Pre- and Post-Feedback Sensitivity

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.

taguchi monckton equationORIGINAL 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.

toa olr vs sst ceresFigure 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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101 thoughts on “Pre- and Post-Feedback Sensitivity

  1. “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.”

      • This is just a test, to see how to generate an “approximately equal” symbol in WordPress…
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  2. 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

      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.

      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.

      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.

      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 the negative of the change in outgoing radiation (∆W) per one degree change in surface temperature ((∆T).

        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.

  3. 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

      I just wonder how applying the evident curve of effects of CO2 changes the numbers from a linear measure.

      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.

    • 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.

      • “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”

  4. “,,,,,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.

    • 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.

      • “…. 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.

  5. “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.

  6. 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?

  7. 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.

  8. 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

        Hi Willis
        Mark of a good scientist is to be able to admit errors. That happens sometimes to everyone, especially in blogs.

        Errors are my guideposts to the correct path …

        You have spelled my middle name incorrectly by the way.
        Jan

        Fixed, Jan. My motto is “Perfect is good enough” … and thanks for all of your contributions.
        w.

    • Jan,
      You say:-

      What would then happen if you increased the radiation globally?

      You then add 150 W/m2 to both locations in your model example.

      For simplicity, consider that the radiation increases with 150W/M2 so we get 400 W/m2 to C2 and 650 W/m2 to W2.

      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.

  9. 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

        • My calcs based on non-linear regression of Hadcrut4

          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.

  10. 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?

  11. 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.

  12. 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.

  13. 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.

    • 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?)

        • 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.”

          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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. Willis,
    “This implies a pre-feedback sensitivity…”
    How can you be sure that no feedbacks are involved in the data, especially the cliff?

  19. 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.

  20. 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.

  21. 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:

    [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 … ]

    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.

  22. @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.

  23. 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.

  24. Monckton of Brenchley August 20, 2016 at 10:13 pm
    Christopher, always good to hear from you. To take your objections one by one:

    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;

    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:

    “Bony et al. (2006), also cited by IPCC (2007), do not state a value for κ. However, they say –
    “The Planck feedback parameter [equivalent to κ–1] is negative …”

    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?

    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;

    You may not have noted up at the top where I said:

    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.

    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.

    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;

    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 …

    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 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.

    and he was incorrect in imagining that the value of lambda-zero had been determined without regard to latitudinal non-linearities.

    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?

    Apart from that, Mrs Lincoln, how did you enjoy the play?

    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.

      • 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.

          • 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.

            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.

            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.

            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.

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