Richard Tol’s climate sensitivity estimate

In his interview with Roger Harrabin, Richard Tol said something quite interesting. He claimed:

RT: The very start of my career was about trying to show that CO2 and other greenhouse gases cause climate change. We were one of the first to establish that on a satisfactory statistical basis.

Quite a remarkable claim. So, I went and looked at Richard’s publication list and found a paper called Greenhouse Statistics-Time Series Analysis. It really is what it says in the title; simply a time series analysis. Compare various time series with the known temperture record, some with a CO2 term, some without, some with an additional linear term, and find which correlates best.

One obvious problem is, as it says in the Conclusion:

many climatologists classify this type of results as ‘correlation calculations’, which refers to the many wrong and misleading results obtained by this type of analysis.

So, yes, it might show that a time series with a CO2 correlates best with the observed temperature timeseries, but claiming that this shows that CO2 and other greenhouse gases cause climate change, seems a bit strong. However, they do state:

We have casted the hypothesis that the increase in atmospheric greenhouse gases causes global warming in a sophisticatedly simple model which enables efficient statistical testing; ….. The hypothesis of no influence is rejected. We have not found a proof or an explanation of the phenomenon though we can describe it. We have shown with much statistical care that the data are in line with the climatological hypothesis; the combination of the econometric techniques and climatological theory confirmed it in sign;

There are a couple of interesting issue relating to this. On an earlier post there was a rather acrimonious and contentious exhange between myself and Richard, mainly as a result of Richard defending Doug Keenan. Doug Keenan’s claim to fame (in the climate arena, at least) is making accusations of fraud and claiming that the surface temperture dataset is not significant. Richard said things like

The context is whether or not there is a statistically significant trend in the temperature record. That is a time series question if there ever was one.


He is correct in this case

At no point did Richard mention that he had published a time series analysis of his own, which he claims shows that CO2 and other greenhouse gases cause climate change. That would seem to be rather significant, given the context of the thread about Keenan. I wonder why he failed to mention this?

There is, however, something else interesting about Richard’s paper; it makes estimates of climate sensitivity. For a CO2 rise of 300ppm (which I assume is intended to be about a doubling since pre-industrial times) it estimates a 95% range of 2.99oC to 7.02oC for one model, and a 95% range of 3.4oC to 5.7oC for the other. Hmmm, quite a bit higher than the IPCC range, even at that time.

Credit: Tol & de Vos (1993)

Credit: Tol & de Vos (1993)

However, in the paper they then argue that they used CO2, rather than CO2-equivalent, which rose more than CO2 only, and that they should therefore reduce their climate sensitivity estimates accordingly. They then produced the table on the left, which shows that their estimate for climate sensitivity hovers around 3oC.

Now, there are a few things to bear in mind. Their model is simply a time series, with no real physics. They do introduce a lag of 20 years between the CO2 time series, and the temperature time series, but this still means that their climate sensitivity estimate is probably something like a mixture of an Effective Climate Sensitivity and a Transient Climate Response. Also, even though CO2-equivalent rose more than CO2 alone, when you include all the anthropogenic emissions, the anthropogenic effect is actually quite close to the CO2 only influence. Hence, maybe they shouldn’t have adjusted their estimates down.

Either way, though, we can now state that Richard Tol’s published estimate for climate sensitivity – which is based on a sophisticated time series analysis – suggests climate sensitivity is probably around 3oC, maybe even higher. Who’d thunk it? 😉

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62 Responses to Richard Tol’s climate sensitivity estimate

  1. anoilman says:

    Sounds good to me! I’ve already stopped using Cook’s 97% consensus and told any deniers to go with Tol’s 95%. Soo… Good work Tol! Jolly well done!

  2. dana1981 says:

    I don’t find it surprising. Tol has never argued for low sensitivity as far as I’ve seen, and his recent comments that we’ll see >3°C warming by 2100 are in line with standard sensitivity estimates. I’m pretty sure his economic analyses use the standard range of sensitivities as well. It’s only his cohorts like Ridley who irrationally argue for low sensitivity. They cite Lewis on sensitivity and Tol on economics.

  3. They cite Lewis on sensitivity and Tol on economics.

    Yes, I was thinking a little about this myself. Ridley, for example, cherry-picks Tol’s analysis suggesting impacts will be positive till 2C, and then cherry-picks Lewis’s work to suggest we won’t warm much by 2100.

  4. 0^0 says:

    Oh rats. You have blown the cover of our ultra secret warmist mole. It will be dangerous for him in all those denialist circles he has so successfully penetrated.. 😉

  5. Indeed.

    I think our 1993 is mainly of historical interest. The 1997 paper in Climatic Change is much better: It tests the hypothesis of greenhouse-gas-induced warming against the hypothesis of natural warming. (The former wins by a landslide.) That paper also produces a complete PDF of the climate sensitivity, where we find — as others would later — that the left tail is thin, i.e., low climate sensitivity is unlikely, but the right tail is thick, i.e., high climate sensitivity cannot be excluded.

    I have not done much in this area since. I am proud to have co-advised Francisco Estrada’s PhD, whose joint work with Pierre Perron sets the current standard.

  6. I hadn’t seen that one. Interesting, and you even used the logarithm of CO2.

    While you’re here. Why would you not have deleted your recent tweet? I’ve been trying to think of why that tweet might be acceptable, or if you’re trying to make some kind of subtle point, but I’m struggling. It just seems offensive.

  7. @wotts
    The one about the polar bear suit? I think the climate negotiations are a forgone conclusion. I don’t think security is. I am a surprised that Joe Curtin and Greg Laden seem to think that environmentalists have a monopoly on dressing up.

  8. Yes, that one. I’m still struggling to see why it isn’t simply offensive, but suit yourself.

  9. @wotts
    Well, we’ve just learned that someone tried to blow up a stadium with 45,000 people by disguising a explosive-laden truck as an ambulance …

    The problem with suicide vests is that they are either small or conspicuous. Polar bears are big and fat.

  10. Richard,
    I don’t really want to discuss it. If you’re happy posting that tweet, then carry on.

  11. Because the U.S. Congress seems to have somehow gotten the wrong idea the last time, hopefully Prof. Richard Tol would be willing to testify again regarding these parts:

    “… The only solution to the climate problem is if we decarbonise the economy, right? We need to go to zero emissions. … we should be trying to decarbonise the economy as fast as we can but I think we will need a century to do so. …” [Prof. Richard Tol, 2015-11-16]

    “A simple carbon price. From the perspective of the atmosphere, it doesn’t matter where the CO2 comes from and therefore it also doesn’t matter where the CO2 reduction comes from. If you impose a carbon price then you give everybody who emits CO2 an incentive to emit less and you let the market and the households and companies sort out what is the best way to do it, or pay the price if it can’t be done.” [Prof. Richard Tol, 2015-11-16]

    “… Yes, a simple carbon tax. A carbon tax can be managed by perhaps ten civil servants in the Treasury, that’s all you need. Instead we have a large department of climate change that employs many, many civil servants, all of whom are making up silly rules. And I would simply abolish that whole department and replace them with a working group of ten civil servants or so in the Treasury and that’s all we need.” [Prof. Richard Tol, 2015-11-16]

  12. Joshua says:

    ==> “Well, we’ve just learned that someone tried to blow up a stadium with 45,000 people by disguising a explosive-laden truck as an ambulance …”

    Can someone give me context for understanding how that comment ties into the ongoing discussion?

  13. Oh, it was simply coincidence in that Richard commented here just after tweeting this. I should probably not have said anything, but I just find it a somewhat offensive/obnoxious tweet, but if Richard thinks it’s worth tweeting, then that’s his choice.

  14. semyorka says:

    That’s the sort of thing a 15 year old would tweet with a hashtag like “#bantz”.

  15. izen says:

    @-“The problem with suicide vests is that they are either small or conspicuous. Polar bears are big and fat.”

    ‘Explaining’ the joke just makes it a lot worse.

  16. Ethan Allen says:

    ATTP you need a translator, I don’t think I’m that translator, but I’ll take a whack.

    “Real question for Paris: How many explosives can fit in a polar bear suit?”

    Polar bears don’t count when we all have more pressing problems.

    See for example … Crusades …

    All ISIS really wants to do is replace the current set of despots with their own version of despotic rulers … oh and get rid of the Christian and (much more recently) Jewish hordes … that have been poking a stick in their eye for the better part of a millennium.

    “And up from the ground came a bubblin’ crude. Oil that is, black gold, Texas tea.”

    This is about as old as time itself … being territorial.

  17. I think the @RichardTol tweet, even if badly phrased, can just be taken as noting that there is a potential security issue with large public street demonstrations during the climate talks. It seems the Parisian authorities are evaluating that.

  18. Magma says:

    “Their model is simply a time series, with no real physics.”

    Hold on, that last word…? You mean these anomalies aren’t just a random-ish series of numbers? There’s physics involved??

    Re. Tol’s twittering: retweets may not imply endorsement, much the way not every low-slung waddling animal with a white stripe and a bad smell is a skunk. Some may simply be badgers that crossed paths with a skunk.

  19. Russell says:

    All Toll has to do to join the Tolstoi Club is stand in a corner for ninety seconds, and not think about a polar bear wearing an explosives belt.

  20. Eli Rabett says:

    Tol’s positives come pretty much completely from agriculture. He never really answered (biology, etc) Ackerman and Muntz’s criticisms

  21. Tom Dayton says:

    ATTP, funny that you mentioned Doug Keenan, because he is offering a $100,000 prize to anyone who can prove that global temperature trends are not a random walk, using “purely statistical” methods. No one should participate especially since there is a $10 entry fee, because the contest is rigged: Keenan has created 1,000 randomly generated datasets, some containing an artificial trend and some not, with the challenge for anyone to correctly identify which of them has the introduced trend. No actual climate data are involved. Keenan is free to generate the datasets to make the trends arbitrarily hard to detect. Also, his “purely statistical” requirement is so stringent that it is nonsensical. Very much like Monckton and whats his name the Statistician to the Stars; rather an undergraduate’s “understanding” of statistics and its application.

    Actually interesting, though, is his mention of two textbooks that he claims have “proven” that there is no “purely statistical” evidence for any trends in climate data. I haven’t read them, but suggested to Tamino that he have a look.

    Keenan’s challenge:

  22. Tom Dayton says:

    Well, heck, I should have known Tamino already would have addressed the random walk challenge. James commented at WTF that Tamino did that five years ago:

  23. Joshua says:

    ==.> “I think the @RichardTol tweet, even if badly phrased, can just be taken as noting that there is a potential security issue with large public street demonstrations during the climate talks. It seems the Parisian authorities are evaluating that.”

    Ah. Makes sense. Doesn’t reduce the incredibly poor taste of the “joke” (or Richard’s follow-on explanation) but at least now I get what it was supposed to mean.

  24. Tom,
    Yes, I’ve just read Tamino’s post. It’s very good. I’ve posted a link to it at BH too. That should sort this out, once and for all 🙂

  25. @David Sanger
    Indeed. And it was not meant to be a joke at all. I expect that nothing much will happen at the climate negotiations themselves. Things may well be happening outside. Al-Qaida focused on buildings and planes. ISIS has realized that crowds make targets too.

  26. Richard,
    That doesn’t really mean that it wasn’t in bad taste, but suit yourself.

    Oh, and if you don’t like that people often regard you as a climate science denier, maybe you shouldn’t positively associate with Doug Keenan’s nonsensical challenge. Of course, if you don’t care that people sometimes regard you as a climate science denier, carry on.

  27. Ethan Allen says:

    Odds of “winning” DK’s contest p = 4.7E-192
    Odds of getting all 1000 correct p = 9.3E-302
    Odds of getting in the ballpark of 500 correct p ~ 1
    Odds of “winning” Powerball jackpot p = 3.4E-09
    Odds that DK suffers from DK p = Infinite 🙂

  28. @wotts
    You can interpret Keenan’s challenge as an attempt to deny something. You can also interpret it as a test of statistical skill, as an opportunity to win money, as a way to test respondent’s attitudes to risk and skill, or an insight into Keenan’s mind.

  29. Richard,
    Given that his site says this

    the prize will be awared to anyone who can demonstrate, via statistical analysis, that the increase in global temperatures is probably not due to random natural variation.

    and then says

    A prize of $100 000 (one hundred thousand U.S. dollars) will be awarded to the first person, or group of people, who correctly identifies at least 900 series: which series were generated by a trendless process and which were generated by a trending process.

    It’s hard to interpret it any other way than him thinking that by correctly identifying the trendless, or trending, time series’ it will say something about whether or not the increase in global temperatures is probably due – or not due – to random natural variation. You keep defending this type of nonsense though, and then you can wonder why people seem to associate you with climate science denial. To be clear, though, I don’t really care either way. I’m just pointing out something that should be pretty self-evident.

  30. dikranmarsupial says:

    “You can also interpret it as a test of statistical skill, as an opportunity to win money”

    The challenge begins:

    “There have been many claims of observational evidence for global-warming alarmism. I have argued that all such claims rely on invalid statistical analyses”

    so it is pretty clear what the challenge about, and it isn’t statistical skill.

    The way to demonstrate statistical skill in this case is to ignore it as being a pointless exercise (as the nature of the random process is unconstrained). If you want to demonstrate statistical skill, and win money, there are much better opportunities such as Kaggle, where the tasks are at least meaningful, rather than just a way of drawing attention to an argument about climate that is already known to be misleading (as pointed out by Tamino and RealClimate and various others).

  31. I like this

    The way to demonstrate statistical skill in this case is to ignore it as being a pointless exercise

    Richard wants us to assume that he is a trained statistician who doesn’t make elementary errors and yet seems incapable of recognising that by defending Keenan’s exercise he’s making it pretty hard to regard this as a reasonable assumption.

  32. Ethan Allen says:


    The site also sez …

    “Some series then had a trend added to them. Each individual trend averaged 1°C/century—which is greater than the trend claimed for global temperatures. Some trends were positive; others were negative.”

    Since it’s NOT expressed in a strict mathematical form (e. g. equations instead of just words) no one other than DK knows exactly what was done or assumed. Linear trends? Median trend = 0 and mean trend = 1.

    Pointless exercise.

  33. dikranmarsupial says:

    It would increase confidence in the competition if there were some evidence that the challenge was actually achievable by statistical means. I have been involved in the organization of several open statistics/machine learning challenges, and an important part of organizing the challenge is to determine whether it is actually possible, and provide baseline solutions (in this case perhaps some R code). for the contestants to aim at.

    I suspect however that the challenge is a purely rhetorical one designed to make the point that it is difficult to detect trends without some constraint on the nature of the noise process. Of course we all know that already, however in the case of climate (and most practical statistical inference problems) we have prior knowledge that can be used to supply these constraints. For instance we know that planetary heat content is not a random walk, as that would violate the laws of thermodynamics.

  34. An old friend of mine never read the words in a paper. He just read the equations. They were much simpler to understand, he said. A new friend of mine works on the same rule. And indeed, regardless of what Keenan says, this is an exercise in statistics.

    The challenge is twofold:
    (a) identify the data generation process
    (b) estimate a linear trend

    (b) is simple but these tests have little power, so Ethan is correct to say that your chance of winning this is low because of Type II errors
    (a) would be hard if this is the only thing Keenan has ever written

  35. dikranmarsupial says:

    Richard “(b) is simple but these tests have little power” is essentially admitting that the challenge is pointless and not a useful test of statistical skill. Note that winning the challenge requires getting the answers right to 900 of the 1,000 datasets, which isn’t going to happen if the tests have little power.

  36. Richard,
    That doesn’t make it somehow relevant to what he’s apparently trying to illustrate. The main thing it illustrates is his ignorance of this topic. The main thing your defence of this illustrates is that people are perfectly justified in regarding you as someone who associates with climate science denial. Feel free to own that, or not, it doesn’t make any difference really.

    I realise that you are named in this post, so I am reluctant to delete your comments. However, I’m going to ask really nicely that you keep your spreading of misinformation to sites that appreciate that type of thing.

    would be hard if this is the only thing Keenan has ever written

    I’ve yet to see anything that Keenan has written that wouldn’t rightly allow one to regard him as a clueless buffoon and a nasty one at that. These posts may provide some insights.

  37. dikranmarsupial says:

    BTW, I think only reading the equations is pretty stupid and a recipe for misunderstanding the work by not paying attention to the caveats. It would be hubris to think that one would also see those problematic issues just by looking at the equations. I would recommend your friends to avoid this behaviour (however I suspect they are just showing off and actually do read the paper).

  38. Roger Jones says:

    Climate is not a random walk. It’s a non-Gaussian system. All wagers based on such are either trolling or misconceived (and therefore non-falsifiable within their priors) and should be regarded as such.

  39. This probably explains a great deal

    He just read the equations. They were much simpler to understand, he said. A new friend of mine works on the same rule.

    It might be worth Richard listening to the podcast that Grant McDermott suggests in this comment. That the person being interviewed has a background in physics and is South African has no bearing on my suggestion 🙂

  40. verytallguy says:

    So, the only person enjoying the dialogue with RT, is RT.

    Not exactly a novel experience, that.

    Oh, and the polar bear gag. Good grief.

  41. @dikran
    Maybe that’s the real answer. Anyone willing to pay £10 for a bet that alpha+beta<0.1 …

  42. Anyone willing to pay £10 for a bet that alpha+beta<0.1 …

    Illustrating why I asked Doug if his challenge was legal. I’ve no idea if it is or isn’t, but I have a feeling that you can’t simply set up something that could be perceived as a lottery without having some kind of licence.

  43. dikranmarsupial says:

    @RichardTol – yes, as I said, the best way to demonstrate statistical skill is to ignore it as a pointless rhetorical exercise.

  44. Ethan Allen says:

    COP21 climate marches in Paris not authorised following attacks
    French government says demonstrations in closed spaces can go ahead but not those in public places

    Hmm, so given only three choices …
    (1) Fight ISIS in the closed or open places of Paris unarmed or
    (2) Get airdropped over ISIS territory sans parachute (getting lucky and squashing a terrorist) or
    (3) Same as (2) but from a landed helicopter and full battlegear

    It does make one wonder, so much so, that one would have to ask oneself why ISIS didn’t wait another 2-3 weeks, trial run?

  45. Eli Rabett says:

    There are two styles of science. The grinders who fill notebooks with statistical drivel because their assumptions are ignorance, and the smart ones who think about the implications of their assumptions before starting. You can publish a lot of papers full of gremlin drivel if you don’t think

  46. anoilman says:

    Eli, As an engineer, I have to tell you that you that its much quicker to build things full of gremlin drivel. We often build things without understanding what really makes them tick. Its not hard to imagine why… there’s always a lot of pressure to develop products, and zero interest in researching how they work. Yet invariably its research that results in progress. (This is the result of accountants, they do not want to spend money on anything that will not be sold soon.)

    Makes you wonder about those pesky Think Tanks since by definition their pay masters don’t do research, and are at best adverse to it.
    “It is about the rise of the modern Think Tank and how in a very strange way they have made thinking impossible.

    Think Tanks surround politics today and are the very things that are supposed to generate new ideas. But if you go back and look at how they rose up – at who invented them and why – you discover they are not quite what they seem. That in reality they may have nothing to do with genuinely developing new ideas, but have become a branch of the PR industry whose aim is to do the very opposite – to endlessly prop up and reinforce today’s accepted political wisdom.”

    Now, who do we know who likes to work this Think Tanks I wonder? Hmmm….

  47. Marco says:

    Maybe just me and dunno if someone else pointed that out, but when Tol says “The very start of my career was about trying to show that CO2 and other greenhouse gases cause climate change. We were one of the first to establish that on a satisfactory statistical basis.”
    does he not contradict himself when he promotes Doug Keenan’s claims?

    That is, if Tol believes Doug Keenan is on to something, Tol admits his study does *not* have a satisfactory statistical basis, since he would have been using incorrect statistics.

  48. does he not contradict himself when he promotes Doug Keenan’s claims?

    Well, yes, that was my basic view. I have pointed this out on Bishop Hill, but noone seems to have noticed.

  49. @marco
    Nope. Keenan’s a statistical challenge.

  50. Richard,
    Wow. I’ll point this out one more time. If he simply phrased this as some kind of statistical challenge, then maybe you’d have a point, but he has not. He is explicitly claiming that this is related to the claim that the increase in surface temperature is not due to random natural variations. He seems to think that those who fit straight lines to the temperature dataset are somehow claiming to have found an actual underlying linear trend, rather than simply determining the best-fit straight line. He is savaging a strawman. It is ridiculous. That you would suggest otherwise is also ridiculous. It is one reason why assuming that you don’t make elementary errors is clearly a silly assumption.

    I have no idea why you would defend Keenan’s nonsense. It’s hard to believe it’s because you think it actually has some merit because that would be utterly bizarre. I guess it could be just because you like winding people up, but that you would be willing to damage your own credibility just to wind a few people up seems equally bizarre. On the other hand, this mostly goes un-noticed, so maybe that does make sense.

  51. dikranmarsupial says:

    “Nope. Keenan’s a statistical challenge.”

    A pointless challenge with a criterion for success that is likely to be, to all intents and purposes, impossible to achieve (which would make the entrance fee rather cynical).

  52. Dikran,

    which would make the entrance fee rather cynical

    That’s why I wonder if this is technically legal. Offering a large prize for submitting a set of numbers for either “trendless” or “with trend” which you may only get right by chance and which you have to pay to enter. Sounds a bit like a lottery to me.

  53. As a lottery it’s a crap business model. I suspect that the only people tempted to enter such a complex challenge would be people who are clever enough to work out there’s no hope of winning. Clearly the ‘challenge’ has been designed to provide yet another denial meme for ‘skeptics’ to use.

    The entry fee would appear to be to stop casual, multiple, repeat entries — which in sufficient numbers is the only way to win: ie, by sheer chance.

  54. john,
    I realise it’s a crap business model, but I’m not sure that that is a particularly good defense if what one is doing is illegal. I don’t know if it is, or isn’t, but if the chance of getting it right is vanishingly small, and there is an entry fee, I suspect that it could be perceived as a lottery, even if that wasn’t the intent.

  55. dikranmarsupial says:

    It is entirely possible that the odds on winning by chance are so small that it isn’t even a lottery. The probability of getting 900 or more successes out of 1000 independent Bernoulli trials with a probability of success of 0.5 is a *very* small number indeed (hint if you flip a fair coin 1,000 times, what is the probability of getting 900 or more heads).

  56. dikran,
    Yes, possibly, but I imagine “no one was ever going to guess the correct answer” is also not a particularly good defense 🙂

  57. dikranmarsupial says:

    Indeed, it does show though that the $10 entrance fee is not required to prevent someone winning by submitting multiple entries. Wolfram alpha (assuming I used it correctly) suggests the probability is about 7E-167, so if you submit a billion entries, you have only increased your chances of winning to 7E-158.

    I suspect it is a purely rhetorical exercise, relying on skeptics not noticing how unreasonable it is as a statistical challenge.

  58. I suspect it is a purely rhetorical exercise, relying on skeptics not noticing how unreasonable it is as a statistical challenge.

    I think you mean “skeptics” 🙂 I’m not sure, though. I think you’re giving Doug Keenan too much credit here. Given what I’ve seen, I get the impression that he really thinks that this is illustrating something significant, rather than illustrating his ignorance. It is possible that it is entirely cynical, but it could just be stupid.

  59. dikranmarsupial says:

    Good point, as a firm believer in Hanlon’s Razor (or at least moderately worded versions thereof), I withdraw that suggestion.

  60. Tom Curtis says:

    Tol: “Nope. Keenan’s a statistical challenge.”
    Richard Tol seems to think Keenan is himself a statistical challenge, but deniers are depressingly run of the mill, so I don’t see how he can be a statistical challenge at all.

  61. BBD says:

    Tom cracks a joke? Now that doesn’t happen every day. Truly these are strange times. 🙂

  62. Willard says:

    I just want to say one word to you. Just one word. Econometrics.

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