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Lu Blames Global Warming on CFCs (Curve Fitting Correlations)

Posted on 5 June 2013 by dana1981

A paper just published in an obscure physics journal by the University of Waterloo's Qing-Bin Lu (2013) has drawn quite a bit of media attention for blaming global warming not on carbon dioxide, but rather on chlorofluorocarbons (CFCs, which are also greenhouse gases).  However, there are numerous fundamental flaws in the paper, which is based almost entirely on correlation (not causation) and curve fitting exercises.

Lu's hypothesis can be disproven very simply.  He argues that the radiative forcing (global energy imbalance) from CFCs matches global surface temperatures better than that from CO2 over the past decade.  This is because as a result of the Montreal Protocol, CFC emissions (and emissions of other halocarbons) have been flat over the past decade, and global surface air temperatures have also been essentially flat during that short timeframe, while CO2 emissions have continued to rise.

However, a global energy imbalance doesn't just impact surface temperatures.  In fact, only about 2% of global warming is used in heating the atmosphere, while about 90% heats the oceans.  Over the past decade, ocean and overall global heating have continued to rise rapidly, accumulating the equivalent of about 4 Hiroshima atomic bomb detonations per second (Figure 1).

Fig 1

Figure 1: Land, atmosphere, and ice heating (red), 0-700 meter OHC increase (light blue), 700-2,000 meter OHC increase (dark blue).  From Nuccitelli et al. (2012).

So while CFCs might match surface temperature changes better than CO2 emissions over the past decade, CO2 emissions better match the relevant metric – overall global heat accumulation.  Since a global energy imbalance influences global heat content and not just surface temperatures, this by itself is sufficient to falsify Lu's hypothesis. 

But let's dig into the details of the paper to see how Lu built his case and where he went wrong.

Unphysical Curve Fitting, Misrepresenting Cited Research, and Circular Logic

Here at Skeptical Science we have previously examined several cases of curve fitting.  This describes the practice of scaling several variables without any sort of realistic physical constraint until the model closely matches the observational data, and then declaring that you've proven that those variables caused the changes in the observations.  Loehle and Scafetta used this strategy to blame global warming on astronomical cycles, and Roy Spencer used it to blame global warming on ocean cycles.

In this paper, Lu used curve fitting to blame global warming on a combination of solar activity and CFCs.  First he randomly scaled a total solar irradiance (TSI) reconstruction to match the surface temperature record as closely as possible.  He claimed that this practice was justified by Solanki and Krivova (2003).  Lu says:

" can be seen that the global temperature indeed closely followed the TSI variation up to 1970; the y-axis for TSI can be scaled so that the magnitudes of the temperature and TSI variations are similar during 1850-1970. This was actually shown previously by Hoyt and Schatten50 and Solanki and Krivova52, and an excellent linear correlation with coefficients of 0.83~0.97 between the TSI and the temperature was obtained.52 This implies that the TSI values can be converted into temperatures using the linear correlation.52 The observed data indicate that the solar effect played the dominant role in climate change prior to 1970."

But Solanki and Krivova didn't say TSI can be scaled willy nilly to fit the temperature data.  They tried a similar approach in their 2003 paper simply to show that using the most generous possible assumption, solar activity still can't explain recent warming (emphasis added).

"We have shown that even in the extreme case that solar variability caused all the global climate change prior to 1970, it cannot have been responsible for more than 50% of the strong global temperature rise since 1970 through any of the channels considered here. We believe that even this fraction is too high."

There is a proportional relationship between changes in TSI and changes in surface temperatures, but it's a physical relationship.  You can't just choose whatever proportionality is convenient for your argument.  In fact what Lu has done is assume that TSI explains most pre-1970 global surface warming, and then claim that he's proven this is the case.  It's circular logic, like fixing a card game and then claiming you're a great card player when you win.

The only reason Lu's TSI model matches the surface temperature data is because he forced it to match through curve fitting – by refusing to apply any physical constraints to his model.  Then when his unphysical model fits the temperature data reasonably closely, he declares that he's shown "that the solar effect played the dominant role in climate change prior to 1970."  In reality he's shown no such thing, he's simply assumed that his conclusion is true.

Lu also uses a solar reconstruction from Hoyt and Schatten (1993) in his curve fitting exercise.  Why use the results of 20-year-old study?  Perhaps because it helps Lu arrive at his end conclusion that global warming isn't due to CO2.  The Hoyt and Schatten paper claims that the equilibrium climate sensitivity to doubled CO2 is a mere 0.19°C – a factor of 15 lower than today's best estimates.

Perhaps the gold standard of TSI reconstructions comes from Wang, Lean, and Sheeley (2005), updated by Kopp and Lean (2011), whose data are available here.  They estimate that the increase in the amount of solar radiation reaching Earth from 1860 to 1970 was not very large (a radiative forcing of less than 0.2 Watts per square meter, compared to the 1.7 Watts per square meter CO2 forcing from pre-industrial times to Present), and only sufficient to account for approximately 0.07–0.15°C average global surface warming.  Thus TSI can probably only account for less than half of the observed 0.3–0.4°C surface warming during that time, contrary to the 100% solar attribution Lu claims based on his curve fitting exercise.

Yet More Circular Unphysical Arguments, Curve Fitting, and Misrepresentation of Cited Research

Lu faced the conundrum of having to explain how the increased greenhouse effect from CFCs can cause global warming while the much larger increased greenhouse effect from rising CO2 can't.  To accomplish this, he used what the climate scientists at RealClimate have described as the saturated gassy argument – claiming that increased CO2 can't cause more warming because there is already so much in the atmosphere that its greenhouse effect has become saturated.  However, as the climate scientists at RealClimate (and we at Skeptical Science) have explained, that argument is quite clearly wrong – disproven by observational data.

Here Lu is again guilty of circular, unphysical logic.  He doesn't actually physically demonstrate why he thinks the CO2 greenhouse effect is saturated.  Rather he merely argues that because CFCs seem fit the surface temperature data better than CO2, that means CO2 can't be causing global warming, which means the CO2 effect must be saturated.  Once again he has merely assumed his conclusion is true rather than actually providing physical evidence for it.

Perhaps worse, Lu claimed that a paper by Anderson et al. (2004) supported his saturated gassy argument, claiming the CO2 absorption band is missing from the observed spectrum data.  On the contrary, Anderson et al. concluded,

"The spectra in Fig. 8a are the result of a superposition of two different effects. First, there is an increase of greenhouse gases from 1970 to 1996 that gives rise to recognizable bands in the observed spectrum..."

And once again, Lu tried to demonstrate that CFCs can account for the recent global surface warming through unphysical curve fitting, multiplying the CFC forcing by whatever value allowed the CFC data to best fit the temperature data.  When using physical constraints, CFCs (included in "halocarbons" in Figure 2) can account for only about 20% as much warming as CO2.

AR4 forcings

Figure 2: Global average radiative forcing (RF) in 2005 (best estimates and 5 to 95% uncertainty ranges) with respect to 1750 for CO2, CH4, N2O and other important agents and mechanisms, together with the typical geographical extent (spatial scale) of the forcing and the assessed level of scientific understanding (LOSU).  From the 2007 IPCC report.

In his Figure 11, Lu also exaggerates the difference between expected CO2-caused warming and observed temperatures by plotting the observational data against the surface warming we expect at equilibrium.  This is wrong because there is a global energy imbalance, which means there is more warming "in the pipeline" for several decades to come before we reach that equilibrium state.  In reality the Earth has warmed as expected from the increased CO2 greenhouse effect.

Why did the Media Cover this Paper?

Frankly this paper should not have passed peer-review, but was perhaps aided by publication in a physics rather than climate journal, and in fact in the physics journal with the lowest impact factor by a wide margin.  The paper was then trumpeted by a University of Waterloo press release and a Science Daily article, both of which used exaggerated language like "Lu’s theory has been confirmed."  The Science Daily article did not discuss any of the problems with the paper that we have detailed in this post, or ask any climate experts about it.

ABC did a better job, talking to climate scientist David Karoly, who expressed appropriate skepticism about a paper which purports to overturn decades and even centuries of well-established physics and climate science in one fell swoop.  Characteristically, The Australian then criticized ABC for failing to be "fair and balanced" because they interviewed an actual climate expert about the paper.

Frankly, the paper is a non-story.  It may seem like news due to the grandiose claims of overturning the vast body of scientific evidence supporting CO2-caused global warming, but it is very rare for a single paper to accomplish this type of feat.  More often the single paper claiming to overturn the body of established scientific research is wrong.  That is clearly the case for Lu (2013), which is based on assuming rather than proving the hypothesis, unphysical curve fitting, and misrepresenting the cited research.

Moreover, this study isn't new.  It's actually the third Lu has published about his CFC warming hypothesis.  The first two were addressed by RealClimate, two peer-reviewed published responses, Skeptical Science, and others.  Andrew Gilkson at The ConversationClimate Science Watch and Rabbett Run (here and here) are also good resources for debunking Lu's latest effort.

As we've previously discussed, the media need to be more careful in avoiding single study syndrome, misinforming the public by overhyping a single supposedly game-changing study before it has survived the scrutiny of the scientific community.

Note: this post has been incorporated into the rebuttals to the myth "it's CFCs"

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Comments 51 to 76 out of 76:

  1. (-snip-).

    A word of advice, you have now posted argumentative messages on several threads.  This is usually a sign of drive-by trolling, becuase very few people would have the time and energy to engage in meaningful discussions of so many scientific topics in one go.  If I were you I would (a) restrict myself to one topic at a time and (b) pay attention to what is actually written in the responses to your posts.  Fail to do so and I suspect that you will find yourself recieving even more attention from the moderators.

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    Moderator Response:

    [DB] Response to snipped off-topic and sloganeering snipped.

  2. Chordotonal, where did this become about Lu's basic use of curve-fitting.  The problem all along has been his lack of providing the necessary mechanics to support that fitting.  Should that be the basic requirement for publication? If so, Willis Eschenbach just smiled. The number of pedal strokes I used to get to work this morning was exactly the same as the number of strokes used by Paris Hilton to comb her hair this morning. I say the two are causally related. It has to do with the . . . ummm . . . gravitational resonance from the friction in my bottom bracket. The frequency of the resonance matches Hilton's brain structure, causing the repetitive motion at just the right time. What? She combs her hair every morning, even when I'm not riding my bike? Not listening! Not listening! I'll be publishing soon in Journal of Auras and Dweomers.

    In a world where rapid global warming is not an issue, does Lu repeat and publish the analysis?  SkS is also about the communication of climate science, and Lu's garbage looks like gold to the paid misinformers of the general public.  If you perform poor science and then try to get it published, knowing that it will be used to confuse the general democracy . . . what's up with that?

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  3. "The problem all along has been his lack of providing the necessary mechanics to support that fitting. Should that be the basic requirement for publication?"

    If you are saying he needs a good apriori case yes I agree. If you are saying that he does not have one, yes I agree with that also.  But we ought not get too precious about publication.  So we are saying he has a good one-shot correlation but he doesn't have a good apriori case.  So its just a matter of making a start on an hypothesis that is likely going to wind up failing for lack of convergent evidence.  We ought not be treating him as some sort of heretic, since this is how you go about proving things. 

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    Moderator Response:

    [JH] You are skating on the thin ice of sloganeering and excessive repitition -- both of which are banned by the SkS Comments Policy. Please read the Comments Policy and adhere to it. Thank you.     

  4. Chordotonal, Lu has been riding this pony for a while.  He's received published feedback on it.  He's ignored it (look at the links at the bottom of the main article).  When does it get real?  

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  5. Chordotonal: You most recent post was sloganeering and was therefore deleted. Please read the Comments Policy and adhere to it. 

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  6. Again, you build a strawman in the form of an alleged attack by SkS posters on correlation in general.  No.  If you're going to claim correlation = causation, as Lu did, you'd better damned well start talking about the physical mechanism in a methodologically sound way.  Lu's method was unsound.

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  7. chordotonal, "sloganeering" is clearly defined in the comments policy.  Please read them.

    I for one am not going to bother responding to your posts while you continue to use phrases such as

    "That is a real bread and butter concept of science that is being attacked in service of what amounts to religious belief."

    If you want to discuss the science, that is fine, but drop the rhetoric, nobody here is interested.

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    Moderator Response:

    [JH] Chordotonal's subsequent post was sloganeering and was therefore deleted. 

  8. Chordotonal:

    Please note that posting comments here at SkS is a privilege, not a right. This privilege can and will be rescinded if the posting individual continues to treat adherence to the Comments Policy as optional, rather than the mandatory condition of participating in this online forum.

    Moderating this site is a tiresome chore, particularly when commentators repeatedly submit offensive or off-topic posts. We really appreciate people's cooperation in abiding by the Comments Policy, which is largely responsible for the quality of this site.

    Finally, please understand that moderation policies are not open for discussion. If you find yourself incapable of abiding by these common set of rules that everyone else observes, then a change of venues is in the offing.

    Please take the time to review the policy and ensure future comments are in full compliance with it. Thanks for your understanding and compliance in this matter.

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  9. Chordotonal:

    Please note that posting comments here at SkS is a privilege, not a right. This privilege can and will be rescinded if the posting individual continues to treat adherence to the Comments Policy as optional, rather than the mandatory condition of participating in this online forum.

    Moderating this site is a tiresome chore, particularly when commentators repeatedly submit offensive, off-topic posts or intentionally misleading comments and graphics or simply make things up. We really appreciate people's cooperation in abiding by the Comments Policy, which is largely responsible for the quality of this site.

    Finally, please understand that moderation policies are not open for discussion. If you find yourself incapable of abiding by these common set of rules that everyone else observes, then a change of venues is in the offing.

    Please take the time to review the policy and ensure future comments are in full compliance with it. Thanks for your understanding and compliance in this matter, as no further warnings shall be given.

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  10. Chordontonal, you seem to be unaware of... well, the entirety of climatology.  So you consistently have made comments that are entirely off base (e.g., wrong, not even wrong), as you try to apply your general knowledge of science and philosophy.  I suggest you start by learning the history of the science behind our knowledge of global warming.  Then learn more about the fundamental physics of the greenhouse gas effect--physics that are known from actual experiments in the lab and observations in the field.  Physics knowledge that was established without any thought to humans increasing global warming.

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  11. Chordotonal has recused himself from positng on SkS.  

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  12. The stratospheric cooling associated with increasing greenhouse gases is not a new idea. It shows up in 1-D radiative-convective modeling work in the 1960s. Two such early studies are:

    Manabe and Strickler, 1964.

    Manabe and Wetherald, 1967



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  13. Many thanks Dana for correcting the reference to hydrofluorocarbons in the second para just now, but as mentioned in my tweet, it is radiative forcing that has remained roughly stable, the emissions picture is rather more complex. As I've said on the "It's CFCs" thread, and over at Eli's Rabett Run blog, the rapidly rising emissions of HCFCs and particularly HFCs are deserving of more attention in the climate change policy debate.

    If anything useful comes from the publication of Lu's discredited theories about CFCs, I hope it's a greater recognition that by phasing out the very high GWP ozone depleting CFCs, the Montreal Protocol has done 5 times as much as the first committment period of Kyoto to reduce radiative forcing emissions. Because the CFCs have very long atmospheric lifetimes (and emissions from 'banks' are larger than projected and lamentably very little is yet being done to prevent them), the halocarbon 'stock' is not declining very much yet, although the 'flow' has been radically reduced.

    Alarmingly, the climate benefits acheived by the Montreal Protocol are now threatened by rapidly rising emissions of HFCs used as substitutes for Ozone Depleting Substances, which are increasing at around 9% p.a. (and HCFCs, which although being phased out are still increasing by around 4.3% p.a.). Using the Montreal Protocol to phase out the HFCs is entirely possible with available natural refrigerant solutions (and arguably emerging expensive and less efficient patented synthetic alternatives, for those concerned with protecting the profit margins of the chemical companies responsible for the F-Gas problem). Worthy amendment proposals to achieve a less ambitious "phase down" are up for discussion for the 5th year in a row in Bangkok later this month, and again in November at the Meeting of the Parties. While the EU (and Australia) at the UNFCCC talks are urging the Montreal Protocol to act on these, you need to look hard to find coverage of these proposals.

    In both the ABC radio AM piece cited above, and the ABC Science article "CFC Warming Theory Challenged" the climate impact and significance of CFCs, HCFCs and HFCs is not clearly explained and understated. I'm concerned these articles, and the much warranted rebuttals of Lu's paper are contributing to the mistaken notion that the halocarbon problem is fixed.

    Extending the Montreal Protocol (and implementing end use bans and carbon pricing mechanisms) to control and reduce use and emissions of HFCs are among the most fast acting and cost effective tools at our disposal for reducing emissions and preserving the significant climate benefits of the Montreal Protocol, yet this remains a complete surprise to most people, even those highly engaged in the climate debate.

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    Moderator Response:

    [JH] Would you be willing to expand your excellent comment into a guest article?  

  14. Geencooling's concerns about the role of HFCs in climate change are shared by the Chinese and US governments as documented in Andrew Revkin's DoT Earth post of yesterday (June 8).

    As some environmental analysts had hoped, President Obama and President Xi Jinping of China found room to maneuver on global warming in their California desert retreat. They sidestepped the super wicked issues impeding restrictions of the greenhouse gas of greatest concern, carbon dioxide, and staff released a joint statement on plans to cut releases of hydrofluorocarbons, or HFCs, a potent group of heat-trapping gases.

    Source: With CO2 Cuts Tough, U.S. and China Pledge a Push on Another Greenhouse Gas by Andrew Revkin, DoT Earth, New York Times, June 8, 2013 


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  15. Chordotonal, the good Professor Lu did not fit a curve, he tortured the poor dear with thick lines until it cried enough.  The level of curve fitting was "look at that" without any statistical analysis. Follow the link

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  16. I commented at #4 with a double-check on Lu's regression analysis. Lu claims he did an analysis where he removed the effects of the solar component. What is interesting is I used his correlation recipe but only sliding by a lag of 9 years and got the same R^2 as he got.

    I think this has important implications because his correlation coefficient didn't improve by removing the solar component. This could only happen if it was just a random effect in the first place. IOW, he didn't do a null test, but simply claimed that the solar improved the fit.

    I might be missing something, that is why it is nice to have the SkS blog available.

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  17. Thanks again for such a clear, concise rebuttal.

    But I have to admit I got completely lost in the comments. This is an informative, if sometimes scary place, for us right-brainers.

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  18. I was curious about Dana's reference to the "impact factor" (for people like me who need that explained, it is a measure of average number of citations to articles in the journal over some unit of time, probably a year?) of the journal that published Lu's article.  The title of the journal itslelf is not mentioned in Dana's post - it is apparently the International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Applied Physics.  Indeed, its impact factor of 0.361 is by far the lowest, being the only one below 0.591.  Arguably, comparing the impact factor of a branch of a journal subdivided by topics to that of another entire journal is not a fair apples-to-apples comparison.  However, a quick scan reveals that there are a few other journals or branches of journals directed to statistical physics (I assume that is where Lu fits into IJMP B), each having a significantly larger impact factor: Journal of Statistical Physics (1.397),  Physica A: Statistical Mechanics and its Applications (1.374),  Physical Review E: Statistical, Nonlinear and Soft Matter Physics (2.255).  

    As another type of comparison, the impact factors of the entire IJMP added up (4.1) seems to put it more or less into a well-populated second-tier of journals, not remarkably tiny, but far behind some of the leading journals (it looks like there are six of them with impact factors ranging from 10 to 40+).  

    A modest pedigree that I wouldn't be inclined to think impugns the credibility of the article by itself, but certainly not one that is proportional to the media attention the article received, or that would tend to suggest the article was thoroughly vetted by climate experts.  

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  19. A strong argument.

    But should we pay more attention to Lu's Physics Reports (2010)?  Phys Rep has an impact factor of 20.574, whereas he did nothing more than a random correlation in that paper!

    It might be an open question to target the impact factor, because some stupid scientists have pointed this out:


    We should focus on the point that Qing-Bin Lu is not a climate scientist at all; he knows nothing about global warming!  Far enough.

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  20. John0001 @69, yeah, I think that's why Dana made only a passing reference to the impact factor, musing as to a possible explanation of why the article passed peer review despite its low merit, which is addressed in the rest of the post.  I was just curious as to what an "impact factor" even is, how much lower this journal's was compared to others, etc., and thought I might save other curious individuals like me some legwork.  

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  21. jdixon1980 @68, it doesn't make sense to add up impact factors over a number of journals. Since the impact factor is the number of citations per paper, about all you can do is average the impact factors for IJMP[A-E]

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  22. I can't find Lu's two postings. Can you help?

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  23. Moderator,

    I was going to reference your site regarding your posting on Q-B Lu's recent paper and his two-part posting discussing the paper and your response. I haven't been able to find his posts. If I have simply missed them this time, please provide a link. If you have removed them, I would suggest that you post a comment that you have done so and your reasons for doing so.

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    Moderator Response:

    [TD] I don't see any comments by Lu in the deleted comments.  I also don't remember seeing Lu's comments on this thread.  Nor are any comments by Lu on the "It's CFCs" thread.

    [TD] Maybe you are thinking of Lu's response over at Climate Science Watch.

    [DB] There is no registered user at SkS under any variant of Lu's name.

  24. tcflood @73

    Have you got Lu mixed up with KK Tung ?

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  25. Phil @ 74

    I certainly did confuse the two, and I apologize. Must have been a senior moment - they're becoming more frequent these days.

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  26. Waterloo alumni aren't all that impressed

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    Moderator Response:

    [RH] Hotlinked URL that was breaking page formatting.

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