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Comments on Lindzen & Choi (2009)

Posted by Ari Jokimäki on December 5, 2009

Lindzen & Choi (2009) (“L&C” from hereafter) are studying how outgoing longwave radiation (OLR) and outgoing shortwave radiation (SWR) are responding to the changes in sea surface temperature (SST). L&C already have been criticized by others, but I’ll add some comments. Some of the comments I present here I have already made in some online-discussions. First, I’ll take a look at what others have said on this so far.

James Annan noted that L&C selection of models was curious. Instead of more generally used AOGCM’s, L&C selected to use AMIP model runs. Gavin Schmidt also noticed that. He said:

Additionally, AMIP runs are known to have very counter-intuitive behaviour when it comes to surface energy fluxes (for instance, an oceanic warm anomaly caused by atmospheric anomalies in the real world is associated with an anomalous downward flux of heat – however in an AMIP run, the flux anomaly is upwards (completely opposite)). AMIP runs are useful, but it may be that Lindzen’s analysis is one of those things that is particularly sensitive to that.

So, L&C used model runs that are known to sometimes give exactly the opposite behaviour than in the real world. Also Roy Spencer (of all people) noted the AMIP model selection, and he said that he had got different results (indicating positive feedback) using CMIP model runs.

Rob Dekker had noted that L&C had offset of 4 W/m2 in the shortwave data in their Figure 3. He said:

Of course, after correcting this error, the conclusions of his paper would need to be adjusted as well. Not only is the ERBE data essentially is in line with the model predictions, but also the ERBE data shows that there is NO feedback at all (feedback factor 0) for short-term sea surface temperature changes.

“AJ” also noted the same problem (link is to Finnish discussion, I also make there some of the comments presented below), and so did Luboš Motl. Below, I’ll discuss this problem more thoroughly.

Roy Spencer also noted the smoothing problems I’ll discuss next.

Knowingly working with faulty data

L&C say:

The anomalies include a semiannual signal due to the temporal aliasing effect that needs to be eliminated [Trenberth, 2002]. The relevant sampling error of the tropical monthly ERBE data is about 1.7 W m–2 for SWR and 0.4 W m–2 for OLR [Wielicki et al., 2002a, b]. This spurious signal, particularly in the SWR, can be removed in a 36-day average, reducing the SWR error to the order of 0.3 W m–2.

So, they know that there is a false signal in the data, and they know how to eliminate it. Nevertheless, their action is not to correct the data:

However, in this study, the 36-day average was not applied because we wish to relate monthly SSTs to monthly ERBE TOA fluxes.

It seems to me that there’s not much point to this study after this. Whatever you find, you cannot be sure if it’s real or an artifact due to the false signal in the data.

Unsmooth smoothing

Above we saw L&C say that they are not correcting the data because they want to compare monthly values, but then they say anyway:

Instead, the moving average with a 7-month smoother was used for the SWR anomalies alone;

They left data uncorrected because they don’t want to mess monthly values, but then they go ahead and mess them for one dataset? And they do it by using strange value of 7 months, which they don’t explain. They do say that they are later going to show that this smoothing doesn’t affect their results. But later they show it by comparing it to equally strange smoothing values of 3 and 5 months. Let us also emphasize this: they only smoothed one dataset out of the three they are using.

Temporal and spatial coverage

The study of L&C is limited to tropics. They try to generalize this by suggesting that higher latitudes are neutral and therefore the negative feedback factor would reduce by a factor of two. I would rather have it measured.

The study is limited to short time variations (from few months to less than 2 years), of which they use only 9. They don’t study long time response at all. They say:

Simple calculations as well as GCM results suggest response times on the order of decades for positive feedbacks and years or less for negative feedbacks [Lindzen and Giannitsis, 1998, and references therein].

Assuming that this claim is correct, by limiting their study to timescales of years or less, they are focusing their study only to the feedbacks they are claiming to be negative. In other words, they are not even trying to study positive feedbacks by their own words.

Keep also in mind that they are not trying to measure the feedbacks relating to the theory of AGW where the changes in the forcing are slow, measured on interdecadal scales. Here in this blog we already have seen that water vapor feedback has been measured to be positive. Cloud feedback has been more uncertain, but recent paper by Clement et al. (2009) measured a positive feedback for low level clouds which has been the primary cause for the general feedback uncertainty. For clouds, situation has been uncertain because we haven’t had observations that are stable enough in decadal timescales, but that situation has improved in recent years (Loeb et al. (2007)).

Some minor issues

In the first paragraph of their introduction L&C say:

This is important since most current estimates of climate sensitivity are based on global climate model (GCM) results, and these obviously need observational testing.

One would need to quantify the “most” and “current” here, but it seems to me that this statement is belittling the situation, as there are many empirical estimates made on climate sensitivity in recent years.

Let’s also remember that the Iris hypothesis of Lindzen has been tested by others with bad results, no closing iris is seen.

Here’s some earlier discussion where Lindzen apparently didn’t use most recent data that was available, and when most recent data was used, the results changed remarkably, and not in Lindzen’s favor.

Forcing the feedback

As mentioned above, there is a problem in L&C handling of direct response of SST change. When temperature of SST increases, the sea surface starts to radiate more thermal energy, which causes OLR to increase according to Stefan-Boltzmann law. L&C correctly noted that when trying to determine the feedback component from OLR, one has to subtract the direct response from the OLR, leaving only the possible component caused by feedbacks. L&C say:

In the observed ΔOLR/ΔT, the nonfeedback change of 4 W m–2 K–1 is included. Also ΔSWR/ΔT needs to be balanced with ΔOLR/ΔT.

First part is correct, the nonfeedback change is the direct response I described above. But it is the second part here that is wrong. ΔSWR/ΔT is basically the change in the albedo of the Earth, it is the amount of change in the reflected sunlight. ΔOLR/ΔT is the change in OLR. Now, when the SST changes, it directly affects the amount of OLR, but L&C are suggesting here that it has a direct opposite effect of equal size to the reflected sunlight. Why would Earth’s reflectance change directly in accordance to changes in SST? There is a known feedback effect that affects the reflectance; the amount of high level clouds changes and causes a negative feedback, but remember that here we are not dealing with feedbacks yet, we are dealing with direct response. What direct response a warming event in SST could cause Earth to reflect more sunlight? That is what L&C are claiming here. Perhaps the reflecting properties of sea surface changes when it warms? Perhaps the reflecting properties of clouds change when the warmer thermal radiation from sea surface hits them? There might be some minor effects like that but L&C claim that they are of equal size to the change in OLR.

There is no reason why the Earth’s reflectance should be balanced with direct response shown in OLR. With this action, they are adding an extra 4 W/m2 to the SWR which works in the negative direction, so basically L&C are forcing (perhaps not intentionally) the feedback to be negative.


For argument’s sake, despite what we said above, let us assume that it is reasonable to balance the OLR and outgoing SWR like L&C suggested. So, how do we do balancing? We have a situation where there is an extra component of 4 W/m2 in OLR side. In that situation we can balance the situation by either A) taking the 4 W/m2 out of OLR or B) adding the 4 W/m2 to SWR. How L&C decided to do it? Here’s what they say about it:

From the consideration, FLW = –ΔOLR/ΔT + 4 and FSW = –ΔSWR/ΔΤ – 4.

As you can see, they did both. They took the 4 W/m2 out of OLR and added 4 W/m2 to the SWR. That means that they didn’t balance the situation, they just moved the unbalance to the other side.

I thank Kaj Luukko and AJ for enlightening discussions on this paper.

UPDATE (January 9, 2010): There has been some studies published dealing with L&C. They are still “in press” so there’s not much to link to yet, but see these RealClimate articles: First published response to Lindzen and Choi and Lindzen and Choi Unraveled. The comments presented are largely different than the ones presented here, so the articles are “must read” for anyone interested in this particular issue. The comment sections there also contain interesting stuff.


Clement, Amy C., Robert Burgman, and Joel R. Norris (2009), Observational and Model Evidence for Positive Low-Level Cloud Feedback, Science, Vol. 325. no. 5939, pp. 460 – 464, DOI: 10.1126/science.1171255 [ABSTRACT] [FULL TEXT]

Lindzen, R. S., and Y.-S. Choi (2009), On the determination of climate feedbacks from ERBE data, Geophys. Res. Lett., 36, L16705, doi:10.1029/2009GL039628 [ABSTRACT] [FULL TEXT]

Loeb, N. G., B. A. Wielicki, F. G. Rose, and D. R. Doelling (2007), Variability in global top-of-atmosphere shortwave radiation between 2000 and 2005, Geophys. Res. Lett., 34, L03704, doi:10.1029/2006GL028196 [ABSTRACT]


13 Responses to “Comments on Lindzen & Choi (2009)”

  1. AJ said


    That’s a pretty good summary of all the things that are, umm, strange about the L&C paper.

    I would like to go on a bit here by considering what if L & C were, by some rather odd definition of a direct response, right in their consideration of FLW = –DOLR/DT + 4 and FSW = –DSWR/DΤ – 4.

    If we assume this is correct, then a surface temperature change of dT would change the upward radiation budget by dT*DFlux/DT = dT*(DOLR/DT+DSWR/DT) = dT*(-FLW+4-FSW-4) = dT*(-FLW-FSW) = -dT*F. In order for this to equilibrate a radiative forcing Q, we must have dT*(-F)=Q, i.e. dT = -Q/F.

    If one uses the more common definition of what’s “direct” and what’s a “feedback” instead, i.e. FLW = –DOLR/DT + 4 and FSW = – DSWR/DΤ, a similar calculation to the one above result in dT*DFlux/DT = dT*(-F+4). This means that in order to balance a radiative forcing Q, we must have Q=dT*(-F+4) which results in dT = Q/(4-F) = Q/4 / (1-F/4). This is Eq. (3) of L&C paper.

    Now, what L&C are assuming is that both FLW = –DOLR/DT + 4 and FSW = –DSWR/DΤ – 4 AND dT = Q/4 / (1-F/4). But, as the above calculation shows, these two equations contradict one another and thus, only one of them can be correct, and another one must then be wrong.

    Why is this important?

    Well, what Lindzen finds at the short time scales he studies, is essentially DFlux/DT = 4 W/(m^2 K), which in the more usual definition would be a non-feedback climate. At short timescales, this is exactly what one expects, since the response time of the “direct” process is much smaller than that of any of the “feedbacks”. Therefore there’s absolutely nothing surprising, or in contradiction with climate models, in this result (not sure what L&C do with the climate models, though, but from what they write, it seems they’re not so sure themselves either…).

    In fact, from the above derived equation dT = -Q/F one can see that in L&C’s definition, one will always obtain a negative feedback factor F, because a positive one would imply a climate that is unstable to a fluctuation in the radiative budget. Even if L&C did study the more AGW relevant longer time scales, and got a DFlux/DT = 1,3 W/(m^2K) equivalent to approximately 3 degrees of warming in response to a CO2 doubling, this confusion with the equations would have made them conclude that a CO2 doubling would only lead to a 1/(1+1.3/4)=0.75 degrees warming.

    Let me conclude here what I personally think about this paper as a whole. Many people consider this L&C paper a strong proof for a negative feedback in the climate system. After carefully reviewing it, I actually consider it the opposite. I mean, let’s face it: Lindzen is a professor of meteorology at MIT, and not so many people make it as a professor by an accident. Therefore, he’s probably an expert in what he studies. Therefore, if he really had a point, I’ve no doubt that he would also had the expertise to properly demonstrate his point. Now, even though this professor is (for some odd reason) desperate to disprove AGW, all he can do to support his “adaptive iris” herecy is playing these tricks by filtering the data in an odd way, and then interpreting the result he gets in a way that is just fundamentally wrong. And he can’t even hide these tricks in a way that would make it difficult, even for a non-professional in this field like myself or Ari, to spot them! I mean, think about it… If it takes this much effort and (perhaps intentional) misinterpretation of the data for professor Lindzen to find any evidence for a negative feedback in the climate system, I really think that’s just one more implication that the true feedback of the climate system is positive!

  2. Ari Jokimäki said

    Thanks for the insightful comments, AJ! 🙂

    Could you clarify one minor detail? You say:

    This means that in order to balance a radiative forcing Q, we must have Q=dT*(-F+4) which results in dT = Q/(4-F) = Q/4 / (1-F/4). This is Eq. (3) of L&C paper.

    Looking at L&C equation 3, I notice that it’s not exactly the same as your equation, they have ΔT = ΔT0/(1-f). It’s almost the same but perhaps you could connect the dots here?

  3. AJ said

    Oh, sure.

    If we take L&C’s equation (3), dT = dT_0/(1-f) and we use their definitions, then from the definition of f given under Eq. (3) we get f=G_0*F = F/4 (because G_0 is the “non-feedback” Planck sensitivity = 0.25 = 1/4 degrees per W/m^2) ,and from Eq. (1), dT_0 = G_0*dQ = dQ/4. Plugging these definitions in their Eq. (3), we get dT = dQ/4 / (1-F/4), which shows that these equations are indeed the same.

    Sorry for being sloppy about that… I hope this clarified things.

  4. Ari Jokimäki said

    It certainly did, thank you. 🙂

  5. syphax said

    Has anyone (besides Roy) done the exercise using CMIP results? That’s outside my expertise, but it would seem like a relatively straightforward thing to do.

    I mean, the use of AMIP results stuck out like two left feet to me, and I barely know anything about climate modeling.

  6. Ari Jokimäki said

    Syphax, I haven’t seen others do it yet. But there are plenty of other research on feedbacks. The article by James Annan I mentioned gives the link to the abstract of Forster & Gregory (2006). Here’s the PDF. They use ERBE data and find positive climate feedback parameter. You can also check my lists on water vapor feedback and cloud feedback for at least somewhat similar studies.

  7. rob de vos said

    I had a good look at this climate site, and what I have noticed is that so many posts agree with the ideas of Ari Jokimäki. I thought science is all about being sceptic in the first place? Main stream swaying is for politicians and laymen. This is what is called autogamy, which will finally lead to inbreeding.

  8. Distant Observer said

    AJ, I think you have made a crucial error when you write dT = -Q/F.

    I think Lindzen calls “feedback” all temperature dependent mechanism except Stefan-Boltzmann radiation. This co’ordidate transform sure is somewhat unusual, but I am sure he has his reasons. This becomes natural when one considers that one of his main goals is to evaluate the validity of feedback factors calcuted by the climate models. Please note that he compares the SW and LW radiations separately against models. All the models always have the 4 W/(m^2K) factor included and for this reason he must include it also in his data.

    Now for the sum SW + LW this of course needs to be compensated, but Lindzen is not that specific. The paper is an abridged version.

    But since Lindzen does not explicitly show the comparison method, we do not know for sure.

    I would not get hooked on this point.

    We all would like to see slightly more specific information over Lindzen’s mathematics.

  9. AJ said

    To “Distant Observer”,

    Thanks for your comments.

    I’m well aware that writing “dT = -Q/F” would be a crucial error, IF L&C did use the common definition where, as you wrote, “feedback” is indeed all temperature dependent mechanisms except Stefan-Boltzmann radiation, i.e. F = –(DFlux/DT – 4). However, in their article, L&C explicitly write “FLW = –DOLR/DT + 4 and FSW = –DSWR/D? – 4” from which one gets, by a trivial summation, F = -DFlux/DT. From that, one gets to the dT = -Q/F. So while I agree with you that this equation would be a crucial error in the usual definition of what’s a feedback, it is correct IF one uses L&C’s definitions “FLW = –DOLR/DT + 4 and FSW = –DSWR/D? – 4” instead of the usual one. I’m sorry if I wasn’t clear enough about it earler.

    Not having seen the codes, I cannot be a 100 % sure what L&C do when comparing their results with models – but I must say it seems to me, they’re not so sure themselves either. That’s the conclusion I draw from example from this part of the text:

    “Indeed, Fig. 3c suggests that models should have a range of sensitivities extending from about 1.5°C to infinite sensitivity (rather than 5°C as commonly asserted), given the presence of spurious positive feedback. However, response time increases with increasing sensitivity [Lindzen and Giannitsis, 1998], and models were probably not run sufficiently long to realize their full sensitivity.”

    So, from their funny way of analyzing AMIP model runs, they conclude that some models have an infinite sensitivity, and “probably” those others just have not run their models for long enough. Now let’s just think with some common sense, which is more likely, (1) the modelers just don’t know their models (or haven’t realised they haven’t run them long enough), or (2)this “infinite sensitivity” is a flaw in their analysis? You decide. Add to the common sense thinking the fact that if any model really had an infinite sensitivity, then “response time increases with increasing sensitivity” does not hold any more. Instead, as a model with infinite sensitivity would have the outward radiation flux decrease when temperature increases, you cannot even define a “response time” because the temperature would increase (or decrease) exponentially after being initiated.

  10. AJ said

    To Rob De Vos,

    In case you didn’t realise, we are actually being quite sceptic right here in this post. Perhaps it’s hard to realize that, because we’re actually being sceptic towards a sceptic.

  11. Distant Observer said

    Two more comments to “AJ”:

    A. “However, in their article, L&C explicitly write “FLW = –DOLR/DT + 4 and FSW = –DSWR/D? – 4″ from which one gets, by a trivial summation, F = -DFlux/DT.”

    In this case a “trivial summation” is not correct. If you read carefully, Lindzen starts the chapter by “When considering the LW and SW fluxes separately,….”. The whole notion refers to comparing the SW and LW radiations separately. In this case Lindzen’s notion is correct, but for a combined SW + LW comparison a different adjustment has to be made. This makes Lindzen’s definitions rational. But once again: This just my guess. Lindzen is not specific enough in his paper.

    B. The other reason why you are threading on a slightly dangerous path with your dT = -Q/F notion is due to the question of causality. Lindzen clearly and correctly states the case of a feedback system (forget about his somewhat unusual definition of “feedback” by leaving the Stefan-Boltzmann out). If you define F = -DFlux/DT, then you should be specific over the direction of causality. In a feedback system both of these equations cannot be valid simultaneously. A feedback system is not linear system and thus you cannot make arithmetic operations freely. F has to be considered to be a transfer function. Now, depending on which of the two equations you pick to be correct F is either the feedback factor (with of without Stefan-Boltzmann) or the system transfer function. It is important to note that these two are different animals. (My understanding is that Lindzen picked the latter to be correct and for this reason your dT = -Q/F is incorrect in this context.)

    I think this is Lindzen’s main contribution to the topic. Lindzen understands causality the way it should be understood.

    But once again: This does not prove his mathematics is correct. For that we need more information.

  12. Ari Jokimäki said

    I added a brief note above about the RealClimate articles: First published response to Lindzen and Choi and Lindzen and Choi Unraveled.

  13. […] Would appreciate any other good links that you know of. The most significant critiques include: […]

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