During the last three months, a paper by Lindzen and Choi (full text, PDF) has been repeatedly mentioned in the climate blogosphere.

Anthony Watts wrote about it July 2009. The key graphs were already announced in June, see Climate sensibilities and sensitivity on The Reference Frame.

This test of intelligence (which of the graphs depicting models doesn't belong here? The red one - it's reality) appeared in Climate feedbacks from measured energy flows, before I studied the paper more carefully.

The point of their paper is that in the reality, as measured by ERBE, the amount of outgoing radiation increases if the temperature increases. Lindzen and Choi claimed that all the 11 climate models had the opposite property: the outgoing radiation was shrinking if the Earth were getting warmer.

This conclusion of the models is paradoxical, contradicts the measurements, and Lord Monckton has elegantly promoted this disagreement on Glenn Beck's show. Unfortunately, I am going to argue that the falsification is not quite correct.

Update:Dick is convinced that I am missing something important and that the genuine response of the energy flows in the tropics to changing temperatures substantially and qualitatively differs from the Stefan-Boltzmann intuition. So please be assured that your humble correspondent may still be wrong about the essence and the paper by Lindzen and Choi may be completely correct. However, let me continue with the previous text.

**Criticism of the paper**

A week ago, under one of the TRF articles, a reader named Rob claimed that Lindzen and Choi have made a mistake. Rob Dekker claimed that they confused radiative forcing with its effect, i.e. with the increase of the black body temperature.

Because I had previously written a similar observation to Richard, I had to agree with Rob's point. They have essentially forgotten to subtract the "zero feedback" radiation from the total radiation when calculating the feedback; they have basically confused "f=0" and "f=1".

Because the nature of the mistake may sound confusing, there is a simple way to clarify what we mean. The key question is what a "zero feedback" situation predicts for the energy flows. Some elementary thermodynamics is helpful to answer this question.

The average Earth's surface brightness temperature is something like -15 °C: see the daily UAH data. Using the Stefan-Boltzmann constant and the "sigma T^4" law for the black body radiation, it is not hard to see that the radiation at this temperature, 258 Kelvin, is 251.22 W/m^2. Similarly, for 259 Kelvin, it is 255.14. For 1 °C of a temperature increase, we obtained the increase of the outgoing radiation by 4 W/m^2.

If the outgoing radiation depended on the temperature with this slope, 4 W/(m^2.K), then the feedback would be zero. You see that there is a lot of room for positive and negative feedbacks here. If the feedback were negative, the outgoing radiation would increase by more than 4 W/m^2 per 1 °C of warming. If the feedback were positive, the figure would be less than 4 W/m^2.

**But it's important that this figure remains positive.**

Lindzen and Choi claim that the models predict a negative value of this slope. That would be pretty dramatic because the models would not only fail to be quantitatively realistic: they would be unstable and predict a qualitatively wrong behavior.

In fact, the models would say that if the temperature increases, the Earth reduces its heat radiation, at least initially. That would clearly lead to an even higher warming and the temperature would start to diverge from the previous equilibrium exponentially: a classical unstable runaway behavior. It would be somewhat surprising if the models suffered from such an obvious flaw.

**Roy Spencer offers his wisdom**

Yesterday, Roy Spencer wrote his comments on the paper by Lindzen and Choi,

Some Comments on the Lindzen and Choi (2009) Feedback Study.He clearly agrees that the paper by Lindzen and Choi suffers from the significant flaw discussed above.

As you can see, climate skeptics are not really building their opinions on mindless groupthink, also known as the consensus. ;-)

See a talk by Richard Lindzen for the Cooler Heads Coalition (video, 6 parts per 10 minutes)Moreover, Spencer discusses some more subtle points, too. He praises the authors for looking at events with high temperature changes where the slope can be extracted with a rather high signal-to-noise ratio. And he criticizes them for using different averages of the ERBE data than the recommended averages over 72-day intervals for generic, non-equatorial latitudes (which can be reduced to the 36-day averages over the tropics): 36 days is the period of the precession of the satellite.

Spencer tries to reconstruct the paper by Lindzen and Choi. He concludes that when the errors known to him are fixed, no significant discrepancy between the models and the observations can be found by this method. Well, I am convinced that Spencer is right and the reason why the sensitivity is actually smaller than the models claim is more subtle and is linked to the fake feedbacks caused by "feed-forwards", i.e. the opposite causal relationships between the temperature and the would-be feedbacks such as changes of the cloud cover.

**Feedback factor**

I've had an e-mail exchange about this issue with Lord Monckton who used the main statement by Lindzen and Choi, too. Everything he wrote sounded pretty convincing. And concerning the sign predicted by the models, Lord Monckton told me: Believe me, the models really

*are*that stupid.

Well, such a statement is hard to disprove if I can't play with the models right now. But I knew that Lindzen and Choi - and Lord Monckton - couldn't be right because they were also implicitly making a model-independent statement about the relationship between the feedback factor, "f", and the changes of the outgoing heat. In fact, they were saying that if "f" were positive, and maybe even if the amplification ratio were a rather high positive real number, as the IPCC claims, the outgoing radiation would have to decrease if the temperature increases.

This is simply not the case. If there were no feedbacks, i.e. for "f=0", the temperature would increase by "Delta T_0". With the feedbacks, the temperature will increase by "Delta T = Delta T_0 / (1-f)". The IPCC clearly wants to send "f" towards "+1" (from below) to make "(1-f)" really small, and the resulting "Delta T" much larger than "Delta T_0". But if "f" goes to "+1" from below, no paradoxical or unstable behavior occurs, and the outgoing radiation remains an increasing function of the temperature.

If you wanted this slope to change the sign, "f" itself would clearly have to exceed "+1". That would result in an unstable, runaway behavior. If that occurred, one couldn't even talk about the warming (increase of the equilibrium temperature) caused by the CO2 doubling because there would be no equilibrium in this system (except for one in the asymptotic past haha).

But the IPCC do extract some value from their models, something like 3.5 °C which is 3 times the bare value of 1.2 °C. That simply means that their value of "1/(1-f)" is around 3, "(1-f)" is around "1/3", and "f" is therefore close to "2/3". I don't think it's the case - "f" is more likely to be closer to zero or slightly negative - but right now, I don't think that Lindzen and Choi have ruled out the possibility by their particular method.

And that's the memo.

P.S. I: To make things more dramatic, Roy Spencer informed me that he "examined the AMIP run for the CNRM CM3 model, and it, too, shows a negative slope between temperature and radiative flux, just as Lindzen and Choi found. So, the problem might NOT be neglect of the sigma*T^4 effect, which [he] believe[s] is already contained in the AMIP model fields. Maybe the AMIP models can not be used for this... [He] do[es] not know."

P.S. II: By the way, it is natural to expect that the "a priori" probabilistic distribution for "f" is continuous and non-singular, even around "f=+1", because "f" is proportional to the additional energy flows added by the feedbacks. Because we know that the climate is not "completely unstable", "f" must be smaller than one.

And from the non-singular distribution for "f", it follows that it is "very unlikely" that "f" is "very close" to +1, i.e. it is "very unlikely" that the climate sensitivity is much higher than 1.2 degrees Celsius. All this reasoning is just hypothetical: there are more concrete ways to estimate the climate sensitivity. For example, because the 20th century warming was just 0.6 deg C or so, it follows that climate sensitivity won't be too different from 1.2 °C, and "f" is close to zero.

By the way, if you cared about the time scales used in our discussions of the Lindzen-Choi paper: the whole discussion based on ERBE only tells us about the feedbacks that materialize within days or at most months, and they're still "fast feedbacks". It is likely that these feedbacks are pretty small ("f" won't be too different from zero). One may still argue that slower processes (e.g. 10-year-long ones) lead to a different value of "f". Note that "different" may mean both smaller and larger, depending on the sign of the slow correction.

While the champions of the climate alarm would like to make the long-term "f" more positive, I am convinced that the long-term "f" is actually smaller, or more negative, than the short-term "f". That's because of La Chatelier's principle - also promoted in the context of economics by Paul Samuelson in 1947.

Why?

It's because the longer time scale you consider, the more processes you will find that will "adapt" to the changes and "consume" (and therefore reduce) the heat that you have added into the system. So my bet would be that the short-term "f" is very close to zero and the long-term "f" is somewhat negative.

## snail feedback (3) :

Lubos,

I've been posting on this on a number of blogs yesterday.

It looks like Dick Lindzen has jumped the boat somewhat on his 'de-construction of global warming' at the moment. His work at this stage eratly doesn't appear o cast any significant doubt on the vaildity of the GCMs. In fact as best as i can judge at the moment he's made a basi error and not compared apples (ERBE data) with apples (CMIP GCMs) but apples with oranges (AMI GCMs) instead.

Lord Monckton's claim of the models the GCMs climate sensitivity being SIX times greater than the ERBEdata shows is therefore not justifiable at this stage.

KevinUK

Dear Kevin, thanks for your comments.

Many of us have reached the same - or similar - provisional conclusion about the Lindzen-Choi method. But I think that there's no reason to overhype this provisional conclusion. Lindzen and Choi can still be right about the models and about the real tropics for some reason that is not yet obvious to us.

So I would recommend all of us not to be repetitive concerning the criticism of the paper by Lindzen and Choi. I am confident that within a few months, we will have a much safer picture because some people will add more detailed analyses of the models, measurements, and theory of the tropics (and extratropics), not just the general impressions about the paper that we have already mentioned.

Thanks,

Lubos

Einstein pointed out that he could not be proved right no matter how many experiments were carried out. He knew that science can never be "settled". He also pointed out that a single experiment could prove him wrong.

The Global Climate Models (CGMs) all predicted that global temperatures would rise during the last decade in sharp contrast with reality. It follows that ALL the CGMs are wrong and it would be folly to allow such models to influence public policy.

If the CGMs were modified as suggested by Lindzen and Choi would the accuracy of their predictions be improved?

I ask this question in all humility as a physicist rather than a climate scientist.

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