John August 15, 2016 at 10:56 pm
Thanks, John. I read that the opposite way. The drop in the outgoing longwave radiation is because it is intercepted by the clouds, both cumulus and thunderstorms.
Mmmm … there’s a good description of oceanic carbonate chemistry here.Calcium carbonate (calcite) is odd in that unlike most solids, it dissolves more easily in cold water than in warm water. For this and other reasons, what that means is that in the ocean, below a certain depth (typically around 4,500 metres down, called the “calcite compensation depth”) calcium carbonate simply dissolves.
And while this has an affect on the buffered nature of carbon in the ocean, I doubt that it has a huge effect on surface temperature. Recall that it’s happening way down below the “mixed layer” that is in contact with the surface, so it can’t respond much to current conditions.
But I’ve been surprised before …
w.
Willis, I gather from this comment that you are using ‘all sky’ data here. It would be good to be clear about that in the article. I was left guessing and had to interpret the graph to see what that guess should be.
Now if it is all sky outgoing LWIR, I don’t see why you call this the Planck feedback.
The Planck feedback is defined as the change in radiation emitted by the sea surface as a function of its change in temperature. What you have in CERES all-sky is a mix of everything which is happening: CO2 GE, water vapour , cloud change ….
This graph may tell us something useful but it will not give a value for Planck feedback.
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.
… unless I’m misunderstanding what you wrote.
Willis, the more that I look at figure 2 the more I am convinced that this represents a more complex process than we could imagine. Your comment
“Thanks, John. I read that the opposite way. The drop in the outgoing longwave radiation is because it is intercepted by the clouds, both cumulus and thunderstorms.” says that the cooling effect we expected from thunderstorms carrying heat high in the atmosphere is not the way the cooling happens. It says that cooling is caused by clouds shading the Earth from the Sun. Or it could be a combination. But something is limiting the ocean temperature while the radiation to space is being limited. Is there any way that you can include the reflected energy off the clouds and compare it to longwave radiation in the same format you used in figure 2?
The calcium carbonate chemistry in the ocean is complicated. The inorganic process occurs at the ocean’s surface and I have read that the tropical ocean on a quiet night can actually bubble due to the reaction. I have tried to confirm this statement, but cannot. The Carbonate Compensation Depth CCD is stated to be where “calcium carbonate simply dissolves”. However; “dissolves” is not a good description, it becomes hydrated.
Something I see in my weather station data, is when air Temps near dew point cooling slows a lot, while at the same time zenith temp is still 100F colder, maybe the same happens in at high sst’s. Willis, what is rel humidity doing as outgoing starts to fall?
micro6500 August 16, 2016 at 6:47 pm
Heat of condensation. The amount of energy released by condensation is the exact same amount of energy required to make a liquid evaporate into a gas. For instance, 1 gram of water needs 600 calories of energy to transform from a liquid to a gas. This same amount of energy is released when water condenses back into water droplets from water vapor.
When heat is released by condensation, the air around the water droplets become warm. This heat continues to carry water vapor higher into a thunderstorm and rejuvenates the storm. This water then cools off and falls back through the cloud, keeping the storm active.
Latent heat is defined as heat released or absorbed as water changes phases between a solid, liquid and gas. The latent heat of melting is the energy absorbed by ice to make water, the latent heat of fusion is the energy released by frozen water turning into ice and the latent heat of vaporization is the thermal energy needed to evaporate water. The latent heat of vaporization is how human sweat cools a body when the substance evaporates and absorbs heat simultaneously.
Something about water condensing during night slows cooling.
The difference in ground temperature vs Tsky doesn’t change much between evening and early morning, on low humidity days it’s easily 100F. And it’s 100F still in the morning, I see the temp of my front grass, 10F below air temperature.
But the cooling rate is a quarter the rate at sun up as sun down, and it all changes as reliable humidity get into the 80 or above.
I have also learned the Tsky ss a measure of precipitable water vapor, even so, it is the ir radiation equivalent to the measured temp from a black body at that temp.
Wind speed goes flat at night, Tsky delta doesn’t change, yet after sunset Temps drop like a rock until air temp nears dew points.
This is nonlinear cooling with the transition point based on dew points, co2 is irrelevant.
This is why observations (measurements, not gmst) don’t match any of the expectations.
As I already said in a post elsewhere in these comments (probably appearing well below), I suspect the heat from the warmest oceans is being transported to other parts of the world before being radiated to space as longwave IR.
And I have found this to be true, surface records show slightly more cooling at night, than it warmed the prior day, due to exactly this cause.
So Willis E. calculates a sensitivity even lower than Lindzen’s? I just wonder how applying the evident curve of effects of CO2 changes the numbers from a linear measure.
Tom Halla August 15, 2016 at 11:05 pm
Thanks, Tom. Nothing that I showed above depends directly on or is affected by the logarithmic nature of the effects of GHGs on radiation. All I’ve shown here is shown how much radiation results from a given change in temperature (pre-feedback), and how much temperature change results from a given change in radiation (post-feedback).
w.
There’s absolutely no doubt that during an inter-glacial the climate has negative feedbacks for warming. So, all this talk about positive feedbacks is utter BS.
This was a PR trick by the IPCC, which unfortnuately Monckton has decided to co-operate with .
Overall feedbacks are without question negative. ( There’s probably a 97% consensus to had about that ).
The debate is over whether net feedbacks are more negative or less negative than Planck alone. When IPCC talk about feedbacks being positive they mean all feedbacks EXCEPT the Planck f/b which is in any reckoning greater than all the others put together.
However, if you can suggest the possibility of “net feedbacks” being positive you can scare people with the possibility of tipping points , death spirals the the rest. Carefully omitting to say that ( pretend ) “net positive” still means real net negative.
I believe his surname is spelled “Monckton”.
Typo, fixed, thanks.
w.
“sometimes infuriating but always fascinating Lord Christopher Monckton, for his essay yclept ”
What is a “yclept” ??
To Marcus:
“sometimes infuriating but always fascinating Lord Christopher Monckton, for his essay yclept ”
What is a “yclept” ??
Old English, “called” or “named”
“,,,,,this would imply an overall climate sensitivity on the order of 0.4°C to 0.7°C per doubling of CO2.”
This statement is climate heresy and will doubtless attract the attention of the Klimate Inquisition. I thought this article was brilliant and I await the non-troll comments of those with better mathematical minds than my own.
However, on a much more practical point, this estimate of Willis has to be approximately correct and the IPCC one has to be exaggerated or we would not be here today. Evolution/natural selection could not have reached where it is today if the IPCC’s estimates were correct, the short term changes in temperature would have been far too violent.
Like most sceptics, I accept the temperature forcing effects of CO2, but utterly reject the IPCC’s estimates of temperature feedbacks as a result of that forcing. If the IPCC were correct, the evidence would be clearly seen in the geological record and it is simply not there.
Proof read this please, there are a lot of errors.
Dear heavens, aelfrith, I both proof read it many times and used the spell checker on it. If you think such a procedure prevents typos and misspellings, you’re not an author.
If you see errors, please either point them out and I’ll gladly fix them … or ignore them.
Regards,
w.
(Typos . . The infinity Mr. Einstein failed to mention ; )
“…. run AROUND on a reef …. ”
Aground?
Proof reading makes you cross eyed and spellchecker doesn’t know what you are trying to say.
Can’t win either way.
“I’ve used the “potential temperature”, which is the temperature that a parcel of air would have if you could transport it down to sea level. Since air is warmed by compression as it is brought down to sea level, the potential temperature is warmer than it would be at altitude” I would question whether this is the correct way to measure the effects of elevation.
The difference in temperature is not, I believe, based on how much the temperature would change by transporting it. It seems to me (this is intuition, not calculation) that the difference in temperature is due to the (misnamed) “greenhouse effect”. The energy from the sun does not hit as many atoms of the “greenhouse gasses”, especially CO2, so there is not as much heat retained at the higher elevations.
The math may work out to be similar, I do not have enough mathematical knowledge to verify, but the reasoning/method seems incorrect.
Related – I am shocked at how difficult it is to get the correct answer to an internet query “Why is it colder at higher elevations?”. Most of the responses rely on what happens to a gas as it changes pressure with a typical example being “releasing gas from an aerosol can makes it cold” or filling a tire makes it warm”. But the amount of air moving up and down is in equilibrium so those laws, it seems to me, do not apply. If so, then tires should be warmer than the surrounding air at all times and we have free energy.
Again, I am not sure if this affects the result, but I am offering it for consideration.
“‘Why is it colder at higher temperatures” should have been “Why is it colder at higher elevations”
Fixed. -w.
Would one expect a different response from L/W flux vs solar S/W insolation? Same watts per sq meter, but a different response due to LWIR vs SW.
Also, along the same lines, is not some of the additional Solar consolation penetrating well below the surface, and thus not directly agecting the surface?
Hate typing on my phone, solar insolation and affecting the surface.
Lomborg calculates COP 21 mitigation to be about 100 trillion $ by 2100 and this will reduce temp by 0.05 to 0.17 C. IOW no measureable difference at all. What a lousy bloody investment.
Interesting article, but I think your notion that
“the slope of the graph above is a good approximation of the equilibrium climate sensitivity of the ocean“, Is wrong. The reason is as you writes yourself:
It can be argued that the reason the slope of Figure 3 is so flat is that heat is constantly being exported from the tropics (at the top right of the graph) down to the polar zones at the lower left. And that is certainly true … but heat will continue to be flow from the tropics to the poles whether the earth warms or not—it is an inherent characteristic of the system.
You are right in the first part, but as I explain below, the latter part, after the …, does not weigh up for the first.
To analyze it you may consider a simplified model consisting of only two elements:
One cold (C1) receiving 250 W/m2 and having a temperature of 5 C.
One warm (W1) receiving 400 W/m2 and having a temperature of 25 C.
There must be an energy mix between the two and without this energy mix, the temperature in C1 would have been lower and the temperature in W1 would have been higher.
What would then happen if you increased the radiation globally? Let us call the elements in this increased radiation environment ‘C2’ and ‘W2’.
For simplicity, consider that the radiation increases with 150W/M2 so we get 400 W/m2 to C2 and 650 W/m2 to W2.
In this model, the coldest element C2 would still be heated by the heat exchange with W2. In addition, since C2 now receive the same incoming radiation as W1, and now receive extra energy from the energy mix with W2, it means that C2 must be warmer than W1.
This proves that the sensitivity are higher than the slope between C1 and W1.
/Jan
Thanks, Jan, always good to hear from you. It is an interesting example and sadly, I suspect that you are right. As a result, I’ve put the post on hold until further notice … I suspect I can fix the problem by including the amount of energy transferred from the tropics to the poles (advection), but that’s for another day.
Ah, well, that’s why I put the IF in capital letters above.
w.
Bonus points Willis,for behavior that demonstrates what being skeptical is really about!
Hi Willis
Mark of a good scientist is to be able to admit errors. That happens sometimes to everyone, especially in blogs.
You have spelled my middle name incorrectly by the way.
Jan
Jan Kjetil Andersen August 16, 2016 at 1:43 pm
Errors are my guideposts to the correct path …
Fixed, Jan. My motto is “Perfect is good enough” … and thanks for all of your contributions.
w.
Jan,
You say:-
You then add 150 W/m2 to both locations in your model example.
I don’t follow the logic of your argument. The globe of the Earth is illuminated by the beam of light from the Sun. If the beam intensity increases by 150 W/m2 at tropical location WI (e.g. The Sahara desert at the tropic of Cancer on mid summer’s day at local noon), then polar location C1 will not increase by 150 W/m2. This is because at the high latitude of location C1 (e.g. the north pole) the attitude of the collecting surface relative to the illuminating beam cannot exceed 23.5 degrees. Consequently the beam intensity will be spread out over a larger latitudinal area and not increase by 150 W/m2 but by about 60 W/m2 (because 60 ~= 150 * sine 23.5).
Philip, you are probably right that a uniform additional increase in radiation around the globe is unlikely, but that does not affect my argument. My point was to analyze what would happen with the cold element if it got an extra radiation so that the total radiation to the cold element would equal what the warm element had before the increase.
How much the warm element then increase is irrelevant.
/Jan
Jan,
Thanks for the reply and explanation. On an illuminated spinning globe with a low axial tilt, latitude is the overarching control on climate. High latitudes automatically receive a lower intensity of sunlight because of spherical geometry.
Philip,
Yes, which makes dividing satellite data into constant latitude slices a good way to quantify the sensitivity since the main variable between slices is the yearly total pre and post albedo solar energy that arrives where the difference in post albedo solar input between slices is the definition of forcing per the IPCC.
http://www.palisad.com/co2/sens
This link has dozens of presentations of the the ISCCP satellite data supplied by GISS which I aggregated along 2.5 degree slices of latitude that plot the relative relationships between pairs of variables supplied (or trivially derived from) the variables supplied in the data set. The results are quite revealing, especially the ones in the link called “Sensitivity to/from IPCC forcing”. The relationships with clouds and water vapor are also revealing as they confirm the hypothesis that led me to test this in the first place, which is that the fraction of the surface covered by clouds comprises a regulatory mechanism that converges to a solution adapted to the conditions on the ground and in the atmosphere, where the input radiance and output emissions are in balance and along with evaporation, tends to regulate the surface temperature. i.e. is equivalent to net negative feedback. I say equivalent to negative feedback since the mapping from Bode to climate system feedback is so broken that feedback in the climate science sense is a meaningless concept.
Willis: Something that may be of interest to you.
Cess and colleagues have done a series of assessments of cloud feedbacks in models.
Cess, et al. Cloud feedback in atmospheric general circulation models:An update
http://pubman.mpdl.mpg.de/pubman/item/escidoc:1852492/component/escidoc:1852575/jgrd4249.pdf
What could account for the fish-scale appearance of your Figure 2?
What could account for the fish-scale appearance of your Figure 2?
As I have done before, I add some comments on the climate sensitivity (CS). The original specification of CS applied by IPCC is that the doubled concentration of CO2 from 280 to 560 ppm would increase the absorption of LW radiation emitted by the Earth’s surface by 3.7 W/m2 (Radiative Forcing = RF). This absorption reduces the outgoing LW radiation and forces the climate system to increase the surface temperature, which increases the outgoing LW radiation coming finally to the balance. Because the atmosphere behaves in an almost constant way for small radiation level changes, the CS parameter (CSP or lambda) can be used and its official IPCC value is still 0.5 K/(W/m2), which include the positive water feedback.. That is why the transient CS would be 0.5 * 3.7 = 1.85 K.
If the skeptics want to show that this calculation is not scientifically correct, they have to find out, what is wrong. I think that there are three possibilities: 1) SCP value is wrong, 2) the RF value of 3.7 W/m2 is wrong, 3) the feedback of the climate is different (for example not positive but negative even compensating the CO2 warming effects). The option 3 is the simplest way, if somebody can show reliably that the feedback is not positive but negative. I think that this post of Willis is in this category.
My own calculations show that the SCP value is 0.268 K/(W/m2) (uncertainty range of 0.23 – 0.32) and the RF value of 2.16 W/m2, which means that the CS is 0.576 degrees (uncertainty range (0.46 – 0.6 degrees). The SCP value of about 0.27 can be calculated also by a pen and paper from the Earth’s energy balance, and it includes no feedback, i.e the absolute water content of the atmosphere is constant. These results are based on the spectral analyses and I have used two different calculation tools. The CS value of mine is the range proposed by Willis but now this portion is on hold.
Reference: http://www.seipub.org/des/paperInfo.aspx?ID=17162
aveollila
“This absorption reduces the outgoing LW radiation and forces the climate system to increase the surface temperature, which increases the outgoing LW radiation coming finally to the balance. ”
I don’t know if it makes any different to your train of through but isn’t it technically true that the middle of the atmosphere, or mathematically, the effective altitude of radiation into space, is what must increase in temperature in order to balance the LW radiation of energy?
If, between the effective radiation layer (which is really a large vertical region) and the ground there are interposing clouds, for example, then the surface temperature doesn’t have to rise as much as ‘theoretical’ numbers might require.
Consider: Anything (at all) that interferes with re-radiated energy reaching the surface means the surface temperature will not raise as much as a clear sky calculation says. Only under a clear sky can the predicted surface temperature ‘rise as much as predicted’. In short, any imperfection in a clear sky calculation subtracts from the maximum possible rise in surface temperature.
If the whole atmosphere was laterally static, this wouldn’t matter, but air (and clouds) move around and ‘heat holes’ are punched through them.
With a thunderstorm moving huge amounts of heat up into the ‘radiation zone’ while simultaneously blocking downward radiation of just about everything, we have an example of what I am describing. As long as the upper side is warmer, the radiation balance can be maintained. At the same time, it could be (much) cooler directly underneath that hotter zone. Further, that cooler zone under the storm is directly associated with the storm and the hot zone above.
All the fuss has been made about surface temperatures inexorably rising with increased GHG concentrations. Well, as a model of the real world it is not very good. The hot zone does have to get rid of the same amount of heat, but it does not necessarily hold that the surface temperature has to go up in order to do so in the real world where it rains. And it does rain.
Another good post, and remember (which I think you hint at) the surface temperature profile is not symmetrical, and likely only has to balance over potentially longer periods of time than one year, and to get such a measure would require 100% logging of all the outgoing LW over the complete surface over very long periods of time.
The spectral analysis of mine has been calculated in the clear sky conditions but in the final results are calculated for all-sky conditions. We can speculate and make approximations, where is the final layer, which emits the the outgoing LW radiation into space. In the end the outgoing LW radiation will be the same as incoming SW irradiation. The measurements show that this is true. There are regional differences and seasonal differences but the average values over the year and very well in balance. The theory and reality are very close to each other.
I’ve skimmed your paper, it looks very interesting. I plan to dig into it later. What caught my eye right off the bat is your sourcing of the logarithmic forcing-vs-CO2 concentration formula to Myhre (1998). Myhre did not derive the equation (whose provenance seems shrouded in mystery. See the CA threads see here and here) but simply modified the constant. If you know the source of the derivation I’d love to see it.
I’m skeptical of the lograrithmic form which infers a linear emissivity vs. line-path relationship. The gray-gas model as well as the iconic experimental work of Hottel (as modified by Leckner, consult any text on heat transfer) all show the curve flattening at longer path-lengths. If the emissivity flattens, so does the sensitivity, i.e it may not be a constant but rather a decreasing function of CO2 concentration. Line-by-line compurter models shouldn’t trump experimental data, especially data that has proved itself correct over decades of use in combustion engineering. Gas chromatography analyzers are calibrated to these curves so if they’re off, seems like someone would have noticed by now.
I’m also unsure how the GCM models account for water vapor. Schmidt shows a table on RC which shows the total emissivity exceeding the sum of CO2 and H20 alone, when the correction should be negative (see Redmond 1980 or again Hottel).
I think that the logarithmic relationship is based purely on the curve fitting. At least in my case it is true. The fitting seems to be almost perfect.
My calcs based on non-linear regression of Hadcrut4 v CO2 to a gray-gas model give lambda_0 = .501, dF=1.89 W/m^2 and TCS of 1.92. Using the log-linear path-length model per the IPCC (and you) my regression matches yours, i.e dF=3.31Ln(C/285) but I get a TCS=2.28 with that method. Those figures are uncorrected for water vapor. If you use the Redmond (1980) emissivity correction (reduces emissivity by ~ .05) then dF=1.37 W/m^2
Unfortunately it’s the temp data that’s the issue.
The results Hadcrut4 does not represent what’s actually measured, but what the programming teams opinion on how the measurements get turned into a GMST that has never been measured.
Temps have not gone up as a log forcing would dictate, but more like how moving pools of warm water that alter the direction water vapor being blown by winds would. But they hide that in GMST by using mean temps for one.
I haven’t finished studying this article yet, but I did stumble across a relevant paper:
Kimoto, Kyoji (2009). On the Confusion of Planck Feedback Parameters, Energy & Environment, Nov 2009, vol. 20 no. 7, 1057-1066., doi:
26.5 degrees immediately leaps out at me, with a big klaxon and red light. It is the minimum sea-surface temperature for the development of tropical revolving storms (hurricanes etc.). Is this a coincidence?
quote : “If you disagree with me or anyone, please quote the exact words you disagree with”
– Ok…
quote : “His claims and musings, while not always correct,”
– From what I saw (its two previous post, he is more often wrong than correct. By the ways, happy to see that the “eq” in the equation shown in the heading post came back. It disappeared in its previous post whereas it was there in the first post (he tred to hide that they are major differences between transient and equilibrium warming).
quote : “Lord Monckton says that the IPCC has overestimated climate sensitivity.”
– by a factor 2, he said. And he claimed that he gave a demonstration… with a wrong calculation (related to some extent to the “eq” he made disappear).
quote : “The crux of his argument revolves around the “Planck feedback” parameter.”
– No. He don’t use it in its calculation. Did you try to do the calculation ? If yes, you should go back to school.
quote : “The Planck feedback is how much the outgoing longwave radiation of the globe increases per degree of increased temperature.”
– assuming constant “effective emissivity”… Saying the way you say it, it’s wrong.
quote ” 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.”
– in fact, “pre-feedback” means nothing and suggest a time dependency that is no there. It’s important because Mr Monckton suggest that there is a time dependency (see his responses to comments of his posts) where there is not (which he also ackowledges in some responses to comments).
Sorry to not find the courage to read more. Maybe later.
So according to Figure 2, the heat loss decreases as ocean temperature increases past 26.5 degrees C? This does not make sense to me – I thought heat loss from the ocean was supposed to blow up when the ocean temperature increases past some point around there.
My guess is that the heat given up by the warmest ocean waters is not being radiated as IR to space from clouds over the same location, but being transported to other parts of the world and then being radiated as IR to space.
Meanwhile, the positive slope portion of Figure 2 indicates negative feedback – heat loss increases as temperature increases. The lambda is, as you said, a climate sensitivity term. If that is multiplied by the IPCC figure of 3.7 W/m^2 per 2xCO2, this means pre-feedback sensitivity of 1.85 degrees C per 2xCO2. This sounds high to me for pre-feedback climate sensitivity.
Oh, maybe that’s the point evaporation really gets going, and water vapor is blown about by the wind.
Feedback is the most misunderstood concept in all of climate science. This is evidenced by the fact that they claim a runaway feedback effect is likely, or even possible, while anyone who as studied feedback systems knowns intuitively that passive systems are unconditionally stable.
Ding, Ding, we have another Winner!
Well, I don’t know that I would classify the world’s climate as a passive system, but you are correct that the fear of “runaway feedbacks” is a product of superstition.
With my background in Systems Science, I see feedback mechanisms everywhere. One develops a nose for them. In the natural world, as in engineering, most feedbacks seem to be negative (stabilizing) mechanisms, which attenuate, rather than amplify, forcings.
I’ve attempted to compile a list of all known and hypothesized climate-related feedback mechanisms. It currently has 13 or 15 (depending on how you count) negative feedbacks, and five positive feedbacks:
http://www.sealevel.info/feedbacks.html
That’s intended to be a complete list. If anyone knows of one that I missed, please tell me. (David Appelll claimed there are “hundreds,” but he can’t name any that I haven’t listed.)
daveburton,
Of course the climate system is a passive system. An active system like an audio amplifier can add joules to the system distinct from the stimulus because active elements like vacuum tubes, transistors and op amps all have an implicit power supply which the climate system does not have.
“Feedback” is almost invariably misunderstood in “climate science,” often being confused with strightforward nonlinear or time-varying response characteristics in a dissipative system, totally absent any physical closed feedback loop. Nor are there any independent sources of power in the wholly passive climate system. Thus positive–energy multiplying–feedbacks in the climate system are the illegitimate offspring of analytically misguided imaginations.
Dave read your list.
Got a couple others to consider.
Above about 80 or so degrees incident angle between open water and incoming solar, the reflected light increases albedo to nearly the level of ice, plus as you note open water radiates far more energy to space than ice does. But remember that angle also depends on the local time of day, more than 3 or 4 hours from local noon will also have a incident angle greater that 80 or so degrees. This reduces the impact of open arctic water. My back of the envelop calculates show depending on cloud cover, open arctic water is net cooling, not net warming.
Rel humidity feedback, at night, a lot of the planet, air temps near dew points, this limits the amount of water vapor and would prevent a run away water vapor feedback. a lot of that water re-evaporites in the morning, but a lot ends up in the water table.
Related to this (I think), during the night while air temps are far from dew points, temps drop very quickly, near dew point the cooling rate drops, even though the skies temp is still close to the same difference from air temp the night before. This is part of the non-linear nightly cooling cycle.
These are the two i can think of for now, I’ll let you know I think of any others.
davidburton
Compliments on your collection.
Suggest further exploring biomass feedbacks. e.g.,
Ocean-photosynthesis: Besides your 5) CLAW, changing photosynthesis in the ocean affects biomass concentration which affects absorption/albedo which affects temperature and CO2.
Land biomass: Increased H2O and CO2 cause more rainfall and more biomass which affects surface albedo and local/regional weather patterns.
Oscillations in a simple climate–vegetation model
http://www.nonlin-processes-geophys.net/22/275/2015/npg-22-275-2015-discussion.html
Ocean currents affect albedo
https://wattsupwiththat.com/2011/02/24/a-mircobe-albedo-effect-for-ocean-light-absorption/
Negative carbonate feedback – more CO2 increases ocean bacteria which increases the rate of CO2 sequestration via carbonate (shell) formation from diatoms etc.
I thank y’all for the helpful feedback! I’ve tweaked the wording & numbering of my climate feedbacks list, because of it.
co2isnotevil & 1sky1, the power source for the climate system is the sun.
Nothing short of a nuclear reactor truly adds “adds joules to a system.” What happens, instead, is that through an “amplifying” mechanism a weak effect regulates a larger one, like a valve regulates water flow. Indeed, on the other side of the pond, electronic vacuum tubes, the “active” elements in old amplifiers, are called “valves.”
There is no fundamental reason that systems powered only by the sun cannot be unstable, possibly even with extreme oscillations. It’s rare, but it can happen, and on November 7, 1940 such instability proved fatal to a three-legged cocker spaniel named Tubby:
micro6500, I agree: w/r/t open water vs. ice cover, an insulating layer of ice unquestionably warms the water beneath it at night, making sea ice an unambiguously negative feedback mechanism at night:
colder temps => increased ice cover => reduces evaporative heat loss => less cold
warmer temps => decreased ice cover => increased evaporative heat loss => cooler temps
During daytime (only!) albedo positive feedback competes with evaporative cooling:
colder temps => increased ice cover => lighter, more reflective surface => less sunlight absorbed => cooler temps
warmer temps => decreased ice cover => darker water surface => more sunlight absorbed => warmer temps
I don’t know how high the sun has to be in the sky before positive albedo feedback exceeds negative evaporative cooling feedback.
These two competing effects are listed as “Sea Ice / Evaporation Feedback” (#6) and “Ice / Albedo Feedback” (currently #15). Those two obviously “go together,” and should be discussed together, but since I grouped my list into negative and positive feedbacks, those two feedbacks aren’t listed together. I did, however, add reciprocal links between them, just now.
The humidity / dew effects you mention are real, as well, but I don’t think I would call them “climate feedbacks.” A feedback is a mechanism through which an “input” (forcing) has effects which loop around and “feed back” to affect the same input. I don’t see a “loop.”
David L. Hagen, thank you for the suggestions and the links. I do already list CO2 / coccolithophore feedback (#10), through which increased CO2 levels increase CO2 sequestration via carbonate (shell) formation, which decreases CO2, and I do list CO2 fertilization feedback (#9), but that’s a good point about how CO2 fertilization affects water color/albedo, in sometimes unobvious ways, which presumably affects water temperature, which affects CO2 absorption.
I probably should add that under “unknown sign climate feedbacks.” As a feedback it’s presumably minor, but probably not as minor as some others that I included in the list.
I’m not really impressed with simple oscillating computer models, but that 2011 microbe-albedo article is delightful.
(My, that’s a lot of links. I wonder how many of them I botched?)
I see it as a negative feedback to water evaporated during the day, regulating night time cooling, and by extension temps.
But it’s your list 🙂
daveburton,
The point is a passive system can not be unstable. This is shown by Bode and summarized on page 108 of his book. The Earth is clearly a passive system. There are several tests of an active system.
1) Does the system have power gain: climate -> NO
2) Does the system contain an active element like a tube, transistor or op amp: climate -> NO
3) Does the system contain a source of power other than the stimulus: climate -> NO
4) If you take the stimulus away is there any possibility that the output will not drop to zero: climate -> NO
Consider a transformer. It can increase the output voltage but has less than unity power gain. Is it an active system: -> NO
Consider an RLC circuit. If you apply a stimulus, all the nodes will wiggle, potentially with higher p-p voltage swings than the stimulus. Does this dynamic behavior signal an active system -> NO
Consider an RLC resonant circuit. Excite it with a step input and it will ring, not oscillate. Ringing is not a marker of instability as it intrinsically falls off to zero unless more stimulus arrives. When an active device with power gain is added to the system, ringing turns into oscillations which is unstable. In a mathematical sense, R becomes negative and instead of damping oscillations, it amplifies them. Can you see the difference? Bode demonstrates how instability arises by where the poles in the response are relative to the real and imaginary components in the S domain representation of the circuit. Active gain is the ingredient that migrates a pole into a region where instability can exist.
What climate science fails to understand (and this goes back 3 decades to Hansen/Schlesinger) is that there’s a difference between power delivered by the stimulus and power supplied to the implicit power gain element assumed by Bode. In fact, they fail to even acknowledge that Bode’s assumption of active gain means that COE is not applied between the input to the system and the output and this is the only reason that CAGW is still considered viable.
Consider an amplifier whose stimulus is rectified and turned into a DC voltage that powers the active devices. If you believe that more power can come out of the amplifier than goes in as stimulus, you will become incredibly rich as the inventor of free energy.
Oscillations are not unstable unless they persist once the stimulus is removed. The typical positive feedback oscillator has no stimulus (input) and only positive feedback, yet continues to oscillate indefinitely.
There are many errors with how Hansen/Schlesinger mapped Bode to the climate system:
* Assumption of unit open loop gain
* Assuming runaway feedback is possible
* A failure to conserve energy between the input and output of the feedback network
* Assuming Bode’s linear analysis applies to quantify relative changes in a non linear relationship between T (temperature) and R (forcing)
* Choosing temperature as the output of the system, rather than the equivalent BB emissions at that temperature
* Choosing non linear units for feedback coefficients and then implicitly assuming that the coefficients are linearity to temperature
* Calling the closed loop gain the gain before feedback (the fudge factor that multiplies the sensitivity at 255K to arrive at lambda0 quantifies the closed loop gain)
* The assumption of approximate linearity, which is around the reference T=255K, is not met by the system at its operating point of 287K
* The assumption of active gain does not apply to a passive system like the climate
* Feedback power can either contribute to output power or be fed back to the input, but not both at the same time
* Dividing the open loop (pre-feedback) gain by the closed loop (post feedback) to calculate G is a meaningless metric
* dT/dR is not equal to T/R, thus a feedback network can not model dT/dR directly
Hansen and Schlesinger explicitly stated that the temperature output of the model is the surface temperature. Roe (2008), who simply restated Schlesinger’s analysis using different variable names is somewhat less specific on what T is. Christopher Monckton (apparently after discussing this with Lindzen) came to the conclusion that T is the temperature of a hypothetical equivalent ’emitting’ surface where input == output == 239 W/m^2 corresponding to the emission temperature of the planet of 255K. However; if you look at the emitted spectrum and apply Wein’s law, the temperature based on the peak spectral emissions is far closer to 287K than it is to 255K.
The hypothetical surface is the boundary between the planet and space that more or less corresponds to the ‘surface’ that the IPCC defines forcing to be relative to. While I certainly agree with CM that the model output is not modelling the surface temperature, its not modelling the temperature of any surface, hypothetical or not, that has anything to do with the response of the climate. Adding more errors on top of an erroneous analysis doesn’t fix it, but only makes it less representative of reality.
Willis, you used a different value for forcing per meter than what I did, can you explain that? I presume it’s normalized to a 24 hour average, but is there any other adjustments?
But when you take your CS value, convert it to F, and then adjust for the different way we each describe solar forcing, or CS values are close, I’m at CS < 0.02F/Whr based on TSI and calculated days total forcing for a flat surface at the specific location of the surface station 0.21C = ~0.11F, then with the calculated daily total watt hours I'm about 1/6 that value. But I'm trying to wrap my head around the different forcing to see how close we really are. I'm also only calculating the extra-tropics, because I use the change in temp from the seasonal change in forcing, and divide temp by this value.
https://micro6500blog.wordpress.com/2016/05/18/measuring-surface-climate-sensitivity/
But I think we are far closer to each other than the published IPCC value.
Two separate distinct methods, both far far lower than the IPCC value, this explains why the wamring from Co2 can not be found in the record.
As I typed this, got me wondering if what you're calculating in forcing from water feedback to temp, and not exclusively from Co2.
I'm curious about your thoughts.
The erroneous lamba0 calculated by Roe (2008) is basically the same that Schlesinger (1986) assumed 3 decades ago (he called this G) and this error has been canonized by the IPCC since AR1.
The calculation starts with the sensitivity of an ideal BB at 255K (0.27 C per W/m^2) and then applies empirical adjustments to get it up to about 0.31. The current state of the system whose surface temperature is about 287K is too far away from the 255K reference for the assumption of approximate linearity to be approximately true. A better way is to choose a more relevant reference by starting with the sensitivity of an ideal BB at the surface temperature (.186 C per W/m^2) and divide this by the effective emissivity of the planet (239 W/m^2 / 385 W/m^2) which results in a value of 0.3 C per W/m^2. This is not the zero feedback sensitivity, but the current sensitivity after all feedback, positive, negative, known and unknown has already their effects on the resulting surface temperature.
Because Earth is homeostatic, ie its climate regulates itself, feedbacks to any “forcing” from increased GHGs are most likely net negative. Hence ECS should be less than the nominal 1.2 degrees C per doubling of CO2 concentration. In some regions and seasons, it could even be less than 0.0 degrees C.
Because Willis admits he misunderstood and errored he cannot be a Warmist.
In fact, he meets the traditional definition of a “Scientist”. No Government job for Willis.
Really appreciate your efforts Willis.
Willis,
“This implies a pre-feedback sensitivity…”
How can you be sure that no feedbacks are involved in the data, especially the cliff?