Pelletier [2002] on Temperature Autocorrelation

Benestad at realclimate here, against Cohn and Lins, argues that their use of time series methods more advanced than Benestad’s IID, somehow offended against the laws of physics, "pitching statistics against physics" – plus other gems. It has to be read to be believed. Now white noise (equivalent to Benestad’s IID, independent identically distributed residuals) has a distinctive horizontal spectrum, while red noise has spectra sloping down and to the right. Before proclaiming that it is against the "laws of physics" for temperature data to have autocorrelation properties, one thinks that Benestad might have examined some actual spectra of temperature and temperature proxy series (rather than exclusively relying on GCM output), to determine whether his IID assumption applies.

As I mentioned before, the redness of geophysical series was remarked upon as long by Mandelbrot. The references in Cohn and Lins [2005] are clear and Benestad would profit from reading these articles. Another interesting recent discussion is Pelletier [PNAS, 2002], who not only shows redness in both temperature and temperature proxy data, but proposes a physical mechanism which could account for the power law properties of the series. I don’t have any views on whether Pelletier’s theory is right or wrong, but it is interesting. Equally important is the mere fact that the series have distinctive power law properties – since the measurements have power law properties, such power law behavior is obviously not against the "laws of physics" (contra realclimate), but a valid topic of inquiry. If GCMs do not capture this power law behavior, as they seem not to do, based on Benestad’s account, then possibly the GCMs are at fault, rather than the data.

Pelletier’s Figure 1 and Figure 2 below show the spectra from Vostok and from 94 GHCN stations. While one can quibble with how Pelletier divides up the diagram, it is indisputable that the spectra are downsloping to the right – characteristic of autocorrelation of the type contemplated by Cohn and Lins [2005].

Original Caption: Left: Fig. 1. Power-spectral density estimated with the Lomb periodogram of the temperature inferred from the deuterium concentrations in the Vostok (East Antarctica) ice core. The power-spectral density S is given as a function of frequency for time scales of 500 yr to 200 kyr. Right Fig. 2. Average power-spectral density of 94 complete monthly temperature time series from the data set of Vose et al. (8) plotted as a function of frequency in yr^-1. The power-spectral density S is given as a function of frequency for time scales of 2 months to 100 yr.

Pelletier’s Figures 3 and 4 show what appear to be different spectra for land and maritime stations – with the maritime stations being considerably redder.

Original Caption: Fig. 3. Average power-spectral density of 50 continental daily temperature time series from the data set of the National Climatic Data Center (9) as a function of frequency in yr^-1. The power-spectral density S is given as a function of frequency for time scales of 2 days to 10 yr. Fig. 4. Average power-spectral density of 50 maritime daily temperature time series from the data set of the National Climatic Data Center (9) as a function of frequency in yr^-11. The power-spectral density S is given as a function of frequency for time scales of 2 days to 10 yr.

Pelletier then combines the spectra for different scales into one composite spectrum as follows:

Original Caption: Fig. 5. Power-spectral density of local atmospheric temperature from instrumental data and inferred from ice cores from time scales of 200 kyr to 2 days. The high frequency data are for continental stations. Piecewise powerlaw trends are indicated.

Pelletier provides an interesting physical hypothesis as to how such power-law behavior could arise in terms of very different heat transfer properties between land and atmosphere as compared with ocean and atmosphere:

We can interpret these results in terms of the vertical turbulent transport of heat energy in the atmosphere in addition to its radiation into space and its exchange with the ocean. The ocean acts as a thermal reservoir, buffering changes in atmospheric temperature. In our model, vertical turbulent transport is modeled as a stochastic diffusion process. Convective instabilities diffuse heat energy within the atmosphere by turbulent mixing. Deterministic diffusion is not adequate to model atmospheric heat transport, however, because the stochastic nature of turbulent flow in the atmosphere gives rise to fluctuations in the transport of heat through time….

In the introduction, we presented evidence that continental stations exhibit an f^-3/2 high-frequency region, and maritime stations exhibit f^-1/2 scaling up to the highest frequency considered. This observation can be interpreted in terms of the diffusion model presented above. The power spectrum of temperature variations in an air mass exchanging heat by one-dimensional stochastic diffusion is proportional to f^-1/2 if the air mass is bounded by two diffusing regions and is proportional to f^-3/2 if it interacts only with one. The boundary conditions appropriate to maritime and continental stations are a layer interacting with two (upper atmosphere and ocean) and one (upper atmosphere only) thermal reservoirs, respectively.The layer considered is taken to have an upper boundary embedded in the atmosphere and a lower boundary at the earth’s surface. For maritime stations, heat is transferred across this lower boundary into the oceans … and therefore the power spectrum of temperature variations is S(f) = f^-1/2. For continental stations, the lower boundary is insulating so…S(f) = f^-3/2. At low frequencies, horizontal heat exchange between continental and maritime air masses limits the variance of the continental stations This crossover occurs at the time scale when the air masses above continents and oceans become mixed. The time scale for one complete Hadley or Walker circulation which mixes the air masses…

The second term is the time scale for transport of the heat energy of the ocean to the top of the atmosphere where it can be radiated from clouds. If the time scale for one of these processes is much larger than the time scale for the other, the crossover time scale will be determined by that rate-limiting step. For the Earth’s climate system, the transport of the oceans’ heat through the atmosphere seems to be the rate-limiting step. This process takes a long time because the atmosphere has a low heat capacity compared to the oceans and is therefore a poor heat conductor. The time scale of radiative damping is estimated to be 600 yr from the well known constants listed in Fig. 6

Elsewhere Pelletier makes an interesting comparison between the stochastic properties of turbulent eddies and Brownian movement. Pelletier has a number of interesting articles at two websites amd they are worth reading. Whether right or wrong, considering the possibility of power law behavior in the spectra of temperature series is not an obvious offence against the "laws of physics", as Benestad would have us believe.

Reference: Jon D. Pelletier Natural variability of atmospheric temperatures and geomagnetic intensity over a wide range of time scales, 2002, PNAS, 99, 2546-2553. URL

Old Pelletier website New Pelletier website


  1. TCO
    Posted Dec 19, 2005 at 1:49 PM | Permalink

    In summary:

    1. The data show autocorr behavior (regardless of whether we have the right physical explanation) so to assume iid (without proof of that) is perilous.
    2. There are some conceiveable physical explanations for the behavior (though not nescessarily the right ones…but then again the modelers can’t model climate either).

  2. Steve McIntyre
    Posted Dec 19, 2005 at 2:19 PM | Permalink


    That climatological series show power-law behavior (a form of autocorrelation) has been known in one way or another for at least 50 years (Hurst’s discussion of the Nile River data is that old) and Mandelbrot is nearly 40 years ago. This is hardly against the “laws of physics”. If GCMs don’t replicate power law behavior, is it conceivable that they are missing some relevant aspect of the physics?

    It’s funny what happens when you turn the stones over.

  3. TCO
    Posted Dec 19, 2005 at 3:42 PM | Permalink

    This is such a key, interesting, and poorly described issue, that it irks me when you throw it in gratitously into discussions of other failings.

    Next meeting you go to (or paper) that you write, write it just on this issue. Don’t put in a bristlecone or anything that is a failing that is not part of examining this issue. Also, my impression is that you don’t have an open and shut case on this issue, so your discussion and publication should not try so hard to be a gotcha of your enemies but rather a call to attention of an issue.

  4. Posted Dec 19, 2005 at 4:17 PM | Permalink

    In science, when real world data and model results do not agree, the models are considered wrong. In climatology, when real world data and model results do not agree, the real world is considered wrong.

  5. John S
    Posted Dec 19, 2005 at 4:57 PM | Permalink


    Sounds just like economics. The similarities grow by the day! And still climatologists would deny their affinity with economists.

  6. Ian Castles
    Posted Dec 19, 2005 at 5:20 PM | Permalink

    The IPCC relies on (poorly specified) econometric models for its emissions projections and therefore for its projections of future climate. As one leading economic modeller, John Reilly of the MIT Joint Program on the Science and Policy of Global Change, said in 2002: “The SRES scenarios were just, in my view, a kind of insult to science.” Asked whether they were also an insult to economics, Reilly replied: “Well, to anything; an insult to serious analysis” (National Post, Toronto, 27 November 2002).

  7. Posted Dec 19, 2005 at 7:12 PM | Permalink

    I, for one, could not believe Steve, so reading the article at RealClimate was necessary. Indeed, Steve is right. Rasmus Benestad essentially denies that any information can be encoded in the autocorrelation of the temperature – such as the power laws determining the “color”. And even if there were some information, he denies that the models should be tested whether they predict the observed autocorrelation properties. And even if they were tested and found to disagree with reality, Benestad apparently prefers the models over reality because their current models is what he calls “laws of physics” – while the observations are “just some statistics”. 😉

    Well, their models could also be wrong and naive laws of physics constructed by naive scientists and pseudoscientists, which is probably what they are. If everyone had the same approach to research as Benestad in the past, we would still be repeating that the world was constructed as explained in Genesis because the apparent existence of animals, the Sun, and the Earth show exactly the same composition as one predicted in Genesis, which means that Genesis contains the laws of physics, and anyone who disagrees with it or tries to modify any details is pitching statistics against the laws of physics – in other words, such a person is a complete heretic who could be misused by “septics”. 😉

    Benestad’s examples with the Schràƒⵤinger equation for small atoms and Brownian motion painted as the only examples of chaotic behavior show completely clearly that he does not believe that there exists any chaotic or fractal behavior at macroscopic scales. Benestad’s opinion is of course completely ridiculous. It is enough to magnify the “water molecules” and “seeds of dust” to see the same mathematics of Brownian motion at arbitrary length scales. Of course that the atmosphere is pretty analogous to a “magnified Brownian motion experiment”. Systems with different pressures and temperatures are systematically colliding, interacting, and make the weather essentially unpredictable.

    The idea that this rich and chaotic dynamics of weather can be ignored when the averages over the whole planet are computed is a hypothesis waiting for evidence. All these things are irrelevant for various Benestads. They already have the truth and don’t want to modify a single letter about it.

  8. Douglas Hoyt
    Posted Dec 19, 2005 at 7:31 PM | Permalink

    One way to make seasonal climate forecasts is to assume persistence. It is a simple technique and yet it works quite well. Persistence means there is autocorrelation.

    In Figures 2 and 3 above, what is the physical significance of the exponents on frequency? Does a high value mean a high climate sensitivity and a low value mean a low climate sensitivity, based upon continental and maritime results? If so, it would imply that climate sensitivity is a function of frequency (Figure 5).

  9. TCO
    Posted Dec 19, 2005 at 7:42 PM | Permalink

    Lubos great post, but you verge near a failing that some of the other skeptics here (but not Steve) fall into, which is to say that since long-range weather forecasts can not be done, climate modeling can not be done.

    To me a good analogy is turbulent flow in water that is undergoing nucleate or film boiling. Yes, I have no idea where a given water molecule will go, but I can still predict how % steam in the pressure vessel will change for a given heat intake.

  10. Posted Dec 19, 2005 at 8:15 PM | Permalink

    <![CDATA[Dear TCO,

    thanks for your warning 🙂 and don't worry, I am still academically rooted in the sector of science where everything is and should be predictable and chaos is not a welcome guest, and where mostly everything is even calculable using perturbative techniques around the "classical", "tree-level", or "deterministic" solution.

    Still, we have many systems – like conformal field theory – where the critical exponents matter and can be calculated. Sometimes – like in 4D – the critical exponents are just small deviations from the "classical ones"; sometimes – like in 2D – the critical exponents are not accessible by perturbative techniques. They take general values but can still often be determined from conformal symmetry and other principles.

    Benestad seems to assume that at long scales, the critical exponents always match the classical prediction for them. That's of course nonsense.

    Similar things can exist – and according to a lot of data do exist – in the climate, and we discussed the critical exponents of the weather one month ago. I find it very likely that these things will be safely predictable in the future, with a small enough error margin, but in order to find increasingly better models, we must be testing them against increasingly difficult tasks. Autocorrelation properties are probably among the important ones.

    The idea that we have already the “complete” models that can’t really be improved is naive. One obvious reason why it is naive is that people have many different models and cannot say which ones are really better. And once we accept that the idea that “we’re finished” is naive, the most obvious path to progress is to look for the greatest existing discrepancies between observations and the existing models. Some people just don’t want to do it.

    Turbulence is sometimes a difficult enterprise. There can be several metastable regimes of a whirlpool in the same tube, for example. Macroscopically in hydrodynamics, you can usually predict (assuming that there is no discrete ambiguity like one mentioned above) the averages at length scales and time scales that “exceed” the scales of the turbulent regime. (This is a bit of exaggeration because no one can really calculate “analytically” the total friction as the function of shape of the wing in the turbulent regime.)

    But there are good reasons to believe that the corresponding time scales of the climate can be longer than many years. More importantly, the correct classical phenomenological laws that are valid at long scales are not the same laws that you would get by simply assuming the “average” of the microscopic laws. There is renormalization going on; all the parameters may be very different than one would expect by a naive classical extrapolation. And new types of terms may be created.

    In effective field theory, we know how to organize the “critical behavior” and in principle, we can write the most general type of dynamics that is conceivable at long scales given a set of degrees of freedom. This does not exist for the climate. The GCMs are still about guessing.

    My intuition is that reproducing the scaling laws is a better clue to find profoundly correct models than the information that temperature grew in the 20th century (or in individual 30 year periods). It may be as useful as reproducing some broad features of El Ninos. Concerning Cohn and Lins, their main thesis is quite obvious. The statistical significance can only be evaluated if we have a good model predicting how things should behave if the new effect were absent. In the case of the climate, this of course requires to know, among other things, the color of the noise and autocorrelations. Natural inertia can exist and could be confused with a “new signal” or “trend”, and one must probably study these systems together unless it can be proved that these two different contributions to the “trend” can be isolated from each other.

    One can never be satisfied with a model if it predicts less nontrivial numbers than the information that we inserted.

    All the best

  11. TCO
    Posted Dec 19, 2005 at 8:31 PM | Permalink

    Oh…quit trying to show off. Be a real man and get a big red tool chest and dig some holes in the concrete to put anchor bolts in and built some big honking vacuum chamber thingie for cool solid state physics work.

  12. Paul Linsay
    Posted Dec 19, 2005 at 9:30 PM | Permalink

    At the time scale of days, Pelletier’s results may be standard turbulence. In 1941 Kolmogorov developed a model of turbulence that had a power spectral density for the energy that falls as k^(-5/3) where k is the wave number. (See for example and notice the verification by the wind tunnel experiment.) If I take a scale of 1 km, a wind speed of 30 km/hr and a kinematic viscosity for air of about 1.38 e-5 m^2/s the Reynolds number of the lower atmosphere is about 6 e8, easily satisfying the assumptions of Kolmogorov’s theory. The short term exponent of about -1.5 is not too different from -5/3.

  13. Steve McIntyre
    Posted Dec 19, 2005 at 9:40 PM | Permalink

    Re #3: TCO, what is the “this” that interests you specifically?

  14. Steve McIntyre
    Posted Dec 19, 2005 at 9:45 PM | Permalink

    Luboà…⟺ you said: “One can never be satisfied with a model if it predicts less nontrivial numbers than the information that we inserted.” Kaufman, the one who posted up at the realclimate thread,has recently posted up a paper asserting that GCMs do not improve the prediction of temperature above what can be obtained with simple (presumably regression-type) models based on the forcing inputs. I’ll try to post up a note on this.

  15. Posted Dec 20, 2005 at 1:49 AM | Permalink

    now if we compare fig 5 of Pelletier with observed climate sensitivities:

    I see some remarkable similarities.

    see also

  16. Posted Dec 20, 2005 at 2:10 AM | Permalink

    the most interesting part of Pelletiers fig 5 is beween 10 and 1000 years, where data is lacking

  17. DF
    Posted Dec 20, 2005 at 2:20 AM | Permalink

    One of the things that gets obscured in looking at the data like this is that some of the fluctuation spectrum is internal variability (e.g. ocean-atmosphere heat exchange) and some externally driven (e.g. Milankovitch and other processes). I am especially struck by the large data gap between the essentially sub-decadal fluctuation spectrum of surface temperatures that was stitched onto the multi-millenial Vostok record.

    At time scales of a few years, the dominant “noise” is ocean-atmosphere heat exchange in the form of ENSO type events where one can observe the effects of energy moving into and out of the oceans. In essence the temperature record incorporates this noise by only measuring the atmosphere component of this two part reservoir. At longer time scales, energy conservation tells us that the ocean-atmosphere system must necessarily average to equilibrium, so using a fluctuation spectrum derived at ENSO timescales would probably tend to overpredict long-term fluctuations.

    The only question is at what scale that is true. Are the decadal to centennial processes also reflecting significant internal variability, or do they primarily respond to long-term external forcings. Most GCM control experiments are in some sense a prediction of the fluctuations that would be observed if external variability is held fixed. Taken at face value, such experiments argue that there is little to no internal temperature variability at multi-decadal to centennial time scales. In other words, the GCMs argue that all long-term climate change can be solely explained as the response to changes in forcings (solar, volcanic, greenhouse gas, etc).

    Whether that conclusion is correct will depend on getting a better grasp of the internally driven fluctuation spectrum on decadal to centennial time scales (the part where Pelletier’s work is data poor) and examining attribution studies to see if there are long-term fluctuations that can’t be explained in terms of what GCMs view as external forcings. On that note, I’m surprised that no one at this site has made mention of Meehl et al. (J. Clim, 2004) which argues that the estimated forcings at their estimated amplitudes are sufficient to explain the long-term temperature record since 1900. In essence that work argues for the GCM view that there aren’t any additional internally driven temperature fluctuations, and all one needs to know is the effects associated with the proscribed external changes.

    I think this is the essence of the physics versus statistics dichotomy. The people at RC are arguing that all you need to know to determine long term climate change is the external forcings and all the physical processes by which they affect the Earth. In their view the statistics is just a little bit of noise put on top of that. And that could be true if most of the fluctuations in the past can be convincingly assigned to known forcing agents (so that in essence the remaining internal/unexplained fluctuations really are small).

  18. Posted Dec 20, 2005 at 2:50 AM | Permalink

    which Meehl et al. (J Clim, 2004) are you referring to?

    Meehl, G.A., W.M. Washington, C.M. Ammann, J.M. Arblaster, T.M.L. Wigley and C. Tebaldi, 2004: Combinations of Natural and Anthropogenic Forcings in Twentieth-Century Climate. J. Climate, 17, 3721-3727.
    Meehl, G.A., W.M. Washington, J.M. Arblaster and A. Hu, 2004: Factors affecting climate sensitivity in global coupled models . J. Climate, 17, 1584-1596.

  19. John S
    Posted Dec 20, 2005 at 2:52 AM | Permalink

    Re #17

    “And that could be true if most of the fluctuations in the past can be convincingly assigned to known forcing agents (so that in essence the remaining internal/unexplained fluctuations really are small).”

    Not really. RC (at least Rasmus) seem to be talking about the philosophical concept of randomness not statistics. Regardless of how deterministic your model or the world is you will still need to provide validation of the model against observed variables. If the model perfectly predicts everything – congratulations. If not, you need to use statistical techniques to validate it (there is no statistics versus physics divide – there might be a determinism versus randomness divide, but regardless of which it is, you will still need to use statistics as an integral part of physics). And in using those techniques you need to be very careful about the properties of the unexplained errors and the series you are modelling. If the series you are modelling is non-stationary (and, just for example, temperature over the instrumental period is) then standard OLS regressions are pretty much guaranteed to give erroneous results. Which seems to be Cohn et als point (but I can’t see the full article because I’m not willing to fork out $9 for the pleasure). At the moment I’m not convinced that some of the people at RC really get it.

  20. DF
    Posted Dec 20, 2005 at 3:33 AM | Permalink

    Meehl et al. #1 “Combinations of Natural and Anthropogenic Forcings in Twentieth-Century Climate”

  21. Posted Dec 20, 2005 at 4:25 AM | Permalink

    Meehl, G.A., W.M. Washington, C.M. Ammann, J.M. Arblaster, T.M.L. Wigley and C. Tebaldi, 2004: Combinations of Natural and Anthropogenic Forcings in Twentieth-Century Climate. J. Climate, 17, 3721-3727.

    Click to access meehl_additivity.pdf

    Where is the aerosol data archive?

  22. TCO
    Posted Dec 20, 2005 at 6:26 AM | Permalink

    Steve, autocorrelation.

  23. Posted Dec 20, 2005 at 8:48 AM | Permalink

    Dear Steve,

    I would indeed be very interested in some assessment of the output vs. input comparison for the models in general or some of them in particular. Do you have some framework how to evaluate the difference between successful predictions and input parameters quantitatively?

    While I agree that it is more natural to try to build models that reflect the description of the phenomena as we understand them in physics – rather than Ross’s correlations with the membership in the Soviet Union, illiteracy rate, and GDP growth 😉 (nothing against Ross!) – choosing the right words and equations that are relevant elsewhere does not yet guarantee a successful model.

    My text about this Cohn Lins story is here

    All the best

  24. Steve H
    Posted Dec 20, 2005 at 9:33 AM | Permalink

    Lubos, excellent posting on your site!

    However, be prepared for accusations from Peter Hearnden of being “insulting” (he seems to be have a bee in his bonnet about this recently), as well being taken to task for barely masking your “underlying contempt for your betters” (but I’m sure you can handle it).

  25. John Hekman
    Posted Dec 20, 2005 at 3:44 PM | Permalink

    It seems that climatology recapitulates economics. In the sixties and seventies, large macro models of the U.S. economy were all the rage. They were remarkably similar to the GCMs, because they incorporated “economic theory” into their structure, and their adherents always had an answer for why the models didn’t seem to tell us anything useful about what was happening to the economy. The most prestigious model (it may still exist for all I know) was the FRB-MIT-Penn model, with over 175 equations modelling all major industrial and monetary segments of the economy. In an article published in the American Economic Review in 1972, then-assistant professor Charles Nelson showed that with the use of Box-Jenkins time series analysis, a simple time-series model (incorporating auto-regressive elements, of course) performed better than the FMP model in predicting economic growth one quarter out. Gradually, the big models lost their sex appeal. By the time I worked at the Fed in 1980, no one really thought they were doing much good.
    It remains for some enterprising assistant professor today to demonstrate the same result in climatology using time series models.

    The Nelson article is here:

  26. TCO
    Posted Dec 20, 2005 at 4:26 PM | Permalink

    Has the title posting on RC been changing? I just wonder if part of the damage control is to fix that without putting an “update notice”. But I admit I read it very quickly first time.

  27. John A
    Posted Dec 20, 2005 at 4:26 PM | Permalink

    The thing about the economic models was that the modellers went bust when they bet on the model outcomes. That’s the key difference with the GCMs: the modellers are putting nothing tangible on the line in case they happen to be wrong (which is going to be difficult since they put no success criteria into their predictions projections scenarios.

  28. Ross McKitrick
    Posted Dec 20, 2005 at 4:38 PM | Permalink

    #23 Yes Lubos, but it’s a mistake to build a physical model to explain data that reflect, in part, extraneous patterns arising from socioeconomic influences during the measurement process. That extraneous signals exist in the underlying data is not itself controversial–all the temperature teams say so and have adjustments to ‘fix’ the problem. But the nature and adequacy of the adjustments is something that needs to be tested, a task the climate field seems largely uninterested in pursuing.

    #25 As John says, there was an economic incentive to abandon models that could be bested by time series analysis. I wonder if a market trader could set up a derivatives product whose value depends on the match between a lab’s GCM output and future observed data, and then we see how many employees of the lab would be willing to invest his or her pension in the fund.

  29. Steve McIntyre
    Posted Dec 20, 2005 at 5:04 PM | Permalink

    #26: it looks shorter to me now that you mention it, but I can’t say for sure. Remember Gavin saying that he wasn’t going to discuss unpublished material – now the magic bullet supposedly showing that the autocorrelation properties of GCMs are alright is an unpublished paper by Stone et al., discussing the new generation of models. I guess that this means that the autocorrelation properties of the generation of models used for IPCC TAR were no good. I’ve been looking at Stone et al. and, at a first look, they model GCMs through EBMs and then calculate autocorrelation properties of the EBMs – which are flat. They do not appear to examine autocorrelation properties of long proxies like Vostok or long GHCN stations, but only the Jones hemispheric averages. More on this some time.

  30. Armand MacMurray
    Posted Dec 20, 2005 at 6:14 PM | Permalink

    It hasn’t been changed since at least Dec 16th, which is the version Google’s cache just displayed for me.

  31. Steve McIntyre
    Posted Dec 20, 2005 at 6:26 PM | Permalink

    I guess it only seems shorter because we savored each word and were longing for more.

  32. TCO
    Posted Dec 20, 2005 at 8:51 PM | Permalink

    Thanks Armand. I wonder if I should start posting my posts that I post there, here. I bet they will soon start censoring me (as continuing a debate or pressing an issue to conclusion is seen as overaggressive by the pseudosophisticate NPR-lite types over there).

  33. Armand MacMurray
    Posted Dec 21, 2005 at 3:51 AM | Permalink

    Re: #31
    You better be careful — it seems that (over?)earnestness is de rigeur for a “real” climate blog.

  34. Armand MacMurray
    Posted Dec 21, 2005 at 4:08 AM | Permalink

    Re: #32
    They seem to be less reflexively censorial since the recent big dustup, although still prone to abandoning dialogs (perhaps for lack of good answers?). If RC wants to limit the intellectual content of their site, it’s their loss. I don’t think there’s any current need to police them for censorship.

  35. Willis Eschenbach
    Posted Dec 21, 2005 at 4:31 AM | Permalink

    One of my writings were attacked on the RC site recently, and they allowed me to post the counter-arguments … I think the heat that this blog put on Gavin et. al. may be getting a bit of traction.

    I don’t like the fact that they close certain threads, though. What, they believe that everything possible has been said on the subject?


  36. Posted Dec 21, 2005 at 5:07 AM | Permalink


    I do not recognise my post on RealClimate in your caricature here. Please re-read my post carefully. I think that you have seriously misundertood my message!


  37. Posted Dec 21, 2005 at 7:34 AM | Permalink
  38. Steve McIntyre
    Posted Dec 21, 2005 at 8:02 AM | Permalink

    Rasmus, you say that you do not recognize his post here. This post was primarily about Pelletier [2002], as indicated in the title. I did mention your post in passing as follows and perhaps you can clarify how the following statements constitute a caricature:

    Benestad at realclimate, against Cohn and Lins, argues that their use of time series methods more advanced than Benestad’s IID, somehow offended against the laws of physics, "pitching statistics against physics" – plus other gems. It has to be read to be believed.

    I felt that this encouraged people to read your post. I’ve added a specific URL to your post and I hope that helps. If your objection is to the second sentence – i.e. that your post does not have to be read to be believed – then I would argue strongly against that.

    The other mention of your post here was:

    If GCMs do not capture this power law behavior, as they seem not to do, based on Benestad’s account, then possibly the GCMs are at fault, rather than the data.

    Again, I do not see how this misrepresents your article. However, in order to minimize the possibility of caricature, I have also made a post entitled "The Sayings of Rasmus", quoting you directly. Speaking on behalf of climateaudit, we appreciate these sayings, pearls before swine as it were, and you are always welcome here.

  39. Peter Hearnden
    Posted Dec 21, 2005 at 8:09 AM | Permalink

    Re #37 Lubos, fall flat undergraduate ‘satire’ doesn’t come well from a university lecturer. I think you need to decide if you are up there with them or down here with us.

  40. Posted Dec 21, 2005 at 8:34 AM | Permalink

    rasmus, it is a mistake to expect Steve or his sock puppets to behave honourably. Don’t waste your time here.

  41. TCO
    Posted Dec 21, 2005 at 9:35 AM | Permalink

    I find Steve to be very honorable. He is irreverant or mocking at times. But honorable. You on the other hand, would mince about tidyness at a crucifixion. You are so off the main points and on to minor distractions as to be tendentious and wormy. ****.

  42. Dave Dardinger
    Posted Dec 21, 2005 at 9:40 AM | Permalink

    re #40

    Well Tim, I suppose I should have gone ahead and posted a message I had mostly written last night (but got too tired to finish) in which I stated I didn’t see anything all that wrong with Rasmus’ post, though I disagreed with some of his points, in particular the one saying that macroscopic action doesn’t exhibit random action. I think I do agree, in some sense that physics rules in many cases. But I think many people, not just Rasmus, fail to understand how random quantum actions percolate up and impart their random character to higher-level entities.

    Consider an asteroid heading toward the earth. Random fluxuations aren’t going to move it either toward or away from the point it’s aiming to either hit or miss the earth. However, the path of the asteroid is the outcome of a great many past encounters with smaller and larger objects in the solar system. You need not go back very many such interactions to reach a point where ignorance of the exact initial conditions of this asteroid to within less than a typical quantum action will make it impossible to say whether or not this object is going to collide with or miss the earth today.

    You can’t suddenly change the track of a hurricane with quantum actions, but you can easily describe mechanisms which will convert lack of knowledge of one butterfly wingbeat to the difference between a hurricane and a mild tropical storm. This is what Rasmus is apparently not willing to accept.

  43. sock puppette
    Posted Dec 21, 2005 at 3:14 PM | Permalink

    Re #39 “..up there with them or down here with us” – another gnomic utterance from the fount of all wisdom.

    Re #40 – now Rasmus, do as Momma tells you and come inside at once – she doesn’t want to see you playing with those naughty, rough boys across the street again.

  44. Steve McIntyre
    Posted Dec 21, 2005 at 3:47 PM | Permalink

    #43- didn’t they say that they were the Hockey Team, not a bunch of figure skaters? Here at climateaudit, we go into the corners; we don’t just dipsy-doodle at centre ice.

  45. John A
    Posted Dec 21, 2005 at 5:12 PM | Permalink

    Hockey Ice Rinks don’t have corners. I think its the law.

  46. Dave Dardinger
    Posted Dec 21, 2005 at 5:43 PM | Permalink

    Re: #45

    But it’s not a law of physics, so it must just be a statistical anomaly. OTOH, cutting corners does seem to be a general rule for the Hockey Team.

  47. TCO
    Posted Dec 21, 2005 at 6:34 PM | Permalink

    Someone respond to Gavin’s latest at the other site, please.

  48. Steve McIntyre
    Posted Dec 21, 2005 at 7:53 PM | Permalink

    #45: John A., are you contradicting a Canadian about hockey rinks? Please.

    #47. It was only a matter of time until Gavin stepped in. I’ll get to this tomorrow.

  49. per
    Posted Dec 21, 2005 at 8:36 PM | Permalink

    hi there
    at RC, they have gone to their “approval” regime. Last time I posted, it went up instantly; now it is in the approval queue. For the record:
    let me see if I can follow gavin’s reply to #52 ?

    Although we have accurate temperature data for the last two centuries, and it does show autocorrelation, you are hypothesising that this is due to the natural and anthropogenic forcing. We cannot extrapolate from this to previous times, because there was no anthropogenic forcing.

    It is very tempting to conclude that you are suggesting that it is only anthropogenic forcing which causes autocorrelation. Clearly, if natural forcings can cause autocorrelative behaviour, then we would have to conclude that previous temperature records could be autocorrelated.

    I have to say it is very difficult to understand why we should accept your hypothesis that only current conditions, and no other, should result in autocorrelated temperatures. It seems to me to be speculation.

    I believe that there are historical temperature records going back over thousands of years. Is there not evidence from these series of autocorrelation ?

    I do not understand your logic with respect to GCMs. You say that the behaviour of GCMs must be validated. But it appears to be an integral part of your case that you cannot do that validation with the temperature records of the last two centuries. How then will we ever be able to test whether gcms adequately represent the autocorrelative (or otherwise) properties of nature, if we do not have a database to test them against ?


  50. Paul Linsay
    Posted Dec 21, 2005 at 8:52 PM | Permalink

    #42: David. You don’t need to invoke quantum mechanics, chaotic dynamics works fine. It’s a purely classical phenomenon that appears in non-linear dynamical systems. In the case of the asteroid, there are points in its orbit, but only certain points, where tiny collisions with rocks or whatever will send it off into wildly different orbits that depend on exactly how it was hit. It’s the principle that NASA uses to send satellites to the outer planets. By carefully selecting the orbit, small rocket boosts at the right time and in the right direction get it to its destination. That’s why the orbits looks so weird initially, sometimes even going off in the opposite direction. A direct shot requiring brute force would never get a satellite to Saturn because they can’t make a big enough rocket with enough fuel.

    More germane to the subject of this web site, it’s why weather prediction is short term, two weeks max, and why GCM’s aren’t worth the electricity they use to predict the climate. It’s a highly non-linear system subject to chaotic dynamics. Small errors in inputs result in wildly different futures. It takes an awful lot of them to get any kind of meaningful statistical average that could tell you anything, assuming that the science is 100% correct, even more doubtful.

  51. Dave Dardinger
    Posted Dec 21, 2005 at 9:32 PM | Permalink

    Quite so, Paul. But the advantage of QM is that not only do the final results depend sensitively in initial conditions, but even having perfect initial conditions wouldn’t help you. There’s no way to ever predict unforced weather more than a few days (though it might be possible to force the weather to do what we want. And the climate, while predictible within certain bounds, isn’t much fun when you consider that the bounds include ice-ages and things like that.

  52. Steve McIntyre
    Posted Dec 21, 2005 at 11:40 PM | Permalink

    Per, look at Pelletier’s spectrum for Vostok dO18 shown above. Vostok dO18 is a temperature proxy – it is highly autocorrelated; the variability is “natural”. If they won’t accept the instrumental record for calibration, then why not Vostok? The relevant issue is “natural forcing”, not “unforced”.

    BTW if realclimate opposition to the use of instrumental records for calibration were applied to other calibrations e.g. MBH, it’s possible that they wouldn’t like the result.

  53. Armand MacMurray
    Posted Dec 21, 2005 at 11:50 PM | Permalink

    Re: #49
    (your post at RC has now appeared and been rather impolitely commented upon by Gavin)
    Per, Gavin is arguing that observed climate variables contain autocorrelation resulting from both (a) internal climate system autocorrelation and (b) autocorrelation due to forcings (including both (b1)natural and (b2)anthropogenic forcings). He argues (I think) that (a) is what we need to know in order to evaluate statistical significance, and that since observations of past and present climate all include (b1) or (b1+b2) in addition to (a), that the proper way to determine (a) alone is by “observing” a GCM in the absence of forcings.
    However, since GCMs can only be validated by comparison with real-world data, one has to run the GCM *with* forcings in order to validate it. Thus, one can only determine (a) alone once one has a GCM that has been validated against observed data. This would seem to leave us without any practical way of determining (a) for at least many years to come.
    Leaving aside the issue of how much data is enough to validate the GCM (since presumably it would have to reproduce glacial/interglacial cycles), I wonder if we really need to go all the way to (a) alone? Since a major goal is to determine how unusual recent decades are when compared with the past behavior of the climate system (which included natural forcings), I would think there ought to be useful information in climate records, even if they include autocorrelation from both (a) and (b1) sources.
    I await enlightenment…

  54. Terry
    Posted Dec 22, 2005 at 12:55 AM | Permalink

    Re: #53.


    This is a little eery. I just posted a question for you on RealClimate asking you what you just asked in your #53 above. I thought YOU knew the answer.

  55. per
    Posted Dec 22, 2005 at 2:12 AM | Permalink

    I have to say this is all spiffingly good fun.
    gavin appears to have conceded that the natural forcings lead to autocorrelation in the temperature record. It would seem to follow that he is now arguing that the natural temperature record should be autocorrelated. Isn’t that what the article was arguing against ?

    anyways, I am so impressed by the logic, that I am inventing a new word to honour it. Gavin has enpretzellated himself !


  56. TCO
    Posted Dec 22, 2005 at 9:10 AM | Permalink

    1. I much prefer the more rapid responses and free posting. (to pursue a technical argument to a conclusion).
    2. I also prefer the more engaged and technically insightful approach here. At times, the hockey stickers seem to be deliberately opaque (in an evasive manner)–similar to Mann’s non-responsive responses to the Barton committee. (Dick Feynmann smiles on us, not them.)
    3. I appear to be cut off from pursuing the thread of the technical argument (my comments are not appearing). However, several of you are quite capably pushing things forward and being allowed to do so.
    4. I posted a (temperate) request to have RC comment on Burger and Cubasch. It has been censored (not posted).

  57. Jo Calder
    Posted Dec 22, 2005 at 9:30 AM | Permalink

    #56 TCO: you could always ask Stoat.

    Cheers, — Jo

  58. TCO
    Posted Dec 22, 2005 at 10:06 AM | Permalink

    Doesn’t seem like he really engages in substantive discussion. He dismissed looking at the RE vs R2 statistics sufficency issue with a “that’s a Bartonism” ad hominem. I don’t feel like messing with someone who is tendentious. I want to hear a sticker who is willing to engage on the content/logic.

  59. rasmus
    Posted Dec 24, 2005 at 2:12 AM | Permalink

    Steve & Re #30.

    I think some of your confusion is due to Luboà…⟠mix-up between intrinsic uncertainty quantum state (randomness) and chaos (unpredictable after a certain time). It’s ironical that you try to frame me on autocorrelation – an faulty grounds as I still think that you misread my post – after you hade such a blunder about the issue yourself in Climate Research. But thanks for bringing up the quotes and thanks for bringing attention to my post though, but I think your presentation of myself and Gavin is a bit silly.

    Anyway, we may see things differently, but I still wish you a Merry Christmas.


  60. nanny_govt_sucks
    Posted Dec 24, 2005 at 3:13 AM | Permalink

    Speaking of blunders, wasn’t it McKitrick and Michaels who wrote the paper you’re referring to, and not McIntyre?

  61. David Brewer
    Posted Dec 24, 2005 at 3:17 AM | Permalink


    You state “Steve…It’s ironical that you try to frame me on autocorrelation – [on] faulty grounds as I still think that you misread my post – after you had[] such a blunder about the issue yourself in Climate Research.” [link provided to

    Please note, Steve is NOT the author of the paper in Climate Research which your link discusses. Do you think you should retract your statement, and do you owe Steve an apology?

  62. Steve McIntyre
    Posted Dec 24, 2005 at 10:02 AM | Permalink

    Rasmus said:

    It’s ironical that you try to frame me on autocorrelation – an faulty grounds as I still think that you misread my post – after you hade such a blunder about the issue yourself in Climate Research.

    Obviously, I made no such blunder. I would like to point out that Rasmus has written extensively on the article by Michaels and McKitrick – both in a journal article and at realclimate here. So this “error” by Rasmus is not an error by a civilian.

    The logic of the confusion is this: our articles were referred to as MM03 and MM05; Michaels and McKitrick could also be abbreviated to MM04. MM04 contained an error. Ergo, McIntyre made an error.

    I criticized Lambert about his role in promulgating this canard. To be fair, he did go back and check his comment lines, reported here as follows (although it was rather after the horse had left the barn):

    Thomas Palm does mention the degrees/radians error but attributes it to McKitrick, not M&M. So contrary to your claim, he was not misled and I don’t believe that anyone else has been either. There were two comments attributing the error to M&M, which is ambiguous and could be misleading. The issue was clarified by later commenters, but I have also added an editorial note to both of these comments.

    Within the last 30 days at Wikipedia, Rasmus’ realclimate coauthor, William Connolley, has once again tried to tar me with the degree/radian error, by attributing the error to M&M in the context of discussion of McIntyre and McKitrick. See the following discussion at wikipedia:

    your admission that your purpose was to discredite M&M[6] :::M&M didn’t make a mistake in degrees and radians I think you mean McKitrick in a not related article made that mistake.

    [Connolley]: Of course M&M did. But McK and McI don’t have a trademark on the M&M label.

    And thereby deliberately misleading people who read this talk page. –MichaelSirks 20:40, 20 October 2005 (UTC)

    I thought that Connolley’s excuse “M&M don’t have a trademark” for his attempt to mislead is particularly lame.

    Rasmus, merry Christmas to you as well. One more thing. If you feel that I’ve mischaracterized your work, you are welcome here to criticize any aspect of what I’ve said. At realcliamte, your coauthors have severely criticized me and then censored my attempts to respond. I will not do the same to you. While you’re here, you’ll be treated as a guest (and Dano, whatever else he might disagree with, can vouch for that.)

  63. Posted Dec 24, 2005 at 10:22 AM | Permalink

    I did not “promulgate the canard”. You are dishonest, Nigel.

  64. Steve McIntyre
    Posted Dec 24, 2005 at 11:06 AM | Permalink

    Tim, Tim, the Golden Bear. I said: “I criticized Lambert about his role in promulgating this canard.” This sentence is obviously true as I did criticize you about your role in promulgating this canard. I then repeated your reply to this criticism verbatim, a reply in which you pointed out efforts on your part to somewhat clarify the matter. That hasn’t stopped people like Connolley from shamelessly perpetuating the disinformation.

  65. Posted Dec 24, 2005 at 11:24 AM | Permalink

    I did not promulgate the canard. You are a liar.

  66. Dave Dardinger
    Posted Dec 24, 2005 at 11:40 AM | Permalink


    You’re confusing the phrase “about his role in” with “for”. Your role was in maintaining examples of the ‘canard’ on your site.

    Of course the whole argument is silly on both sides and all that, but it’s nice to straighten out the logic and language used to fan the flames.

  67. the fist
    Posted Dec 25, 2005 at 7:22 PM | Permalink

    [SM: I’ve snipped a lengthy discussion of Tim Lambert because it does not pertain to this topic. Interested parties can pursue this matter elsewhere.]

  68. Peter Hearnden
    Posted Dec 26, 2005 at 4:04 AM | Permalink

    Re #67 – feel better? Whatever, a belated happy Christmas to you 🙂

  69. Posted Dec 26, 2005 at 4:49 AM | Permalink

    “Nothing’s fact until it’s history, and then it’s debatable.”


  70. the fist
    Posted Dec 26, 2005 at 5:03 AM | Permalink

    [SM: snip. Debate this elsewhere if you don’t mind.]

    Happy new Year to you too.

  71. Posted Dec 26, 2005 at 7:32 AM | Permalink
  72. Ross McKitrick
    Posted Dec 26, 2005 at 11:17 AM | Permalink

    Rasmus’ post, #59, is so inane I bet “rasmus” is an imposter trying to make Rasmus look bad. “rasmus” made such a careless reading of my paper with Patrick Michaels that after all this time in print he hasn’t even noticed that Steve was not a coauthor. My paper with Michaels used a cross-sectional data base. This is a thread about time series autocorrelation. “rasmus” seems to think the latter could somehow be a problem that applies to the former. Rasmus sent a comment to Climate Research raising the possibility that spatial dependency might affect the variance-covariance matrix and exaggerate the t-stats. “rasmus” doesn’t seem to realise that Rasmus didn’t report any changes:

    Here, their results are re-tried in order to check whether the neglect to take inter-station dependencies into account may have influenced their conclusion… The linear and generalised linear models in the R-environment (lm and glm) were used to do the regression analysis. These models gave very similar results, and therefore only the results from the linear model are shown here. Table 1 gives a summary of the regression results given by these models. A comparison with Table 4 in McKitrick & Michaels (2004) (their results are reproduced here in Table 2) suggests a good agreement: The R2 are similar, and all the coeffcients that are considered statistically significant at the 5% level (shown in bold) have similar values.

    Rasmus decided to test the model some other ways too:

    The analysis by McKitrick & Michaels (2004) was repeated using a different statistical modelling technique. If their results were robust, one would expect to find similar patterns with different models. The regression analysis produced similar, although not identical, model coeffcients, t-values, and R2 scores to those reported by McKitrick & Michaels, indicating that the analysis captures similar relationships.

    What Rasmus was left to nitpick over was that if he threw out half the data set, namely everything north of 35N, and used various subsets of the explanatory variables, the resulting regression coefficients were not very good at predicting the withheld data. In Pat’s and my reply we pointed out that this removes almost all the rich countries, thereby taking out the information contained in the socioeconomic contrasts. A better test would be to remove data so as as to retain both rich and poor country data, which is what we did in the paper. We took out the North and South American data and skillfully predicting it using the basis of the rest of the data set. “rasmus” evidently didn’t know this, and since my rebuttal on this point a year ago was not posted at RC I suppose he’d have no way to find it out, except, um, if he’d read the original exchange in Climate Research.

    As for degrees/radians, this again? Code published, error found, error fixed, results upheld, erratum publshd zzzzz…. losing will to type…

  73. the fist
    Posted Dec 26, 2005 at 4:48 PM | Permalink

    Lambert is allowed to call people dishonest and liars-something no one would be allowed to do on his site. So why are his comments allowed to remain while mine aren’t.

  74. per
    Posted Dec 26, 2005 at 5:00 PM | Permalink

    Dear fist
    I should point out that when Tim Lambert starts calling Steve a liar, everyone is free to make their own judgement. Whether that be about Steve, or whether it be about Tim Lambert.

  75. TCO
    Posted Dec 26, 2005 at 9:51 PM | Permalink

    May I call Tim a pussy?

  76. the fist
    Posted Dec 27, 2005 at 5:18 AM | Permalink

    I accept your point Per.

    However when caught being straight out dishonest and then questioning someone’s sexuality as a result does say something about who is calling who a liar, no? Especially when the topic is AGW.

  77. Steve McIntyre
    Posted Dec 27, 2005 at 6:41 AM | Permalink

    fist – I appreciate the support, but please take this discussion outside.

  78. Posted Jun 18, 2010 at 3:29 PM | Permalink

    Thanks for putting the graph it was really useful. Keep posting.

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