Some Comments on the Lindzen and Choi (2009) Feedback Study
by Roy W. Spencer, Ph. D.
I keep getting requests to comment on the recent GRL paper by Lindzen and Choi (2009), who computed how satellite-measured net (solar + infrared) radiation in the tropics varied with surface temperature changes over the 15 year period of record of the Earth Radiation Budget Satellite (ERBS, 1985-1999).
The ERBS satellite carried the Earth Radiation Budget Experiment (ERBE) which provided our first decadal-time scale record of quasi-global changes in absorbed solar and emitted infrared energy. Such measurements are critical to our understanding of feedbacks in the climate system, and thus to any estimates of how the climate system responds to anthropogenic greenhouse gas emissions.
The authors showed that satellite-observed radiation loss by the Earth increased dramatically with warming, often in excess of 6 Watts per sq. meter per degree (6 W m-2 K-1). In stark contrast, all of the computerized climate models they examined did just the opposite, with the atmosphere trapping more radiation with warming rather than releasing more.
The implication of their results was clear: most if not all climate models that predict global warming are far too sensitive, and thus produce far too much warming and associated climate change in response to humanity’s carbon dioxide emissions.
A GOOD METHODOLOGY: FOCUS ON THE LARGEST TEMPERATURE CHANGES
One thing I liked about the authors’ analysis is that they examined only those time periods with the largest temperature changes – whether warming or cooling. There is a good reason why one can expect a more accurate estimate of feedback by just focusing on those large temperature changes, rather than blindly treating all time periods equally. The reason is that feedback is the radiation change RESULTING FROM a temperature change. If there is a radiation change, but no temperature change, then the radiation change obviously cannot be due to feedback. Instead, it would be from some internal variation in cloudiness not caused by feedback.
But it also turns out that a non-feedback radiation change causes a time-lagged temperature change which completely obscures the resulting feedback. In other words, it is not possible to measure the feedback in response to a radiatively induced temperature change that can not be accurately quantified (e.g., from chaotic cloud variations in the system). This is the subject of several of my previous blog postings, and is addressed in detail in our new JGR paper — now in review — entitled, “On the Diagnosis of Radiative Feedbacks in the Presence of Unknown Radiative Forcing”, by Spencer and Braswell).
WHAT DO THE AMIP CLIMATE MODEL RESULTS MEAN?
Now for my main concern. Lindzen and Choi examined the AMIP (Atmospheric Model Intercomparison Project) climate model runs, where the sea surface temperatures (SSTs) were specified, and the model atmosphere was then allowed to respond to the specified surface temperature changes. Energy is not conserved in such model experiments since any atmospheric radiative feedback which develops (e.g. a change in vapor or clouds) is not allowed to then feed-back upon the surface temperature, which is what happens in the real world.
Now, this seems like it might actually be a GOOD thing for estimating feedbacks, since (as just mentioned) most feedbacks are the atmospheric response to surface forcing, not the surface response to atmospheric forcing. But the results I have been getting from the fully coupled ocean-atmosphere (CMIP) model runs that the IPCC depends upon for their global warming predictions do NOT show what Lindzen and Choi found in the AMIP model runs. While the authors found decreases in radiation loss with short-term temperature increases, I find that the CMIP models exhibit an INCREASE in radiative loss with short term warming.
In fact, a radiation increase MUST exist for the climate system to be stable, at least in the long term. Even though some of the CMIP models produce a lot of global warming, all of them are still stable in this regard, with net increases in lost radiation with warming (NOTE: If analyzing the transient CMIP runs where CO2 is increased over long periods of time, one must first remove that radiative forcing in order to see the increase in radiative loss).
So, while I tend to agree with the Lindzen and Choi position that the real climate system is much less sensitive than the IPCC climate models suggest, it is not clear to me that their results actually demonstrate this.
ANOTHER VIEW OF THE ERBE DATA
Since I have been doing similar computations with the CERES satellite data, I decided to do my own analysis of the re-calibrated ERBE data that Lindzen and Choi analyzed. Unfortunately, the ERBE data are rather dicey to analyze because the ERBE satellite orbit repeatedly drifted in and out of the day-night (diurnal) cycle. As a result, the ERBE Team advises that one should only analyze 36-day intervals (or some multiple of 36 days) for data over the deep tropics, while 72-day averages are necessary for the full latitudinal extent of the satellite data (60N to 60S latitude).
Lindzen and Choi instead did some multi-month averaging in an apparent effort to get around this ‘aliasing’ problem, but my analysis suggests that the only way around the problem it is to do just what the ERBE Team recommends: deal with 36 day averages (or even multiples of that) for the tropics; 72 day averages for the 60N to 60S latitude band. So it is not clear to me whether the multi-month averaging actually removed the aliased signal from the satellite data. I tried multi-month averaging, too, but got very noisy results.
Next, since they were dealing with multi-month averages, Lindzen and Choi could use available monthly sea surface temperature datasets. But I needed 36-day averages. So, since we have daily tropospheric temperatures from the MSU/AMSU data, I used our (UAH) lower tropospheric temperatures (LT) instead of surface temperatures. Unfortunately, this further complicates any direct comparisons that might be made between my computations (shown below) and those of Lindzen and Choi.
Finally, rather than picking specific periods where the temperature changes were particularly large, like Lindzen and Choi did, I computed results from ALL time periods, but then sorted the results from the largest temperature changes to the smallest. This allows me to compute and plot cumulative average regression slopes from the largest to the smallest temperature changes, so we can see how the diagnosed feedbacks vary as we add more time intervals with progressively weaker temperature changes.
RESULTS
For the 20N-20S latitude band (same as that analyzed by Lindzen and Choi), and at 36-day averaging time, the following figure shows the diagnosed feedback parameters (linear regression slopes) tend to be in the range of 2 to 4 W m-2 K-1, which is considerably smaller than what Lindzen and Choi found, which were often greater than 6 W m-2 K-1. As mentioned above, the corresponding climate model computations they made had the opposite sign, but as I have pointed out, the CMIP models do not, and the real climate system cannot have a net negative feedback parameter and still be stable.
But since the Lindzen and Choi results were for changes on time scales longer than 36 days, next I computed similar statistics for 108-day averages. Once again we see feedback diagnoses in the range of 2 to 4 W m-2 K-1:
Finally, I extended the time averaging to 180 days (five 36-day periods), which is probably closest to the time averaging that Lindzen and Choi employed. But rather than getting closer to the higher feedback parameter values they found, the result is instead somewhat lower, around 2 W m-2 K-1.
In all of these figures, running (not independent) averages were computed, always separated by the next average by 36 days.
By way of comparison, the IPCC CMIP (coupled ocean-atmosphere) models show long-term feedbacks generally in the range of 1 to 2 W m-2 K-1. So, my ERBE results are not that different from the models. BUT..it should be remembered that: (1) the satellite results here (and those of Lindzen and Choi) are for just the tropics, while the model feedbacks are for global averages; and (2) it has not yet been demonstrated that short-term feedbacks in the real climate system (or in the models) are substantially the same as the long-term feedbacks.
WHAT DOES ALL THIS MEAN?
It is not clear to me just what the Lindzen and Choi results mean in the context of long-term feedbacks (and thus climate sensitivity). I’ve been sitting on the above analysis for weeks since (1) I am not completely comfortable with their averaging of the satellite data, (2) I get such different results for feedback parameters than they got; and (3) it is not clear whether their analysis of AMIP model output really does relate to feedbacks in those models, especially since my analysis (as yet unpublished) of the more realistic CMIP models gives very different results.
Of course, since the above analysis is not peer-reviewed and published, it might be worth no more than what you paid for it. But I predict that Lindzen and Choi will eventually be challenged by other researchers who will do their own analysis of the ERBE data, possibly like that I have outlined above, and then publish conclusions that are quite divergent from the authors’ conclusions.
In any event, I don’t think the question of exactly what feedbacks are exhibited by the ERBE satellite is anywhere close to being settled.
“”” timetochooseagain (21:21:42) :
He meant in the sense that the slope corresponds inversely to the feedback, so the parameter (slope) has the opposite sign.
A system which responds to warming by slowing infrared cooling further is essentially the climatological equivalent of a divide by zero error. The “no feedback” situation is in fact one in which the normal behavior between radiation and temperature occurs, namely that hotter bodies emit more IR. In more typical terms, this would in fact be called a “negative” feedback. See here:
http://www.drroyspencer.com/2009/04/when-is-positive-feedback-really-negative-feedback/ “””
The Planck (and Stefan-Boltzmann) radiation law is NOT a feedback process; it’s the very epitome of a non-feedback relationship. (talking BB radiation)
It’s a perfect reversible process with the same gain parameter in either direction. A BB at a single fixed temperature (K) emits a specific EM radiation; completely specified at all frquencies from DC+ up to infinity -.
The absorption of that same radiation spectrum by another BB will establish the same temperature in it, that the original BB had. This is a complete distortion of the concept of feedback.
kim (09:55:14) :
“Bob Tisdale @ur momisugly 4:45:58
So with the cooling phase now, are there more clouds? That would make the increasing CO2 no longer correlated so not causative. Unless the effect changed, and I wouldn’t put it past the ability of this climate system to be that changeable. Perish the thought, which is immortal.”
Reply: It’s not just the amount of cloud that matters. It’s also important to know the type of cloud, it’s thickness, it’s altitude and colour e.t.c. All these factors effect how a given cloud will mediate climate, in conjunction with what’s happening with the other mechanisms it is related to.
Wheels within wheels. No easy answers I’m afraid – but it would be no fun if it was easy.
kim (09:55:14) :
Bob Tisdale @ur momisugly 4:45:58
So with the cooling phase now, are there more clouds?
Yes, according to Palle et al:
http://www.bbso.njit.edu/Research/EarthShine/
kim (09:55:14) :
So with the cooling phase now, are there more clouds?
http://www.climate4you.com/images/HadCRUT3%20and%20TropicalCloudCoverISCCP.gif
The cognitive dissonance must be painful.
In short, Dr. Spencer is pointing out that Lindzen palmed a card by comparing observations against AMIP simulations, which are diagnostic, not predictive in nature.
AMIP-style simulations are routinely performed at many climate and NWP centers during model development in order to evaluate atmospheric model performance and identify errors.
This model configuration enables scientists to focus on the atmospheric model without the added complexity of ocean-atmosphere feedbacks in the climate system. It is not meant to be used for climate change prediction, an endeavor that requires a coupled atmosphere-ocean model (e.g., see AMIP’s sister project CMIP).
A more relevant link than the wiki is
http://www-pcmdi.llnl.gov/projects/amip/index.php
where it says that:
“AMIP is now an integral part of CMIP
AMIP-style simulations are routinely performed at many climate and NWP centers during model development in order to evaluate atmospheric model performance and identify errors. The systematic intercomparison of atmospheric model components is currently being coordinated under the Coupled Model Intercomparison Project (CMIP), which includes AMIP simulations as an integral part.”
Dr.Spencer,
In the light of the widespread and premature euforia / hysteria (including even appearance on Fox News Glenn Beck show) that followed the Lindzen and Choi paper, a critical scientific analysis of Lindzen’s findings was long overdue.
So on behalf of science, THANK YOU for bringing your findings of the ERBE data to a wider audience, and THANK YOU for being bold enough to expose the shaky scientific basis on which Lindzen based his conclusions.
I have one burning question regarding the work that both you and Lindzen did :
Lindzen found a feedback parameter of an average 4 W/m^2/K (with a fairly wide standard error) from the ERBE data analysis.
You seem to find a lower parameter of 2 – 4 W/m^2/K.
As Lindzen explains in his paper, in climatology the zero-feedback response (f=0) corresponds to a feedback parameter F = 4 W/m^2/K.
So it seem would think that Lindzen found a feedback factor 0.
Similarly, it seems that you found a feedback factor 0 to +1, indicating a mild to strong positive short-term feedback.
The burning question then is : How can Lindzen claim a negative feedback factor -1 ?
“”” Kevin Kilty (20:20:48) :
Dr. Spencer,
You said
“the real climate system cannot have a net negative feedback parameter and still be stable”
I think you meant net positive feedback. “””
Well that is not a true statement either. A net positive feedback CAN be quite stable; and there are many examples of such.
Take the simple Drum brakes that they used to have on cars; before the days of disc brakes. The earlier types of drum brake systems, had two brake shoes which had one end located by a pin attached to the frame of the brake assembly. At the other end of the two shoes, a single hydraulic cylinedr and piston acted to push the two shoes apart, while the other ends were held in place. This pushed the shous outwards to contact the brake drum. Now one of the shoes had the stop pin “ahead” of the moving end, as far as the direction of rotation. This is called a “leading” shoe. When the leading shoe contacts the drum, the friction developed adds to the force pushing the shoe harder against the drum, so a stronger braking torque is generated for a given pedal force. A perfect example of a positive and quite stable feedback system.
Now the other shoe in this simple system has the pin end behind the moving end, in the normal rotation direction; so it is called a “trailing” shoe; and in this case the friction developed between teh shoe and the drum, acts in the opposite direction to “unwrap” the shoe from the drum, and thereby diminish the net friction. this is an example of negative feedback.
Now someone realized that the positive feedback of the leading shoe assisted the driver in applying the brakes with a lower pedal pressure, so they invented a system where the two shoes were linked by a floating pin. and the brake piston moved the floating end of the pair, while the other end was locked by the fixed pin. This gave a “two leading shoe” design which gave much more braking torque than the single leading/trailing shoe design.
But then they discovered a problem. the brake pad material on the shoes had a coefficient of friction which diminished at higher temperatures, and in some cases the resin binder of the pad meaterial would melt and form a shiny layer on the surface of the shoes, with a greatly reduced friction.
With a two leading shoe design where the total braking force depended on the self wrapping feedback, the result of this temperature effect was a serious brake fade, and loss of breaking effect whent he brakes goit hot.
That is one of the problems with positive feedback; the overall gain variability is increased by positive feedback; the system is noisier.
The solution for quality cars was to reverse the system, and make the braking system a two trailing shoe designe; with negative feedback for both shoes. Now the feedback due to the trailing shoes led to self unwrapping, and if the coefficient of friction decreased due to temperature, the unwrtapping feedback effect was diminished so the net force holding the shoes against the drum increased, and the effect of the diminished friction was reduced. The negative feedback of the two trailing shoe designs resulted in a substantial improvement in the brake fade characteristics. The penalty of course was a higher brake pedal force requirement; so additional servo boosters were added to the system to diminish the required pedal pressures.
Of course modern disc brakes have no feedback mechanical effects so the brake fade problem is largely a thing of the past.
Then of course there is the superregenerative receiver, where positive feedback is used to increase the gain of a radiao receiver amplifier. As in the brake case, the presence of positive feedback increases the noise in the system, making the gain less stable; but still not unstable.
The requirement for stability of a feedback amplifier is once again a criterion due to Nyquist. The quantity 1 + AB in Dr Roy’s first post on feedback is known as the Loop gain. The Nyquist criterion for stability is that the complex plane plot of 1+AB from zero to infinite frequency, must not encircle the point -1,0 in that complex plane diagram.
Single pole amplifiers are unconditionally stable, as they can only produce 900 degrees of phase shift at a point where the magnitude of the loop gain is zero, so the locus of the loop gain never crosses the negative real axis at all; or the negative imaginary axis either. A two pole amplifier can produce 180 degrees of phase shift but only at zero magnitude of the loop gain, and the negative real axis is never crossed by the loop gain locus.
With three poles, the phase shift can get to 270 degrees, so both the negative imaginary, and the negative real axes are crossed by the loop gain locus. In some cases the real negative axis is crossed between the origin, and the -1.0 point so the amplifier is stable. In other cases it crosses outboard of the -1,0 point so the amplifier is unstable (oscillator).
A third possibility is for the loop gain locaus to cross the negative real axis beyond the -1 point, but then recross the negative real axis still outside the -1 point, and proceed back to the origin still with a negative imaginary value. This is caalled conditional stability; and it will oscillate and become unstable, if the forward gain is reduced, which will eventually result in the -1,0 point getting encircled by the loop gain locus.
So in the climate system; you could have an overall positive feedback (who knows) but that does not mean that any runaway condition can or will occur. That depends on the loop gain of the feedback system and the root locus plot over all frequencies.
Well climate folks don’t even include time in their feedback circuits, so there is no way they can know whether they are unstable or not.
And I repeat that standard feedback theory assumes that the forward gain block (A) is strictly unidirectional. It is highly unlikely that anything in the climate system that could be compared as an analog of (A), is a simple unidirectional process.
Now this doesn’t mean that feedback analysis cannot be performed on such a system; it just means that the usual simplefied results of ordinary feedback analysis are no longer valid; and the full bidirectional network equations have to be solved fully allowing for the bidirectionality of both the blocks (A) and (B). This complexit will also inevitably get involved in both thdriving point impedance at the signal end, and the load impedance at the output of the fedback system.
I defyt amybody to speculate what those spource and load impedances are; or even what they consist of in the global climate system.
Maybe Peter Humbug has a full bidirectional feedback model of the climate including driving point and load impedances; but I doubt it.
The water cycle has some of the properties of an automobile charging system including the Voltage Regulator. At low charge rates temperatures and water vapor content) there is a positive feedback gain increase; but then whent he temperature gets up to a certain value the “Voltage regulator” kicks in, in the form of formation of precipitation containing clouds; which give a strong negative feedback curtailment of the temperature rise; by stopping solar radiation from reaching the surface, and further raising the temperature.
Only water serves this function in earth’s atmosphere; and that regulated “Voltage” where the warming is terminated; is simply a property of the physical properties of water.
DJ Meredith says:
Really? And, you know this how exactly?
George E Smith says:
You seem to be arguing about definitions. It acts as a feedback in the climate system in the very real sense that any radiative imbalance leads to warming (or cooling) and the rise in temperature and the resulting effect described by the radiation law is to then reduce this radiative imbalance, so it “feeds back” on the original radiative imbalance.
Unfortunately, there has been some confusion in the climate science field because some scientists have used the term in this way (i.e., with the response described by the S-B Eq. being a negative feedback) while others have computed the temperature response to the increase in radiative forcing that is given by the S-B Law as the zeroth-order response and considered this to be the zero feedback case and then talked about net negative or positive feedbacks relative to this that then correspond to either decreasing or increasing the temperature response, respectively. The physics is the same no matter which way one chooses to think about it, but when people talk about the net feedback in the climate science context, one does have to understand whether they are defining it in a way that includes or excludes the radiative response described by the S-B Law as a feedback or not.
George E. Smith (15:48:54) :
“Of course modern disc brakes have no feedback mechanical effects so the brake fade problem is largely a thing of the past.”
What an excellent and detailed (yet understandable) post. Many thanks.
However can I add another angle to the comment quoted?
It is undoubtedly true that disk brakes are hugely better than drum brakes for out and out performence and temperature handling. However there are other factors that can impact the overall result, an obvious one being the additional complexity of providing a full proof handbrake function for a disk based system. Much easier using a drum brake.
On the plus side they are less prone to the negative braking effects of water immersion.
But braking systems have moved on as people have realised other potential uses for wheel speed control in the computer age and so new challenges have been established that many people are not aware of. Under normal use conditions most people will remain entirely unaware of them all of the time. But run something like an Electronic Stability Control system up to its limits and the situation changes.
Whilst a normal vehicle with equal suspension and tyre pressures will apply a balanced brake force (as per a designed loading split front/rear) to all wheels at the same time the ESC system will apply irregular forces to independent wheels on an as required basis. Normally this is not a problem since applications are light and/or short and are well within the heat dissipation capabilities of the system.
The ESC systems are invariable instituted as part of an ABS setup. Whilst ABS will, in most situations, stop a wheel from locking (more than momentarily) it does mean that people can be sucked in to using their brakes more than normal and more harshly than normal in some situations. If a brake locks the disk/pad are no longer in conflict and heat generation ceases at that point and transfers to the tyre/road surface. (In concept).
If the brake does not lock the disk/pad will continue to generate heat. Thus with heavy use of an ABS system the rate of heat creation could be higher than a non-ABS system and whilst the wheels will not lock (usually), fade can still occur although one may not notice it in the same way since it is masked by the ‘feel’ of the ABS system
It would be unusual to experience this during normal road driving but on a closed track at speed or perhaps an Alpine mountain pass at quite ‘normal’ speeds, the potential for the system to become ‘unstable’ through overheating is quite readily apparent – mainly because it likely works so well that you don’t even think there might be a problem.
Now add in ESC. On a straight road the chances are it is doing nothing at all. At speed on unstraight roads it may be doing a little but you won’t feel it. At speed on a closed track, twisting road or Alpine Pass the chances are it will be working quite hard – much harder than you realise. All that handling ability and stability is not just a great suspension setup, excellent tyres and a fantastic driver – its the braking system being used by the ESC system to keep thing under control.
If you are heavy braking as well the brakes and pads will become progressively hotter. Indeed on a twisty road even if you think you have slowed to ‘cool’ the brakes the chances are that the ESC system has taken on some extra work and you are not actually achieving what you thought you were achieving in terms of brake cooling. There will be brake fade – your first warning may be a burning smell and/or smoke as the pads get very warm indeed. If you are really perceptive (or very short – LOL) you may previously have noticed that the distance you need to push the brake pedal has increased somewhat and that even with it pressed hard against the bulkhead things are still rushing past outside …
Hidden feedbacks you see. There is more to the system than meets the eye.
On the other hand if you have a competition car, usually without any of these driver aids, you may have the opposite problem. Tyre pressures and brake temperatures often rely on a lot of heat build up above ambient for their efficiency. If you don’t work the tyres and they lose heat and so pressure, so surface grip suffers. Don’t use the brakes and the temperatures drop and braking effect suffers. They need heat to work in much the same way that we need heat to survive and thrive. Varying temperatures will have other, often unpredictable, effects on the performance of the car as interpreted by the driver (and maybe any passengers!)
Now let us for an example assume that the only criteria we have for cars is that they must satisfy both regular use (but with the odd traverse of mountain passes from time to time) and high speed competition. We ignore all other design inputs (making assumptions about basic functionality being adequate) and focus solely on the brakes, averaging the results from the extremes of use.
How meaningful would the the model for the global average car actually be and how well could the performance of its brakes, with the ‘expected basic functionality feedbacks’ built in, be assessed against all requirements? After all we are only talking about a bit of heat transfer variability from time to time in what is, most commonly, a fairly stable environment according to usage type.
My guess is that both usage types would still experience brake fade with the global car. For different reasons of course.
Footnote.
I have had all four sets of pads on my car (pads and disks almost new at the time) smoking mightily after a few miles of spirited driving (on a closed track). The world did not end and they recovered what seems to be full performance a few miles of use later. It’s amazing how things survive extremes and stabilise about ‘the norm’ given a chance.
AFTER READING ALL OF THE ABOVE, I COME TO THE CONCLUSION THAT IT WOULD BE A GOOD IDEA FOR SPENCER TO GO TO MIT AND SIT DOWN WITH LINTZEN UNTIL THEY CAN THRASH THIS OUT. THIS DISCUSSION REMINDS ME OF A QUOTATION FROM OMAR,
“MYSELF WHEN YOUNG DID EAGERLY FREQUENT
DOCTOR AND SAINT,HEARD GREAT ARGUMENT
ABOUT IT AND ABOUT; BUT EVERMORE
CAME OUT BY THE SAME DOOR AS IN I WENT”
REPLY: THE CAPLOCK BUTTON TOGGLES ON MOST KEYBOARDS AND CAN BE USED FOR TYPING WITHOUT SHOUTING ~ CHARLES THE REALLY LOUD MODERATOR
Re AMIP vs. CMIP: AMIP is not part of CMIP, but it is used to validate it. Here is a comment I left on a recent board:
CMIP and AMIP agree closely in their fundamental predictions. If you remove the positive feedback from the AMIP, they will diverge considerably.
In this paper, the authors state of the CMIP models:
The paper then discusses “two recently developed coupled models that do not use flux adjustment.” I read that as, the CMIP models were tweaked specifically to bring them closer in line to the AMIP results, i.e., the AMIP models were used as “truth” models to validate the CMIP. It follows that if the AMIP models are buggered, so are the CMIP models, yes?
The CMIP typically diverges from AMIP. To bring them in line, researchers use fudge factors. Or, they find a CMIP which agrees with AMIP. Therefore, the veracity of AMIP is fundamental.
And, when I say AMIP, I generally mean an AMIP conforming AGCM model or models and mutatis mutandis for CMIP. I’m writing in shorthand, so don’t anybody give me any grief for what should be understood.
“A net positive feedback CAN be quite stable; and there are many examples of such.”
Only when stabilized by a more potent negative feedback. Your brake pad example has an overriding negative feedback in the ablation of the asbestos pads, which prevents ever increasing pressure. Or, if the pads cannot ablate fast enough, the wheel locks, at which point the positive feedback has driven you to the boundary of the state space.
A positive feedback within an overall negative feedback loop is not unstable, but it does amplify the response and bring the system closer to the boundary of instability.
Consider a very simple heuristic CO2 model. Let the amount of CO2 in the atmosphere be quantified by X. Assume there is a forcing function pushing CO2 into the air, call it U. At the same time, CO2 is being taken out by processes on the ground, and suppose the rate that they take it out is proportional to the amount in the air with a proportionality constant K > 0. The differential equation is then
Xdot = -K*X + U
The -K*X term is a negative feedback. In the steady state, with U constant, X approaches XSS = U/K.
Suppose there is another process with adds CO2 into the air proportional to the amount already there, with proportionality constant eps > 0. The differential equation becomes
Xdot = -K*X + eps*X + U = -(K-eps)*X + U
As long as K > eps, the system is stable. But, the steady state value of X is XSS = U/(K-eps), i.e., the sensitivity XSS/U is increased by a factor K/(K-eps).
If eps happened to be negative, the sensitivity would have decreased. That is what the Lindzen paper is all about. A positive feedback would amplify the temperature, while a negative one would attenuate it. Lindzen says this crucial feedback, which is positive in all the AIMP models, and begets the increased sensitivity upon which the dire prognostications are based, is, in fact, observationally negative.
“…but it does amplify the response and generally brings the system closer to the boundary of instability.”
Bob Tisdale (09:23:45) :
“Richard M (07:02:12) : I believe it could be argued that the paper indicates that the interpretation of the models has been wrong. Regardless, it’s an interesting paper.”
Well, I may have been a little strong but, they did throw out about half the models up front. The others were then re-interpreted based on findings that were not understood by any of the model developers. Hmmmm. Add in the fact that many models are often “averaged” to get meaningful results and my own interpretation is ALL the models are now in question … as they should be.
“”” Bart (20:30:12) :
“A net positive feedback CAN be quite stable; and there are many examples of such.”
Only when stabilized by a more potent negative feedback. Your brake pad example has an overriding negative feedback in the ablation of the asbestos pads, which prevents ever increasing pressure. Or, if the pads cannot ablate fast enough, the wheel locks, at which point the positive feedback has driven you to the boundary of the state space. “””
Sorry; but I don’t agree. In the case of the leading shoe brake positive feedback; it is a very trivial leverage situation designed into the particular geometry of the shoe. The circumferential friction force is simply the net outward force between the shoe and the drum times the coefficient of friction. The fulcrum point of the lever arm at which that friction force acts, is the center of the stop pin at the leading edge of the shoe, and by design (and necessity) that is placed at a smaller radius than the drum radius. The torque set up by that friction force times that short lever arm creates an additional outward thrust on the shoe that is that torque divided by the effective length of the shoe, which depends on the exact design of the shoe. But that additional outward force is a fraction of the hydraulically applied force., so the gain is only fractionally greater than one.
There is no overall negative feedback whatsoever. Any rate of wear of the brake pad material is so slow that there is no geometry change that results from brake erosion during any braking incident.
But that is quite beside the point, because your statement That the positive feedback system can only be stable in the presence of “more powerful” negative feedback is simply not true. the system will only be unstable when the Nyquist condition says it is unstable; meaning the complex plane plot of the loop gain locus encircles the -1,0 point. That condition can occur in “negative feedback” systems, because the propagation delays in both the forward gain block (Dr Roy’s (A),) and also in the feedback block (B). results in a phase shift at some frequency that turns a subtractive feedback into an additive one, and the amplitude is such at those frequencies that the -1,0 point is encircled.
However it is in fact (used to be anyway) quite reasonable to employ positive feedback inside the forward gain block (A) of a feedback system; that employs a negative feedback block (B).
The reason for that is that the magnitude of the forward gain (A) is thereby increased, due to the positive feedback, and that will result in the residual errors (at low frequencies) of the overall system to be reduced..
In feedback systems where |A| is high, the closed loop gain can be made highly independent of (A), and dependent only on the feedback network (B) which in electronic feedback systems, can be made from highly accurate and stable components. The fact that the positive feedback inside the (A) block makes |A| more noisy and variable; does not detract from the potential benefits of having a higher forward gain because of the positive feedback.
Stable positive feedback is similar in concept to the idea of the infinite sum
S = 1 +1/2+1/4+1/8+… which sums to 2.
Whereas the sum 1+1/2+1/3+1/4+1/5+… is unstable.
Certainly positive feedback gain blocks inside negativew feedback loops are not as good as a system where the full forward gain is obtained without regeneration; but they can be a better solution than one that simply makes do with a lower gain (A).
Of course this is all irrelevent to climate systems, since none of the processes of climate have anything like the kind of gains that electronc feedback systems can conjure up.
But the more important point is that as near as I can tell from the literature; absolutely nothing is known about the time domain or frequency domain response of any of the putative elements of any climate feedback system; and I still think the concept of feedback is quite overused when discussing climate; particularly because none of the involved processes are even remotely unidirectional; which is a fundamental assumption of simple feedback analytical mathematics. More often the processes are like chemical reactions where the equilibrium can be driven in either direction depending on the conditions; they are not really gain systems at all.
Once integrated operational amplifiers became popcorn elements of analog circuitry, the op-amp people went totally nuts, and the ideal op amp in their minds had gains of over a million; and they weren’t at all concerned that the open loop frequency respons had a cuoff frequency of 1-10 Herz.
It was always my contention that the open loop forwqard gain of any feedback amplifier system; should be at least that which was required of the closed loop final result; and that the forward gain should be whatever one could muster, while still meeting that bandwidth need. The result of course would be that the dc accuracy of the system might be lower (well it would be) but if for example you were trying to build a hi-fi stereo system; who the hell wants a DC resonse anyway.
The result of using the infinite gain zero bandwidth op amp approach is that since the forward gain starts dopping at very low frequencies, the benefits of the feedback get shed right from those lower frequencies; once the gain of the (A) block starts falling.
But these days; people have no idea what high fidelity stereo sounds like; they are quite happy with MP3 quality; well it is more than adequate for the current song du jour mentality of today’s “music” listeners. Stereo system sound quality has gone steadily backwards since about 1980; and now you can get a whole “hi-fi” system about the size of a match box. it takes 500 Watts to run it; but it sure is small.
All you have to do is play a French Organ work through it to learn what a piece of crap it really is.
None of which has anything to do with climate; but I’m quite sure that the climate science folks don’t know any more about feedback systems than the MP3 people and ipod people do.
I don’t understand either the Lindzen paper or Spencer’s alternative. Here’s my rudementary understanding of thew way things should work from a basic physics perspective. If you can explain how the analysis of the satellite data and the climate system should differ from this, please let me know how and why.
Take the theoretical example of a planet irradiated by a sun and encircled by an imaginary device that measures all radiant energy (black body energy or whatever you want to call it) leaving said planet. Let’s say there is a certain rate of energy absorbed by the planet (actually a sum of energy made by the planet in the form of geothermal energy, plus radiant energy from the sun absorbed by the planet), expressed in watts. Let’s call that number of watts W in. Let’s say that W in is constant over a given interval of time. Now let’s designate the amount of black body irradiation leaving the planet as W out. Let’s start off with the planet very cool, emitting relatively little black body irradiation, such that W out < W in. My understanding of physics, the planet and its atmosphere will gradually warm, this increasing the black body radiation emitted by the planet, until W out approaches and becomes exactly equal to W in. That's the steady state, when the outgoing black body radiation is exactly equal to the incoming radiation absorbed by the planet plus the geothermal energy, W (a measure of power). W out = W in.
Now let's introduce a greenhouse gas into the atmosphere of this hypothetical planet, leaving the input W in the same. What should happen? Well, initially, the amount of black body radiation emitted by the planet should decrease due to the greenhouse gas blocking some of the outgoing black body radiation, such that W out < W in. However, because W out < W in, the planet should gradually warm. How much should it warm? Well, the surface should warm, resulting in more black body radiation leaving the surface, until conditions are met such that, even when some of this radiation is blocked by the greenhouse gas, the total amount of black body radiation leaving the planet once again equals W in. So once again, W out = W in.
So here is the part I don't understand. You have a satellite that is ostensibly measuring black body radiation leaving a planet. It is essentially measuring W out. How can this satellite detect the temperature influence of a greenhouse gas? You may introduce a greenhouse gas into the atmosphere. This will block some of the block body energy leaving the planet; initially the detected W out will decrease, but only for so long as it takes for the surface to warm to compensate for absorbance of the greenhouse case, until W out once again = W in.
So from my perspective as a physicist, a satellite measuring outgoing black body radiation from a planet may see changes in outgoing intensity only under the following conditions:
A) Changes in solar irradiance, resulting in changes in W in.
B) Changes in albedo of the planet, resulting in changes in W in.
C) Changes in the geothermal energy production of the planet, resulting in changes in W in.
D) Changes in the directionality of the flux of energy W out flowing from different parts of the planet (e.g. more proportion of outgoing black body irradiation leaving the equator vs. the poles if the satellite only measures at the equator).
However, a change in greenhouse gases should be completely undetectable to a satellite measuring black body irradiation, even if the surface temperature of the earth beneath the atmosphere changes. And if it is completely insensitive to one greenhouse gas (e.g. CO2), then it will also be completely insensitive to other greenhouse gases (e.g. water vapor, the basis for proposed high climate sensitivities).
What am I not understanding about this discussion?
I guess what I’m saying is, if the surface of a planet warms due to the effect of a greenhouse gas, a satellite measuring outgoing black body irradiation shouldn’t see it. It shouldn’t see any change in outgoing black body irradiation at all.
That is, unless there is some sophisticated stuff aboard that satellite that I don’t understand, or the satellite is measuring something other than what I think it’s measuring. What is that technology?
Bart (19:57:04) :
“Re AMIP vs. CMIP: AMIP is not part of CMIP, but it is used to validate it. Here is a comment I left on a recent board:
CMIP and AMIP agree closely in their fundamental predictions. If you remove the positive feedback from the AMIP, they will diverge considerably.
In this paper, the authors state of the CMIP models:
These coupled climate models have exhibited a problem not evident in the behavior of atmospheric GCMs run with prescribed SSTs and sea ice. Errors in fluxes of heat, momentum and water across the ocean-atmosphere interface can lead to “climate drift” away from observations. Nonphysical, ad hoc flux adjustments were initially regarded as necessary to correct the problem”
The modellers would certain have you believe that ‘flux adjustments’ are no longer required in their latest models BUT who is to say exactly what other ‘adjustments’ they have done to their models in order to keep stable on multi-centennial simulations?
For me, this is just ‘fluff’ and as Steve McIntyre would put it ‘moving the pea under the thimble’ i.e they;ve just swapped in a better numerical method for a lousey numerical method. The fact is the GCMs are full of parameterised equations which can be ‘tweaked’ to produce any desired result and changes to some of these parameters can have dramatic effects on their predictions (or should that be projections?). For example have a look at this link
http://www.climateaudit.org/?p=2564
From AR4 Chapter 8
“In many climate models, details in the representation of clouds can substantially affect the model estimates of cloud feedback and climate sensitivity (e.g., Senior and Mitchell, 1993; Le Treut et al., 1994; Yao and Del Genio, 2002; Zhang, 2004; Stainforth et al., 2005; Yokohata et al., 2005). Moreover, the spread of climate sensitivity estimates among current models arises primarily from inter-model differences in cloud feedbacks (Colman, 2003a; Soden and Held, 2006; Webb et al., 2006; Section 8.6.2, Figure 8.14). Therefore, cloud feedbacks remain the largest source of uncertainty in climate sensitivity estimates.
”
Yet the science is supposed to be settled to the extent that in December we will sign up to the Copenhagen Climate Change Treaty and transfer up to 2% of our GDP annually to developing countries in compensation for the ‘climate damage’ we have done to them? NOT!
KevinUK
If Lindzen&Choi’s ERBE paper were the main argument against AGW, the issue would be settled pretty soon. But of course it isn’t. Real climate feedback are overly complicated.
Lindzen in his Deconstruction: “The fact that _all_models show a negative slope corresponding to a positive feedback, has led virtually all scientific bodies including the IPCC to declare this property to be ‘robust’. But, what does the data show?”
Is this a precise account of the reasons for the widespread assumption of a net positive feedback from CO2 forcing? And if not, should it have any consequences for Lindzen?
Okay, just me being dumb again. But it seems to me that a satellite that measures outgoing black body irradiation from earth, provided its measurements are that of a steady state system (big if), should only be able to detect climate feedback changes originating from changes in albedo (e.g. clouds). It will not detect any changes in outgoing black body irradiation arising from greenhouse-type effects (e.g. CO2, water vapor, maybe also clouds) – because at least in the steady state, there are none.
julian (23:56:40)
Wouldn’t the satellite record a discrepancy between energy in and energy out during the period of time that the system is adjusting it’s temperature to an ongoing change, such as a steady increase in a particular greenhouse gas ?
Presumably, during the period of transition to a new equilibrium the energy out would be slightly less than the energy in.
The thing is that the Earth’s climate is in a state of constantly changing temperature equilibrium, not primarily because of changing levels of GHGs but much more because of the changes in the rate of energy flow through the system caused by large changes in the rate at which the oceans release energy to the air.
Yet the satellites seem not to notice that process of constant change as much as I think they should (do they see it at all ?).
Hence my suggestion that some process in the air is applying an equal and opposite climate forcing to the climate forcing provided by those changes in the rate of energy flow from the oceans.
My favoured candidates are the speed of the hydrological cycle in the troposphere combined with changes in the radiative properties of the stratosphere possibly caused by changes in the height, density and depth of the layers in the stratosphere.
Julian (23:56:40) :
I suppose the ERBE scatter plot, that shows Delta(radiationflow) versus delta(SeaSurfaceTemperature) is part of your
Julian (23:46:09) :
Now let’s introduce a greenhouse gas into the atmosphere of this hypothetical planet, leaving the input W in the same. What should happen? Well, initially, the amount of black body radiation emitted by the planet should decrease due to the greenhouse gas blocking some of the outgoing black body radiation, such that W out < W in. However, because W out < W in, the planet should gradually warm. How much should it warm? Well, the surface should warm, resulting in more black body radiation leaving the surface, until conditions are met such that, even when some of this radiation is blocked by the greenhouse gas, the total amount of black body radiation leaving the planet once again equals W in. So once again, W out = W in.
i.e. the transient part until the new equilibrium is reached, that energy has to leave and is what is being measured. That is why Spencer is picking on the short feedback and long feedback issue, a time issue, but before the new equilibrium is reached. Things do not happen instantaneously and give rise to the deltaXXX plotted. These quantities are drastically different for the AMIP protocol following model runs than for the ERBE data, and thus the models are exposed as giving wrong results and therefore should be scrapped..
If as Bart says the CMIP protocol runs are dependent on the AMIP protocol, all models are then exposed as wrong despite what Spencer is talking about above.
quote from Bart (19:57:04) :
Re AMIP vs. CMIP: AMIP is not part of CMIP, but it is used to validate it.
……..
CMIP and AMIP agree closely in their fundamental predictions. If you remove the positive feedback from the AMIP, they will diverge considerably.
……..
The CMIP typically diverges from AMIP. To bring them in line, researchers use fudge factors. Or, they find a CMIP which agrees with AMIP. Therefore, the veracity of AMIP is fundamental.
Julian, you are correct.
There is a time lag to consider though. How long does it take for “W out” to equilibrate with “W in” if there is an imbalance? The climate models consider this to be lag to be very long. I think this all mostly happens at the speed of light (with some molecules storing up the energy for a short of period) so the W out energy just takes a random walk sort of path on the way “out” but it is still very, very short. As a physicist, what do you think the lag times can be.
Secondly, the climate models consider the level of the atmosphere the W out temperature/radiation occurs on average to be the important metric (the tropopause). If there is more warming, the tropopause just goes up higher in the atmosphere. It is still the same W out, but now it is 500M higher up.
Given a standard lapse rate of 6C/km (temps increase in the atmosphere by 6C for every km below the W out tropopause layer), the surface will now be warmer.
So, if the satellites measured the change in radiation at the exact same layer where the tropopause started at 30 years ago, one could maybe calculate how the greenhouse effect is actually operating. (It sounds too hard to calibrate this properly to me however.)
Given all these complications, it is not hard to see where a climate model/theory could take a wrong turn and not describe the real Earth properly.