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  1. OT, Fukushima radioactive tracers might be used to measure the true lenghts of oceanic cycles, I guess there are enough longlived isotopes released to find them on random measurements around the globe. No need for carefully balanced messages in the bottles.

    On topic, thanks for the good presentation of this powerful method. Can one use the FT method to estimate the period of outliers as in ‘100-year flood’?

    Comment by jyyh — 31 Aug 2011 @ 12:59 AM

  2. Valentine’s Day is also known as π-1 Day among nerds and geeks.

    Comment by Brian Brademeyer — 31 Aug 2011 @ 7:43 AM

  3. jyyh,

    100-year floods are not periodic events. They are, broadly speaking, random events that have a 1% chance of occurring in any given year. You can’t use FT analysis to identify them.

    Comment by Ernst K — 31 Aug 2011 @ 12:27 PM

  4. It appears that Ghil, and others specifically warn against the use of MEM and temperature data:
    “Instrumental temperature data over the last few centuries do not seem,
    for instance, to determine sufficiently well the behavior of global or local
    temperatures to permit a reliable climate forecast on the decadal timescale
    by this SSA-MEM method.” Ghil, et al., Reviews of Geophysics 40(1),2002.

    Comment by BillS — 31 Aug 2011 @ 12:57 PM

  5. Thanks, an interesting post.

    A couple of minor typos, if you care:

    “The tool he used was developed my Michael Ghil” and “the other if far from being auto-regressive.”

    Comment by Kevin McKinney — 31 Aug 2011 @ 1:34 PM

  6. Excellent post, and discussion of meaningful numbers reminds me of intresting numbers paradox. of course, that applies to integers, not reals.

    Of course, Scafetta in particular has a long history of trying numerous mathematical techniques to avoid CO2 and find cycles. I really, really recommend lecture and slides @ EPA.

    1) Watch a bit of the lecture for context.

    2) Then, flip through the slides, get to Rhodes Fairbridge. (Hmm, RF an expert on climate change? That seems to come from J Coastal Research.

    3) Once again, I sure with John Tukey were still around.

    Comment by John Mashey — 31 Aug 2011 @ 2:12 PM

  7. Fourier transforms applied to a time series of bounded length, say the interval [0,t], assumes that all prior and subsequent intervals, [nt,(n+1)t], for all integers n, are identical to the values in the given interval [0,t].

    For geophysical time series this assumption is astoundingly naive. Fourier transforms can be used to identify potentialy (nearly) periodic behavior which must be be justified via the physics. The best example I know tis the ~3.75 year Rossby/Kelvin wave in the North Pacific, for which that ocean basin is resonant at that period.

    However, an attempt to find periodicities in ENSO fails, for me, on the grounds that insufficient (quasi-)cycles have been observed:
    Variability of El Niño/Southern Oscillation activity at millennial timescales during the Holocene epoch

    Comment by David B. Benson — 31 Aug 2011 @ 2:40 PM

  8. It’s pretty obvious that Loehle and Scafetta chose MEM because other (appropriate) methods didn’t give them what they wanted. They further pumped up the number of poles to a ridiculous value because a realistic choice didn’t give them what they wanted.

    Thanks for an insightful glimpse of their “mathturbation.”

    Comment by tamino — 31 Aug 2011 @ 3:22 PM

  9. John Mashey,

    I had a bit of an argy with a poster on SepticalScience about Fairbridge (who seemed a decent sort) a few year ago, and had a good look at Mackey’s silly paper on Fairbridge in J. Coastal Research. Here’s my comments.

    Just shows that there’s a limited amount of this nonsense out there – it just goes round and round…

    Comment by chris — 31 Aug 2011 @ 3:40 PM

  10. I am not a mathematician or scientist (actually, I’m a lawyer), but I think I understand the point this piece makes. But from a layperson’s perspective, it seems to be too indirect. If I understand the argument, fourier transforms allow you to arbitrarily decompose any time series into a sum of sine waves. This is surely fun, but absent some reason to believe the sine waves represent actual physical processes, it’s simply an exercise in curve fitting (akin to curve fitting using higher order polynomials – increasing the power of x increases the R^2 but doesn’t tell you anything useful about whether your equation makes any sense). In fact, where a process has substantial noise (i.e., internal variability) you are probably just fitting your curves to the noise.

    So, couldn’t you take the instrumental record for global mean temperature, subdivide it into chunks (say 10 or 20 years at a time), then analyze each chunk separately using a fourier transform? Assuming that the internal variability dominates over the signal (which I am sure I have read on RC before multiple times), wouldn’t one expect the “cycles” you identify in each chunk of data to be different from every other chunk? Wouldn’t this be a much more direct disproof of using fourier transforms to identify climate trends than what is actually done in this article? (At least, it seems more direct to me. If the process says that each 10 year chunk is dominated by a completely different set of “cycles,” that seems to put the nail in the coffin of the idea that climate is really driven by as yet undiscovered natural cycles and clearly shows that such attempts are just exercises in curve fitting)


    Comment by skg — 31 Aug 2011 @ 4:10 PM

  11. Re 9 chris – I remember that. I tried to follow that whole sun wobbling concept and it seemed to lead to an idea that (as I recall) the planets stir the sun by making it move around. But it’s just in a state of free fall, so how could that stir it? I pointed out that if the planets did anything to stir the sun, it would (so far as I know**) be by tides on the sun, which are incredibly tiny. (**I tried to considered the idea of planets tugging on the solar wind which would tug on the magetic field, or directly wobbling the magnetic field, which would tug on the sun, but the amount of mass involved and the small distortions considering the dimensions… well I don’t know, doesn’t seem likely (it would just be tidal disortion of a much larger object?, so the strain should still be small?).)

    Comment by Patrick 027 — 31 Aug 2011 @ 5:30 PM

  12. (and tides on the sun are dominated by somewhat different planets than the center of mass wobbling; okay, done with that.)

    Comment by Patrick 027 — 31 Aug 2011 @ 5:35 PM

  13. You all, IPCC, sceptics, shroudwavers and riders on the gravytrain
    alike, are all nitpicking around the periphery of this issue. The only
    people who see it in perspective are the geologists.

    I put the issue in perspective a few days ago without any response.

    The Pleistocene Period, in which the ice ages and much of human
    evolution took place, lasted some 2.5 million years.

    That 2.5 million years is a tiny fraction of the 4,500 million year
    history of this planet.

    Compare this 2.5 million year period with the distance between the floor
    and the ceiling of the room you are sitting in. The stud height is
    probably around 2.5 metres. In NZ it is almost certainly 2.4 metres.

    That is 1 mm for each 1,000 years. Modern man entered Europe about
    40,000 years ago; 40 mm or less than 2 inches below your ceiling.
    10,000 years ago the last ice age ended; 10 mm or less than half an inch
    below your ceiling. About 4,000 years ago man started using metals.
    The Abrahamic religions started about 2,500 years ago or less. Most of
    our properly recorded history commenced about 1,000 years ago, 1 mm
    below your ceiling. We have been measuring temperature and the like for
    about 150 years. That is little more than one tenth part of a
    millimetre on the scale we are considering, about the thickness of a
    hair. Our irrelevant lives are measurable on that scale only with a

    All the ranting, raving and political posturing considers only events
    within that miniscule period. It is simply and utterly absurd.

    [Response: And commenting on a blog is even more so. Really, why do you even get out of bed in the morning if everything is so trivial? – gavin]

    Comment by Roger Dewhurst — 31 Aug 2011 @ 6:37 PM

  14. A few notes on the FT, or as we coastal engineers usually analyze ocean wave data call it, the FFT (2^N).

    You have dt and N, multiply N*dt, and you get the timebase, or the lowest frequency possible (1/(N*dt)) from your analysis (zero frequency is just the mean of the time series, if you first haven’t taken out the mean).

    The Nyquist frequency has to be half the sampling frequency, N equations = N unknowns (complex numbers for each frequency represent phase and amplitude).

    The time series must be stationary (or is assumed to be stationary), which is often true for ocean wave climates, same for assuming an ergodic process (spatial vs temporal equivalence).

    Now any time series with a trend, linear or otherwise, must be detrended first, before doing any sort of linear spectral analysis.

    So, for example, take a purely linear trend, run it through an FFT, and what does one get?

    A log-log power spectra that displays 1/f^2 (red) trend at the lowest frequency limit, through to (and pass) 1/f^1 (pink), and ending up as 1/f^0 = 1/1 (white), or white noise at the upper (Nyquist) frequency limit.

    There are tidal cycles, there are water wave period cycles, there are harbor resonance cycles, there are harmonics.

    However, there are no well defined climate cycles at exactly 20 (or even approximately) or exactly 60 (or even approximately) years, meaning having a physical (or physics) basis in reality.

    Most certainly, there is no interaction between Jupiter/Saturn and Earth’s climate, at any periodicities, L&S is quite simply a POS.

    Comment by EFS_Junior — 31 Aug 2011 @ 6:58 PM

  15. 13, Roger Dewhurst: You all, IPCC, sceptics, shroudwavers and riders on the gravytrain
    alike, are all nitpicking around the periphery of this issue. The only people who see it in perspective are the geologists.

    Really? How does that perspective help the rest of us to decide whether, and how much, to spend $$$$$$ and labor rapidly replacing our CO2-intensive energy sector with something that will stabilize or reduce atmospheric CO2?

    Comment by Septic Matthew — 31 Aug 2011 @ 7:49 PM

  16. Gavin’s reply to Mr. Dewhurst @13 should be in the internet hall of fame.

    Comment by Jim Eager — 31 Aug 2011 @ 8:23 PM

  17. Well, this explains the crank that was obsessively spamming over at about planetary cycles. His explanation was (I kid you not) that it’s all down to tidal heating of the Earth by the big planets.

    Comment by Tristan — 31 Aug 2011 @ 9:18 PM

  18. [Response: And commenting on a blog is even more so. Really, why do you even get out of bed in the morning if everything is so trivial? – gavin]

    It is the debate around AGW that would be so trivial if it is not so dangerous. It is all a bit like the EU, corrupt individuals and and a bunch of ostriches with their heads in the sand.

    [Response: So everything is trivial compared to the 4.5 billion year perspective except corruption in the EU and your commenting on blogs. Got it. But are you trying to make some kind of coherent point here? – gavin]

    Comment by Roger Dewhurst — 31 Aug 2011 @ 9:36 PM

  19. Fourier analysis is a rich and intensely complicated subject.

    In general, the FT (Fourier Transform) is not the same as the FFT (Fast Fourier Transform). They give the same result for a finite time series with all the observations equally spaced in time (“evenly sampled”). But for an unevenly sampled time series, the FFT doesn’t give the correct result — one is advised to use the DFT (Discrete Fourier Transform), and even that benefits from modification for best results. That’s one of the reasons there are so many variants (like the Lomb-Scargle modified periodogram or the Date-Compensated Discrete Fourier Transform), many of which have been reinvented multiple times under different names in different disciplines. With irregular time sampling a raw DFT can give misleading results, and these variants are especially popular (and useful!) in disciplines like astronomy for which the time sampling is rarely (if ever) even.

    Also, it is possible to compute the FT for frequencies lower than the “fundamental” frequency (1/”timebase”). Its meaning can be ambiguous, and in most circumstances it’s not recommended, but it’s possible and can sometimes be informative.

    It’s not really necessary to detrend a time series before Fourier analysis, but it usually helps by removing the spectrum of the trend itself, allowing closer inspection of the non-trend spectrum. On the other hand, if you’re really interested in the spectrum of the trend itself then you’d want to leave it in. It’s certainly not necessary for a time series to be stationary, in fact when searching for genuine periodic behavior we expect that the time series is *not* stationary, rather that it might be periodic.

    It’s also possible to compute the FT for frequencies which don’t fall on the “grid” of frequencies usually computed for a DFT. This is “oversampling” the FT, and is extremely useful in some circumstances (especially for period estimation) but is another thing that for which the FFT is inappropriate.

    There are profound issues regarding the use of an observed time series. The straightforward DFT computes the spectrum of a time series which is repeated periodically for all time, but that rarely (if ever!) represents reality. If the time series is inherently discrete, what you really want is the DTFT (Discrete-Time Fourier Transform) but to compute that you’d need an infinite number of data points, obviously an impossibility. The DFT is only an approximation of it, and is no good beyond the Nyquist frequency. Furthermore, the discrete time window creates significant differences between the computed DFT and the DTFT (it’s the origin of the problem of “spectral leakage”), especially since the “window” has such sharp edges. There are various methods to compensate, including a variety of “windows” that can be applied which can reduce spectral leakage but at the cost of a degradation of spectral resolution. In fact there’s a whole field concering window design, sometimes called “window carpentry.”

    Methods like MEM (Maximum Entropy Method) are designed to get a better picture of the FT of the entire signal rather than just the window of observations. However, there are considerable risks involved (as this post makes clear), and they are vulnerable to abuse if certain parameters (like the number of poles) are ill-chosen.

    If the time series is *not* inherently discrete, instead the observations are a discrete sampling of a continuous function, then we really want “the” FT, but again the DFT is only an approximation. Interestingly, in this case there can be distinct advantage to sampling at times which are *not* evenly spaced — a random time sampling may be best of all, because then you are not limited by a “Nyquist frequency,” you can in fact explore the behavior at frequencies far higher than the sampling rate.

    I’ve tried to encourage colleagues in astronomy to randomize the time sampling, not only to allow exploring high-frequency space, but also to ameliorate the problem of “aliasing.” This occurs when two different frequencies give signals which look identical, or very similar, when restricted to the times of observation. When the time sampling itself exhibits periodicity, aliasing can be a severe problem — this often happens in astronomy because the availability of observations is governed by cycles such as day/night and the yearly progress of earth in its orbit.

    One must also be aware of what one wants from a Fourier analysis. A common goal is simply to transform from the “time domain” to the “frequency domain,” often extremely useful, but this may have little or nothing to do with the problem of “period search,” another ubiquitous application of Fourier analysis. Period search exists apart from Fourier analysis (although Fourier is the most common method), and there are a host of non-Fourier methods like PDM (Phase Dispersion Minimization) or minimum-string-length based on “folding” the data with a trial period. In fact, there’s a wonderful variant of PDM based on the analysis of variance, developed for astronomy, which not only gives excellent results, it’s also optimized for statistical efficiency and minimum computational workload (which really helps when analyzing terabyte databases such as come from modern satellite missions). Some of these non-Fourier methods are far better than Fourier analysis when the waveform is distinctly non-sinusoidal, and some astronomical objects (like eclipsing binary stars) exhibit such behavior.

    Fourier analysis is one of the most useful and common methods of analysis, and one of the most beautiful mathematical creations of the human mind. As the post makes clear, it’s also, at times, subject to abuse.

    Comment by tamino — 31 Aug 2011 @ 10:24 PM

  20. tamino @18 — Thank you.

    Comment by David B. Benson — 1 Sep 2011 @ 12:11 AM

  21. Just a bit of inspiration for EFS_Junior in @14 and others who are (legitimately) using FFT: You should spend a moment looking into “(Modified) Allan Variance” and try it on your data, it very often reveals interesting and otherwise unavailable details about the noise processes affecting a time-series.

    Comment by Poul-Henning Kamp — 1 Sep 2011 @ 1:50 AM

  22. The global mean temperature data shows a 60-years cycle as shown in the following graph.

    Assuming the data is valid, should we stop believing what it says?

    Comment by Girma — 1 Sep 2011 @ 2:48 AM

  23. No doubt the Sun indeed runs ‘60 year cycle’, (pi/3 = 60 ; pi/…), as this NASA’s record confirms:

    Comment by vukcevic — 1 Sep 2011 @ 6:14 AM

  24. “π is a fundamentally meaningful number”

    But it’s not a rational one and therefore it’s not countable.

    Maybe it would be better to desribe it as a Function, with an output consisting of an infinite real number series.

    Comment by prianikoff — 1 Sep 2011 @ 6:34 AM

  25. I analyzed the Scafetta paper from an astronomical/physical perspective (I am an astronomer) in, unfortunately in Italian, but also the mathematics is flawed, as shown here.

    A MEM analysis, as performed by Scafetta, is meaningful when you already know that your series is composed by a limited number of sinusoidal (or quasi-sinusoidal) components. Moreover, it is not meaningful to find “correspondences” between components that have distinctly different frequencies, as shown by OBLIQUE lines in Scafetta figure: if they don’t match, don’t match, is like saying you “almost win” the lottery because the winning number is “almost” yours.

    Summarizing my considerations, the velocity of the Sun (or its acceleration) with respect to the Solar System barycenter has no physical meaning. General Relativity Equivalence Principle tells us that a free falling body (as the Sun pulled around by the planets gravity) is exactly equivalent to an undisturbed body at rest, for any physical phenomenon. Only mareal forces (differences in the gravity as seen by different parts of the Sun) are important.

    Computing gravitational tides due to planets on the Sun is straightforward, and it spectrum is obviously composed of a limited number of sinusoids (at the planets orbital periods). But the spectrum is completely different from the one shown by Scafetta, the outer planets contribute very little, the 20 year component is weaker than that due to Jupiter, and the 60 year one still weaker. The strongest components are at short periods (around one year), and filtering anything shorter than a few years leave basically just the Jovian component, that is close (but not identical) to the solar 11 year period. Just to give the right proportions, these tides correspond to MILLIMETERS on the surface of the Sun.

    The 11 year period can be seen in the climate record, with an amplitude of a few hundredths of a degree, so a near-correspondence can be found. The correspondence goes out of phase in about a century, at the point that a resonance of 14/15 (physically VERY unlikely) has been proposed. But on a shorter timescale (as in Scafetta’s paper) it could be quite impressive.

    Comment by Gianni Comoretto — 1 Sep 2011 @ 7:20 AM

  26. Girma, got tired of spouting the same thing over and over again at Open Mind? Do you think your climastrology is going to make more sense the more blogs you post it on? Your imaginary “cycles” (based on far too short of a time series) have no physical basis. Until you can provide one, one that explains why the known forcings over the same period of time had no affect on temperature, they are meaningless. As has been pointed out to you (over and over), if your cycles had really been happening that would mean temperatures were far colder over the last 1,000 years than we know they were. When did your magic cycle begin? When will it end, and why? Mystical gibberish.

    Comment by Robert Murphy — 1 Sep 2011 @ 7:37 AM

  27. Please borehole Girma. Not only has he hijacked and largely wasted one thread over at open mind, as ointed out by Robert Murphy, but he has an entire 2200+ post thread devoted to his nonsense over at Deltoid. Plus top billing at WUWT.

    Surely that’s enough exposure for this particular Galileo, at least until he publishes and wins his Nobel?

    Comment by dhogaza — 1 Sep 2011 @ 8:39 AM

  28. #25 A careful reading of the Scafetta papers (2010; L&S 2011 etc.) shows that the ‘astronomical’ rationale is completely post-hoc. That is, the timescales are chosen based on what was already diagnosed from the temperature time-series, not selected objectively on the basis of any real theory. In 2010, the 9.1 period is added completely arbitrarily because it popped up in the temperature record. The multi-decadal peaks in CMSS are never discussed, the other peaks in SCMSS are ignored. The superficially impressive split-period validation uses periods defined from the full temperature series, not just what would be available from the split periods themselves. All in all, these are classic examples of how not to analyse data.

    Comment by gavin — 1 Sep 2011 @ 9:48 AM

  29. Tamino’s comments are always substantive. Sometimes I can even understand them. Not this time though. I wish I understood more math.

    Comment by skg — 1 Sep 2011 @ 10:19 AM

  30. @14, “Most certainly, there is no interaction between Jupiter/Saturn and Earth’s climate, at any periodicities….” is wrong. Earth’s orbital variations are driven partly by gravitational interactions with the gas giants, and those variations drive the Milankovich forcing.

    Comment by Meow — 1 Sep 2011 @ 12:30 PM

  31. #30

    That paper does mention Milankovitch, but AFAIK, Milankovitch cycles can’t even explain the change in ice age cycles from ~41Kyr to ~100kyr.,000-year_problem

    So,in other words, the Solar System is not deterministic over long periods of time, that much we do know.

    Now, if you were to believe this “theoretical” paper, you would be able to tell me the exact position of all the planets, like 20Mya even, relative to what exactly?

    I stand by my original statement “no interaction between Jupiter/Saturn and Earth’s climate” until such a time when direct incontrovertable empirical evidence is presented. Sound familiar?

    Comment by EFS_Junior — 1 Sep 2011 @ 7:53 PM

  32. “Long periods of time” being the key phrase.
    Laskar’s most recent paper says; “it will never be possible to recover the precise evolution of the Earth’s eccentricity beyond 60 Myr.”

    I don’t think anything he’s done would explain the 100k year cycles.

    See “Strong chaos induced by close encounters with Ceres and Vesta”
    J. Laskar1, M. Gastineau, J.-B. Delisle, A. Farrés and A. Fienga1.

    Comment by prianikoff — 2 Sep 2011 @ 4:26 AM

  33. While I agree that is extremely easy, not to mention tempting, to produce spurious results by tuning the parameters using the MEM method, I would not dismiss the possibility of finding a periodic signal related to the orbital periods of the giant planets out of hand. The reason is that the earth orbits around the barycentre of the solar system, which is slightly displaced from the centre of the sun. Depending on the alignment of the planets, the displacement is less than 1% of an AU, but the effect might be detectable.
    Of course, none of this has any significance for the current warming.

    Comment by Tom P — 2 Sep 2011 @ 11:08 AM

  34. @31: In addition to #32, “direct incontrovertible empirical evidence” is an overly strict criterion for accepting a scientific theory. While Milankovich theory has problems, it’s the best explanation thus far for glacial cycles. On the 100,000-year problem, Ashkenazy & Gildor 2008 speculatively suggest that orbital variations cause equatorial insolation changes that may (along with feedbacks) explain the 100,000 year cycles. Raypierre also mentions an interesting idea (p.467 of his textbook) about variations in precession and eccentricity largely cancelling due to Kepler’s law, leaving variations in obliquity (~40kyr) as the largest effective forcing, with some nonlinearity (CO2?) causing “skipping” of obliquity cycles and thus the appearance of ~100kyr cycles.

    While I don’t currently know enough (yet!) to rigorously evaluate these ideas, Milankovich is far from dead. In any case, thank you for motivating me to look into this topic more deeply.

    What do you suggest causes glacial cycles?

    CAPTCHA: the ntiplik

    Comment by Meow — 2 Sep 2011 @ 1:09 PM

  35. @31: Also suggestive (but hardly conclusive) on Milankovich, Jochum et al 2011 (draft paper) got glacial inception in a CCSM4 model by subjecting it to orbital forcings from 115 kya.

    Comment by Meow — 2 Sep 2011 @ 4:17 PM

  36. Re 33 Tom P – not an expert in celestial mechanics, but given the inverse square law, the Earth is ‘disportionately affected’ by closer masses than farther masses. It is considerably closer to the sun than Jupiter, so while the Earth-moon system won’t exactly orbit the barycenter of the Earth-moon-sun system (in part because the Earth-moon system is not spherically symmetric?), it won’t orbit the barycenter of the whole solar system.

    (I tried to educate myself on the details of how orbital cycles arise and from what I can tell thus far, I wouldn’t expect the cycles to be perfectly smooth on the microscale – precession and obliquity for example should change more rapidly at some times of the year/month/18-year/whatever than others (solar or lunar-driven precession itself can’t (approximately) happen at those times when the sun or moon cross the equatorial plane)- I imagine little jumps in obliquity accumulating over time in a way that can easily be approximated as a smooth cycle (well, not a perfect cycle, but anyway). I can imagine little jumps being associate with eccentricity, which maybe would mean that the Earth sometimes is just a little closer or farther away from the sun on shorter timescales than it would be if the cycle were truly smooth over time. But how big would these jumps be and could they have a multidecadal average effect – even if only through alignment with seasons? I’m guessing it wouldn’t be signficant, but as for the celestial mechanics – is there a website which explains this in more detail?)

    Comment by Patrick 027 — 2 Sep 2011 @ 5:16 PM

  37. My nitpicky side also thought of Milankovitch cycles when the post mentioned that the other planet’s don’t cause changes in Earth’s climate, but I don’t think that is what Scafetta had in mind.

    See my post that goes into more detail on the influence of the other planetary bodies (or even theoretical Milankovitch cycles on other planets) than most other sources that deal with just Earth’s glacial-interglacial applications (which is not dead at all, but I agree with others that a fully coherent theory for how various orbital parameters conspire to pace the ice ages is not yet established with high confidence…but I don’t think anyone argues that Milankovitch plays a large role).

    Comment by Chris Colose — 2 Sep 2011 @ 5:19 PM

  38. It’s one thing to say thay our Solar System does a certain dance.

    So, for instance, the Sun-Earth-Moon would be the dominant dancers (assuming we are all are from the same planet called Earth).

    So, for instance, we know that the moon is “locked” to the Earth, simply because we ever only see the side facing Earth.

    The Earth-Moon are synchronized;

    Then there is the planet Mercury;

    It’s a whole other thing to say that Jupiter/Saturn are phased locked with the Earth at specific periodicities or even quasi-periodicities (e. g. pertubations about a set of mean periodicities).

    So, for example, a spectral plot of all contributions to Earth’s motions is a prerequisite for any meaningful discussion about the dynamics of these celestial drivers upon Earth’s motions alone, without even bringing Earth’s climate into the discussion.

    But, I would hazard a guess, that the dominant drivers, by many orders of magnitude, would be the three body problem of the Sun-Earth-Moon system itself.

    To carry this further, say we do find (quasi-)periodicities between the Earth-Jupiter-Saturn system in the geologic record (which AFAIK hasn’t been shown conclusively (or even at all) to date).

    We then need a physical basis (i. e. a physics based explanation) to relate these arbitrarily small (by several orders of magnitude) net perturbations to Earth’s climate system, you know cause AND effect, or causality;

    And you just can’t wave your hands and say Milankovich cycles, as these, as of today, are not a complete causal answer to the current ice age cysles we see in the geologic record.

    So far, all I’ve seen are rather outlandish conjectures with respect to the the Solar System’s gas giants and there purported impacts on Earth’s climate system, no hypotheses, no theories, just guesswork.

    Comment by EFS_Junior — 2 Sep 2011 @ 5:24 PM

  39. @37: I don’t know what the blazes Scafetta had in mind, but it wasn’t Milankovich cycles. BTW, given the contents of the SS article you cited, shouldn’t “but I don’t think anyone argues that Milankovitch plays a large role” read “but I don’t think anyone argues that Milankovitch doesn’t play a large role”?

    Comment by Meow — 2 Sep 2011 @ 6:10 PM

  40. %34 & $35

    Are Jupiter/Saturn themselves modeled in any of those papers that you just throwed up?

    Remember this discussion in now aboot Jupiter/Saturn and any direct linkage with Earth’s climate, such that, for instance, Jupiter/Saturn are the causative agent of Earth’s 41kyr and 100kyr ice age cycles.

    Also, with respect to L&S2011 and the probative nature of Jupiter/Saturn and Earth’s climate over the past ~150 years, if Jupiter/Saturn are the major drivers of today’s recent climate history, then where were thes two gas giants prior to aboot 150 years ago? Surely, the climate changes seen over these past 150 year would have been there and quite noticable before ~1850AD, correct?


    Comment by EFS_Junior — 2 Sep 2011 @ 6:36 PM

  41. Re my: (solar or lunar-driven precession itself can’t (approximately) happen at those times when the sun or moon cross the equatorial plane) … refering specifically to the component of precession that is wobbling of the Earth’s angular momentum vector in an inertial reference frame; another component comes from shifting of the semimajor axis.

    ReCAPTCHA: “pollutees ontrals”

    Comment by Patrick 027 — 2 Sep 2011 @ 6:38 PM

  42. @40: I never said that the gas giants are “the causative agent of Earth’s 41kyr and 100kyr ice age cycles”. They are one driver of earth’s orbital variations, which probably drive glacial cycles via ice-albedo and other feedbacks. Please see Laskar 1999 (esp. p.1752) for some discussion of the gas giants’ effects on earth’s orbit, along with Laskar et al 2004. I have not attempted to calculate the gas giants’ contribution relative to that of the other bodies, though Jupiter is ~1/1047th the sun’s mass and Saturn 1/3498th, so the solar system’s center of mass is (sometimes) outside the sun itself.

    Also I’m not arguing for L&S at all, nor for the preposterous idea that “Jupiter/Saturn are the major drivers of today’s recent [~150 yr] climate history”. I’m sorry if I gave that impression.

    Comment by Meow — 2 Sep 2011 @ 7:38 PM

  43. Meow,

    Yes you are right. Sorry for the typo.

    Comment by Chris Colose — 2 Sep 2011 @ 8:46 PM

  44. He uses the phrase ‘agnotology’, which is “the study of how and why we do not know things”.

    This makes agnatology the shadow of science. People have an innate propensity to believing propositions, sometimes whole collections of propositions, for which there is little or no evidence: “God gave this land to us”; “[insert name here] was a prophet of God”; astrology, phrenology, psychoanalysis; phlebotomy is an effective treatment; aspartame is dangerous; apricot pit extract can cure cancer.

    Science is unique among systems of knowledge in elevating skepticism and critical evaluation to norms to be followed. To assert that disbelief requires explanation overturns this great advantage of scientific methods.

    Comment by Septic Matthew — 2 Sep 2011 @ 8:59 PM

  45. #42

    Here’s an acronym for you: NALPOS (Not Another Lasker Piece Of Ship)

    From p. 1752 and I quote;

    ” ,,, COULD be obtained by passage through an ice age … ”

    COULD? Not according to the very next paragraph!

    “With these new values, the passage into the resonance s6 − g6 + g5 could NO LONGER BE OBTAINED during an ice age. Nevertheless, the proximity of the resonance SHOULD still have a singular effect on the obliquity solution, and it SHOULD be noted that, due to the tidal evolution of the Earth-Moon system, we will SURELY enter into this resonance in the NEAR FUTURE.”


    Hmm, I’dah be wantin’ to see some cited references in those two sentences, but there are NONE. On NOLPOS’s timescale “near future” probably means within 60Myr.

    I COULD go on, but why bother, when a pure theoretician, assumes the Solar Systen is made up out of constants, and there are no empirical data (the one paper he does cite seems to be all over the place with time scaling issues though) to support the multitude of his various claims.

    It’s like assuming no two bodies in our Solar System have ever collided 250Myr into the past through to 250Myr into the future. Now that’s rich.

    However, he does finish up that page by mentioning the Earth Tide;

    What’s missing from that webpage? Why Jupiter AND Saturn, OMFG!

    From the last sentence of the NALPON 2004 paper;

    “For the calibration of the Mesozoic time scale (about 65 to 250 Myr), we PROPOSE to use the term of largest amplitude in the eccentricity, related to g2 − g5, with a fixed frequency of 3.200 ”/yr, corresponding to a period of 405000 yr. The uncertainty of this time scale over 100 Myr should be about 0.1%, and 0.2% over the full Mesozoic era.”

    PROPOSE? This guy is obviously a moving target, he’s definitely not a constant, that much we do know for sure.

    Here’s another acronyn: OPNAC (Oh Please Not Another Constant)

    Oops, I spotted an error on p. 4, b = 0.00339677504820860133, should be;

    b = 0.00339677504820860133 insert random number generator after the last digit, because we need more digits!

    Does NALPOS ever present any type of empirical data in any of his plots, he kind of reminds me of Pielke Sr. at WTFUWT always self referential.

    So, in closing, I’m still waiting for some skill or predictions of periodicities between the Earth and Jupiter/Saturn, known and confirmed periodicities, because, by golly, I don’t believe everything in our Solar System is actually made up out of literally hundreds and hundreds of constants.

    I need an amplitude and a phase and a period, just one will do, for the Earth and Jupiter/Saturn connection. Then we can go aboot how this is somehow, somewhere, somewho, somewhat, somewhen, somewhy connected to Earth’s climate.

    Comment by EFS_Junior — 2 Sep 2011 @ 11:41 PM

  46. S. Matthew #44,

    This makes agnatology the shadow of science. (…) Science is unique among systems of knowledge in elevating skepticism and critical evaluation to norms to be followed. To assert that disbelief requires explanation overturns this great advantage of scientific methods.

    I don’t think you’ve got that right. First, agnotology professes to study “ignorance”, not “disbelief” as such. In fact, Proctor, in his introduction to the term he coined, explicitly lists “faith” and not “disbelief” as a phenomenon overlapping with ignorance or generating ignorance (along with phenomena such as secrecy, stupidity, apathy, censorship, disinformation, and forgetfulness).

    You might argue that e.g. global-warming deniers are not ignorant, as they are typically well aware of the body of scientific knowledge that they choose to actively disbelieve, so they are not a proper subject of agnotology as I understand it. I’d object that public ignorance that there is a scientific consensus on many aspects of global warming is a proper subject of agnotology, and that no theory of this ignorance can ignore the active efforts of those sort-of-knowledgeable deniers. Besides, doesn’t selective disbelief in mounting evidence qualify as a form of ignorance? Certainly it’s the opposite of skepticism as a scientific virtue.

    Second, the form of ignorant belief you describe perhaps falls under what Proctor calls “ignorance as a native state.” In his brief taxonomy of ignorance, he distinguishes two more forms of ignorance, “ignorance as lost realm (or selective choice)” and “ignorance as a deliberately engineered and strategic ploy (or active construct).” Benson’s concern, in the article Rasmus referenced, is with the latter. We are not discussing people to whom the basic knowledge about global warming have not yet filtered down, but people whose knowledge is distorted by a political campaign of doubt and disinformation; not ignorance as a passive state, but as something actively produced.

    Reference: Robert N. Proctor, “Agnotology: A Missing Term to Describe the Cultural Production of Ignorance (and Its Study),” in Agnotology: The Making and Unmaking of Ignorance, ed. Robert N. Proctor and Londa Schiebinger (Stanford, California: Stanford University Press, 2008).

    Comment by CM — 3 Sep 2011 @ 6:38 AM

  47. Typo: In my reply to Matthew above I meant to refer to Daniel Bedford, an author mentioned in the OP. Dunno where “Benson” came from. Apologies.

    Comment by CM — 3 Sep 2011 @ 6:42 AM

  48. Septic Matthew: “Science is unique among systems of knowledge in elevating skepticism and critical evaluation to norms to be followed. To assert that disbelief requires explanation overturns this great advantage of scientific methods.”

    Uh,… no. Do not conflate skepticism with disbelief. Skepticism is the requirement of evidence to underly belief, and of belief to be only as strong as the evidence. Disbelief need be based on evidence no more than belief need be. Disbelief in anthropogenic climate change requires dismissing literal and figurative mountains of evidence. That requires tremendous credulity–the opposite of skepticism.

    Comment by Ray Ladbury — 3 Sep 2011 @ 10:08 AM

  49. To: vukcevic #23

    “vukcevic says:
    1 Sep 2011 at 6:14 AM

    No doubt the Sun indeed runs ‘60 year cycle’, (pi/3 = 60 ; pi/…), as this NASA’s record confirms:

    Vukcevic: Your link just shows a photo of the sun. It doesn’t confirm anything about cycles (or much of anything else). Kindly post the correct link if you please.

    Comment by MJD — 3 Sep 2011 @ 10:15 AM

  50. To GIRMA #22:

    “Girma says:
    1 Sep 2011 at 2:48 AM

    The global mean temperature data shows a 60-years cycle as shown in the following graph. Assuming the data is valid, should we stop believing what it says?”

    Girma I looked at your graph and it does show two apparent minima about 60 yrs apart. But this isn’t a “cycle.” Just 2 not-necessarily-related data points.

    The chart you refer to is generated using parameters chosen within a plotting application at your link. The chart that people see when they first open your link shows global temperatures remaining roughly constant from 1880 to 2010, but varying within a wide range.

    I experimented with the parameters of this plotting application: When I set the “detrend” parameter for series 1 (“GIS Temp Land-Ocean Global Mean” which shows the 2 minima) from 0.75 to 0 and click the “Plot Graph” button, I see a chart of steadily increasing temperature from 1880 to 2010. NOW there is not even the remotest suggestion of a “cycle.” Just relentlessly increasing temperature.

    Based on this, your comment appears to be, let us say, incorrect.

    Or not: Can you help me understand what, if anything, I am misunderstanding?

    Comment by MJD — 3 Sep 2011 @ 10:39 AM

  51. re 36 Patrick 027

    You may be interested in this animation –
    The centre of mass is not subject to an inverse square law, it’s simply the average of the combined moments. The sun orbits the barycentre of the solar system. The orbit is not constant, but the combined effect of the gas giants is such that the radius can approach 1% of the earth’s orbit.

    Comment by Tom P — 3 Sep 2011 @ 10:45 AM

  52. CM, 46, That is a good post.

    It looks to me like “agnatology” is just one more pseudo-intellectual way to smear some of the skeptics. It’s as one-sided as Oreskes’ “Merchants of Doubt”, who somehow failed to note the “merchants of Belief” like Al Gore (I personally respect Al Gore’s work, but he is a merchant.)

    Your post contributes to a case that I might be wrong.

    Comment by Septic Matthew — 3 Sep 2011 @ 11:40 AM

  53. There’s another way to look at the Loehle and Scafetta paper.

    If (1) the temperature change since about 1850 is approximately the sum of a linear trend and some periodic components;

    and if (2) the estimated function is a reasonable estimate of the effect of a persisting mechanism;

    then their procedure is reasonable. Their paper does not establish or test the truth of either (1) or (2), and there is no good reason to believe that their result is accurate.

    Such a use of mathematics is sometimes called “heuristic” (meaning leading in a useful direction), “hypothesis generation”, “the context of discovery” (vs. the context of testing), or “conjecture”.

    A more elaborate example appears in section 3.3 of Raymond Pierrehumbert’s book Principles of Planetary Climte, which opens with some approximations (slightly reworded for brevity):

    1. the only source of the temperature of the planet is absorption of light from the sun;
    2. the planetary albedo is spatially uniform;
    3. the planet is spherical and has a distinct solid or liquid surface which radiates as a perfect blackbody;
    4. the planet’s temperature is uniform over its entire surface;
    5. the planet’s atmosphere is perfectly transparent to the electromagnetic energy emitted by the surface.

    5 is relaxed later on.

    How much inaccuracy is introduced by the simplifications 1 – 4? I don’t know. Later on (p 163) the derivation of climate sensitivity omits clouds completely — does that additional simplification introduce non-negligible inaccuracy? I don’t know the answer to that either, and I don’t think anyone does.

    To me it seems that the two calculations of climate sensitivity (L & S, P) make testable predictions, but neither is trustworthy for any other purpose than designing more experiments to learn what the climate sensitivity, starting with earth as it is now, really is. They could both be accurate enough (for short term and long term, respectively), or they both could be way off.

    I do not think that either should be judged an example of “agnatology”.

    Comment by Septic Matthew — 3 Sep 2011 @ 12:36 PM

  54. SM at 52

    ‘False Balance’, much…?!

    Comment by Joe Cushley — 3 Sep 2011 @ 12:48 PM

  55. > agnatology

    You’re spelling it wrong.

    This is not a new term. See for example

    “a very early use of the new word agnotology, if not its coining, in an article by Linda Schiebinger titled Agnotology and Exotic Abortifacients: The Cultural Production of Ignorance in the Eighteenth Century Atlantic World…. The article emphasizes the work of Maria Sibylla Merian from 1699 to 1701 in Surinam, then Dutch Guiana. She was the only one of many naturalists and anthropologists active among the indigenous peoples in Africa and the Americas who mentioned extensive use of abortifacients for “menstrual regulation” (population control) …. The silence of the others had to be self-censorship imposed by no authority but by a rather universal cultural bias….

    … Mark Twain called willful withholding of vital information a silent lie….

    A Lesson in Skepticism
    A couple of generations ago (1938) a prominent citizen of Monroe was confronted by his frantic wife, ‘I have heard on the radio that the Martians are invading. What should we do?’
    Pearl Guess answered calmly, ‘Turn off the radio.’

    … Twain is even more concise: The only difference between fiction and nonfiction is that fiction should be completely believable.”

    Comment by Hank Roberts — 3 Sep 2011 @ 2:09 PM

  56. Re 45 EFS_Junior – um, what? I skimmed a little bit of one of those papers and I ‘kinda’ thought that it was basically computer modelling based on physics. Of course if there is some prediction that can be made that can be used to test the output, great, but I would think simply trying to describe how some system likely evolved based on what is known, parameterizing (with care/justification) where grid-scale requires it, etc, can provide something useful. Sorry I haven’t had the time to thoroughly look through Laskar, so maybe I was way off. PS I didn’t think Laskar was proposing that Jupiter and Saturn cause signficant 60-year climate cycles on Earth. Earth’s orbital cycles can/do have great influence on climate, even if the effects are a bit complicated.

    Re 51 Tom P – Okay, I’ll look at those, but while I have the time now: yes, center of mass is shited in proportion to mass and distance, whereas gravity follows an inverse square law, which is roughly why I wouldn’t expect all the planets or the sun to orbit the barycenter – well, at least not neatly as if all the mass was concentrated at the barycenter (perhaps I misunderstood what you meant). Earth’s orbit isn’t affected by all planets in proportion to distance and mass, it should be affected in proportion to mass and some inverse of distance, shouldn’t it? – considering tides on the orbit, maybe an inverse cube for some aspects, but that’s getting a bit outside what I’m familiar with.

    Comment by Patrick 027 — 3 Sep 2011 @ 4:28 PM

  57. 54, Hank Roberts: You’re spelling it wrong.

    Yeh, thanks for the correction.

    Comment by Septic Matthew — 3 Sep 2011 @ 5:11 PM

  58. Re CM #46
    Thank you! This is a very nice, clear post and hits more or less exactly what I was trying to get at in the article.

    Comment by Dan Bedford — 3 Sep 2011 @ 5:53 PM

  59. @45:

    I need an amplitude and a phase and a period, just one will do, for the Earth and Jupiter/Saturn connection….

    Very roughly (just using Newton’s LoUG), the gravitational force between Earth and Jupiter varies from about 8*10^17 N to about 2*10^18 N, which is between about 2*10^-5 and 6*10^-5 as much as the force between the Earth and the Sun. Jupiter orbits the sun in about 11.859 yr in the same direction as earth, but not quite in the same plane. I don’t know the current phase, but it matters only for long-term solutions.

    I haven’t explored planetary mechanics, so I haven’t delved into Laskar’s methods. I’m curious that you find them so defective. You definitely should write a paper criticizing them, because Laskar is very widely cited (his 2004 paper has 367 cites in If he’s substantially off base, the consequences will be significant.

    BTW, the solar system is not “not deterministic over long periods of time”. It’s chaotic, meaning that it’s deterministic in principle, but that the math that describes it is so sensitive to initial conditions that — in practice — it’s impossible to predict its state beyond some point. That said, the more accurately you measure a chaotic system’s initial conditions, and the less numerical error your models contain, the farther out you can validly predict the system’s state. Hence the “b = 0.00339677504820860133” that you criticized.

    Finally, I don’t think it at all strange that a chaotic system’s state might be greatly perturbed, over long spans of time, by a force on the order of 10^-5 that of one of the principal forces in the system.

    CAPTCHA: ready atsentsn

    Comment by Meow — 3 Sep 2011 @ 7:06 PM

  60. #59 & # 56

    Milankovitch cycles? Check mark (i. e. yes they are real but not a full answer).

    Solar System barycenter? Check mark (background in naval architecture, been there, done that)

    I’ve now had a more complete look at Laskar’s papers, quite readable, in fact.

    His latest paper is here (free access);

    Titled “La2010: a new orbital solution for the long-term motion of the Earth”

    So the main issue, as I see it, is eccentricity, from Laskar’s POV.

    95Kyr, 124Kyr, and 405Kyr eccentricities, the 405Kyr has been partially confirmed in the geological record, but not the 95Kyr and 124Kyr to date.

    The major problem I see with Laskar’s work is he assumes the now (today’s Solar System) for the then (60-250Myr in the past) and the to be (60-250Myr in the future).

    So, for example, his modeling goes to the dumpster about 60Myr in EITHER direction. Meaning, that if he were on the Yucatán Peninsula, say 65Mya, a few hours before you know what hit right aboot there, he would claim that 65Myr in to the future (e. g. December 21, 2012AD), the Solar System would be in total chaos, simply bescuse that’s when his theory/numerical model goes to the crapper (he’s doing these calculations at 80-bit extended precision BTW, but I really don’t know why he’s not using quad (128-bit) precision). AFAIK that is what he’s claiming, inevitable chaos, because his model said so.

    There are other issues as well, but basically the instability is highly non-linear, it’s flatlined most of the way, but then literally explodes.

    So like tree rings and ice cores, the geologic record should contain all ~165 405Kyr cycles going back to the demise of the dinosaurs ~65Mya (which I conjecture, is what Laskar is really trying to get to, a more definitive dating of that exnction event). AFAIK that would have to be on the geologists to do list, finding all ~165 405Kyr events in the geologic record.

    Onec that’s been done, then and only then, will I be satisfied with the 405K “constant” resonance issue, and you need other dating techniques to confirm it. All ~165 events will have to be spot on with Laskar’s 405Kyr number, otherwise no go.

    Here are a few more links for you to mull over (in no particular order);

    (e. g. Laskar’s work but the word “around” is used before all cycle periods named there, as if to say it’s not “exact” science)

    My original complaint has always been with those who claim a 60-year deterministic cycle for Earth’s climate, and then L&S2011 go aboot claiming a 20-year deterministic cycle, right aboot there I lose it, I’ve had it with those 60-year cycle nut jobs.

    At some point in time things are no longer deterministic, and as far as the Solar System goes, I happen to thing it is significantly less than 60Myr.

    Laskar should be looking over this current ice age (say 2.4Mya to the present) and try to explain the 41Kyr to 100Kye transition, that’s what I’d be doing if I has his mathematical chops.

    Comment by EFS_Junior — 3 Sep 2011 @ 11:30 PM

  61. #59

    An appeal to ignorance, an appeal to authority, and a double negative.

    Great. :-(

    not not deterministic means deterministic, see;

    See also;

    Set that number to zero then deterministic, set it to any small positive number, chaos eventually ensues.

    So while the Solar System appears to have been markedly stable, oh say these past 4,500,000,000 years, Laskar predicts that that everything goes to hell and a handbasket, in less than 60,000,000 years (in the future, but most importantly, IN THE PAST!).

    Further, he’s even predicted that Mercury will; 1) leave our Solar System, 2) collide with the Sun, 3) collide with Venus, 4) collide with Earth, 5) collide with Mars, 6) collide with itself (oops I made that one up), because … you guessed it … Jupiter did it.

    Read all aboot it here;

    Note the capton on the bottom of that webpage;

    “The orbit sequences are made with real data from the numerical simulations.”

    should read;

    “The orbit sequences are made with let’s make believe data from the numerical simulations.”

    Real data comports the meaning of empirical as in experimental or observational data.

    Similiarly, reanalysis data are also not real data, they are also data taken from a numerical model.

    Comment by EFS_Junior — 4 Sep 2011 @ 3:18 AM

  62. Matthew #52,

    > Your post contributes to a case that I might be wrong.

    I’ll happily settle for that. I think agnotology’s a nifty notion, but I’m not selling it, nor totally sold on it myself.

    > It looks to me like “agn[o]tology” is just one more pseudo-intellectual
    > way to smear some of the skeptics.

    I think it’s mostly trying to be a fancy buzzword for a research program, one that, incidentally, covers broader ground than the climate debate. Possibly too broad, too conducive to intellectual smugness, and too likely to tick off research subjects. (“Hi, I’m studying ignorance. Could I interview you?”)

    Still, it ain’t much of a smear. Us just plain folks who call’em as we see’em, we’ll just stick with “liars” and “cranks” for the deniers. (Not you, Matthew.)

    > one-sided

    Surely there are cases of ignorance-making in progressive and ecological causes, too, research opportunities just waiting for a conservative agnotologist to pounce. Might be healthy for the field.

    > “merchants of Belief” like Al Gore

    I’m sorry, #53 is right, that’s just false balance.

    Comment by CM — 4 Sep 2011 @ 3:26 AM

  63. Dan Bedford #58,

    Cheers! And sorry again about the name thing. I enjoyed your paper. Useful reading list and constructive tips for putting misinformation to good educational use. Defining and measuring success might take some more thinking about. If you train students to see through Crichton’s essay, you’d expect them to do well at an exam question about an op-ed-style text, and that’s a good thing in itself, but do the critical thinking skills and understanding of scientific method gained by considering misinformation carry over to other kinds of problem-solving? And if they’re trained on materials denying an environmental problem (admittedly the vast bulk of misinformation in this field), does it make them better able to spot materials that make similar errors in somehow overstating one?

    Comment by CM — 4 Sep 2011 @ 4:06 AM

  64. Septic Matthew, Excuse me, but what the F*** does Al Gore have to do with any of this. Al Gore is a layman doing his best to present the scientific consensus. The idjit denialists are simply refusing to consider evidence because they don’t like the policy implications. See a difference?

    Hint: One is trying to present science. The other is trying to present anti-science. You figure out which is which!

    Comment by Ray Ladbury — 4 Sep 2011 @ 7:08 AM

  65. Matthew #53,

    The comparison between L&S’s physics-free curve-fitting exercise and Raypierre’s textbook introduction to planetary radiation balance lost me, I’m afraid. Anyway, I think your suggestion about Loehle and Scafetta is testable:

    Hypothesis (H): Loehle and Scafetta is a hypothesis-generating exercise of heuristic value.

    Empirical consequence: Having generated the hypothesis (H’) that there might be a 60-year wobble in the solar system capable of forcing much of the temperature variation on 20th century Earth, Loehle and Scafetta set off to verify the physical existence of said wobble.

    Observation: Well… not so much. Rather, they go off reassessing climate sensitivity, dismissing the role of aerosols, and making 21st-century projections as if H’ could be taken for granted.

    Conclusion: H is falsified. New hypothesis H2: Loehle and Scafetta is a publicity-generating exercise of, uh, agnogenetic value.

    Is this argument wrong or unfair?

    (Captcha: ithink student-)

    Comment by CM — 4 Sep 2011 @ 9:44 AM

  66. Re 60 EFS_Junior – I just thought that the time horizons on Laskar’s work were limits of predictability; that the meteorologist doesn’t bother trying to tell you what’s going to happen more than 1-2 weeks from now doesn’t imply a prediction of the end of the world (PS tying several things together, I’ve heard the same perspective voiced about the Mayan calendar – ie they just never got around to what happens after whatever o’clock on what’s that date, Dec 2012 :) ).

    I thought predictions of possible future interplanetary impacts were a bit of a different matter from the orbital cycles.

    Might there be categories of solar system dimensions with limits of predictability longer or shorter – like you can predict how much snow you will get in tonight’s blizzard but not know where each snowflake will land – you can predict a number of hurricanes of some intensity for the next year but not quite when and where each will be – you can predict in principle that the next ice age may start in 20,000?/30,000? or 50,000 or ? years (contingent on what we do), and the one after that, but at some point there could be some tectonic processes that make things more like the Cretacious – and there is probably some time horizon for the weather of mantle convection, too, while the climate of the mantle (layered vs whole vs mixed convection, general descriptions of cell sizes and rates of motion) may be predicted for longer time frames. (And yes, you need to know the paleogeography in order to calculate tidal torques and thus the evolution of the periods of the orbital cycles as they are affected by the Earth’s rotation rate and the moon’s orbit and oh, Earth’s rotation also determines the coriolis effect which affects the tides and the rotation also affects the weather and climate, and tides are important along with wind and plankton in ocean mixing too, but anyway, there is at least geologic evidence for changes in Earth’s rotation which constrains the possible trajectories over time.) Did the K/T impact throw off things so much in the solar system? For the range of directions and speeds and masses it could have involved, there are a range of possible prior momentum and angular momentum values the Earth could have had – perhaps we should do a ‘spaghetti model’ (as was much discussed on the news for the track of Irene)? Might the ‘weather’ of orbital cycles be impacted by K/T but not the ‘climate’ – perhaps the trajectories of obliquity, precession and eccentricity would become completely different given sufficient time, but maybe with the same general character – periods and amplitudes and average values being similar enough that a casual glance at any given time segment (on the necessary scale to characterize the orbital cycle ‘climate’) wouldn’t look like anything different.

    I don’t see that a potential for future collisions among planets should be preposterous just because it hasn’t apparently happened except near the beginning; I thought it’s been accepted that there is chaos in the long term regarding the orbits. Which would the prediction of a specific incident hard, but may allow some signficant probability for some collision or massive rearrangement at some time.

    Comment by Patrick 027 — 4 Sep 2011 @ 1:15 PM

  67. @60-61: I agree that Milankovich is not (thus far) a complete explanation for glacial cycles. The theory has been (and is actively being) revised in accord with what we’ve learned. I also agree that we hear all kinds of claims that lack physical basis, not just for “60 year cycles”, but also for such amusing (but unfortunately damaging) humbug like the idea that the GHE violates the 2nd LoT.

    On the solar system, it is deterministic — but chaotic. If we could measure all relevant conditions, we could in principle predict its state at any point in time. But we cannot measure all relevant conditions, the ones we can measure all have some error, our calculations are approximations and have finite precision, and the minimum step size is limited by available computational power. These factors limit our ability to predict the system’s state beyond some point in time. Also there is an irreducible prediction limit arising from Heisenberg’s Uncertainty Principle (who knows where the next virtual particle pair will appear?), but I don’t know what it is, and none of the papers I’ve read mention it, probably because non-quantum uncertainties (unknown Kuiper belt objects, anyone?) swamp it by many orders of magnitude.

    The question is thus: for what time span does state-of-the-art solar system simulation yield valid results? Laskar et al 2011 (thanks for the cite), claims usable eccentricity results for +- 50 Myr.

    You say

    So, for example, his modeling goes to the dumpster about 60Myr in EITHER direction. Meaning, that if he were on the Yucatán Peninsula, say 65Mya, a few hours before you know what hit right aboot there, he would claim that 65Myr in to the future (e. g. December 21, 2012AD), the Solar System would be in total chaos, simply bescuse that’s when his theory/numerical model goes to the crapper…. AFAIK that is what he’s claiming, inevitable chaos, because his model said so.

    As far as I understand what you mean by “chaos” here (you seem to be using it in the sense of “disorder” or even “ruin” rather than in the sense of a limit on predictability), I disagree. Laskar et al 2011 claims only that their model can validly predict earth’s eccentricity over +- 50 Myr, not that its eccentricity assumes wild values beyond that time. Similarly, Laskar & Gastineau 2009’s take on Mercury’s orbit’s possible evolution is a probabilistic one, not a prediction.

    All that said, it’d be great to get more geological data to confirm, refute, and/or recalibrate solar system models, a point which Laskar et al 2011 makes in the abstract, p.2, p.8, and elsewhere.

    Thank you for the conversation. This topic is more interesting than I’d thought.

    Comment by Meow — 4 Sep 2011 @ 2:57 PM

  68. Re 51 Tom P – watched the video; and I agree that the sun does wobble around the center of mass of the solar system; the center of mass itself is not tending to wobble around the sun because conservation of momentum applies to the solar system as a whole (except of course for the forces applied to it by nearby stars, the rest of the galaxy, etc, but those are not varying so fast and so the center of mass should generally be moving along rather smoothly on the same timescale as planetary motions). However, the idea that this motion or Jupiter would result in the sunspot cycle is a bit odd – see above comments on ‘free fall’ and tides on the sun. Tides follow an inverse cube law (to a first approximation for systems experiencing tides due to masses relatively far away compared to the system’s size; for systems that are not small relative to the distance to the object producing the tidal acceleration, I think it’s more complicated), and so the inner planets gain in importance relative to the outer planets, although mass is still important (and nonetheless, tides raised on the Sun by the planets are so tiny it’s hard to imagine they could be of any such significance).

    And Earth is not orbiting the barycenter of the solar system. Consider that the Moon is in orbit about the Earth (well, their barycenter), it is not orbiting the barycenter of the Earth-Moon-Sun system except by being part of the Earth-moon system. Jupiter is (from memory) a bit over 5 times the distance from the sun as Earth is; thus, with about 1/1000 the mass of the sun, the gravitational acceleration of the Earth toward the sun due to the sun’s mass is about 1000 * (4 to 6)^2 = 16,000 to 36,000 times that of it’s acceleration toward Jupiter due to Jupiter’s mass, whereas if the Earth were accelerating toward the barycenter of the Sun-Jupiter system, shouldn’t that ratio should be ~ 1000 * 1/(4 to 6) = 250 to ~ 167? The Earth-Moon doesn’t orbit the Earth-Moon-Sun barycenter exactly but it is not orbiting the barycenter of the solar sysem either; to some approximation the innermost planets and the sun must wobble around the barycenter together as they are similarly affected by the outermost planets which happen to be more massive as well as more distant and thus dominate in their effects on the barycenter – things should tend to get more complicated when the planets involved are at more similar distances.

    Comment by Patrick 027 — 4 Sep 2011 @ 5:24 PM

  69. Here is another quote from Raymond Pierrehumbert’s book “Principles of Planetary Science”.

    The thought experiment of varying L{*} in a hysteresis loops is rather fanciful, but many atmospheric processes could act to either increase or decrease the greenhouse effect over time. For the very young Earth with L{*} = 960W/m^2, the planet falls into a Snowball when p{rad} exceeds 500mb, and thereafter would not deglaciate until p{rad} was reduced to 420mb or less (see Fig. 3.11). The boundaries of the hysteresis loop, which are critical thresholds for entering and leaving the Snowball, depend on the solar constant. For the modern solar constant, the hysteresis loop operates between p{rad} = 690mb and p{rad} = 570mb. It takes less greenhouse effect to keep out of the Snowball now than it did when the Sun was fainter, but the threshold for initiatiing a Snowball in modern conditions is disconcertingly close to the value of p{rad} which reproduces the present climate.

    For those of you who like RISK, the predicted (or modeled, or the scenario of) reduced solar output in the next decades ought to lead to even more “disconcert”, and a crusade to spend trillions of $$ to make sure that it does not happen.

    In brief, the knowledge of planetary climate and the many heat flows do not justify any confidence in attributing some of the post LIA temperature rise to CO2, or to forecasting a climate sensitivity of 3.5K per doubling of global average CO2. There is too much that is only roughly known, too much that is not known, to justify a belief in such refined or seemingly precise conclusions. On present knowledge, taken all together, it is possible that Earth will heat (with consequent crop disruption), and it is possible that Earth will cool (with consequent crop disruption.) Both risks should be remembered as you go about advocating the rebuilding of the human energy industry.

    How that fits in with agnotology I leave to you.

    Comment by Septic Matthew — 4 Sep 2011 @ 6:25 PM

  70. Wait, you are attributing that to Ray Pierrehumbert?
    Maybe some of it. But how much?

    Please look for the ” key on your computer and use it before and after quoted material. It’s a courtesy.

    Comment by Hank Roberts — 5 Sep 2011 @ 1:30 AM

  71. Matthew #69,

    If you’re claiming that uncertainty means we cannot know whether we’re affecting the climate and temps can just as well go down as up, the fit with agnotology is clear. Instead of throwing up their hands, people have worked with multiple lines of evidence to bound the uncertainties. For the questions you raise, see e.g. Knutti and Hegerl’s review of climate sensitivity; the IPCC chapter on detection and attribution; or Feulner and Rahmstorf on the effect of a new grand minimum on climate.

    Comment by CM — 5 Sep 2011 @ 4:09 AM

  72. Septic Matthew,
    That the human energy industry will have to be “rebuilt” is inevitable, and it would happen even if climate change were to magically stop. Oil is running out. Coal is finite. Demand is growing.

    As to your other assertion (which, by the way, you should indicate with quotes, block quotes, etc. what is yours and what is Raypierre’s), there is zero evidence that any Grand Solar Minimum is in any danger of putting us into a Snowball Earth scenario. (Read Usoskin) Talk about alarmists!

    Comment by Ray Ladbury — 5 Sep 2011 @ 7:21 AM

  73. Hi MJD
    MJD says:
    3 Sep 2011 at 10:15 AM
    To: vukcevic #23

    “vukcevic says:
    1 Sep 2011 at 6:14 AM

    No doubt the Sun indeed runs ‘60 year cycle’, (pi/3 = 60 ; pi/…), as this NASA’s record confirms:”

    Vukcevic: Your link just shows a photo of the sun. It doesn’t confirm anything about cycles (or much of anything else). Kindly post the correct link if you please.

    Just examine the photo carefully, particularly top left hand side (10 o’clock area), 1024 pix resolution should be good enough. The sun definitely runs ‘pi/…

    Comment by vukcevic — 5 Sep 2011 @ 11:36 AM

  74. @69: In addition to what’s already been said about misleading quote-mining, I’m sure you’ve got ample evidence that solar output will soon fall from ~1366 W/m^2 to ~1312 W/m^2 (a drop of ~4%, probably not seen since ~475 Mya!) for long enough that we should be concerned about runaway glaciation. Oh, wait, you haven’t produced any.

    d (septicism quality)/dt has fallen to << 0, which could indicate an incipient grand minimum. Watch out!

    Comment by Meow — 5 Sep 2011 @ 1:24 PM

  75. 28, gavin: A careful reading of the Scafetta papers (2010; L&S 2011 etc.) shows that the ‘astronomical’ rationale is completely post-hoc.

    True, but it doesn’t make them wrong, only untested and unreliable. The early history of the Bohr model of the atom was similarly confused (? to pick another mild pejorative for unreliable): it was invented post-hoc to explain spectroscopic data, and required repeated revisions until (among other tortures), the hypothetical electron orbits had been replaced by hypothetical distributions, and electrons
    had become subject to Pauli’s Exclusion Principle.

    Loehle and Scafetta’s work should not be relied upon to guide policy, at least not exclusively, but I bet it is worthy of further tests.

    [Response: I hope you aren’t really being serious, but loehle and scafetta’s contribution neither deals with any important uncertainty nor points to any interesting research avenues. They may as well have correlated temperature to the number of Tibetan monks for all the insight their work provides. – gavin]

    Comment by Septic Matthew — 5 Sep 2011 @ 3:25 PM

  76. Re my 68 re 51 Tom P: I worked on it a little more and, for position vectors rS and rJ toward masses MS and MJ, the vector to the center of mass CM is
    rCM = ( MS*rS + MJ*rJ ) / (MS+MJ)
    and the gravitation acceleration at the origin of the position vectors:

    = G* (MS*rS/rS^3 + MJ*rJ/rJ^3) = gS + gJ

    were it not for the r^3 terms in the denominators, this would be parallel to rCM and thus point toward CM. But for the larger mass being MS, we can take gS = G*MS*rS/rS^3, and note that the difference between that and a vector pointing toward CM is (from proportionalities) gJ’ = G*MJ*rJ/rS^3 = gJ * (rJ/rS)^3
    gJ/gJ’ = (rJ/rS)^3, and so the actual g = gS + gJ will point toward a point on the line between S and CM that is ~ (rS/rJ)^3 of the way from S to CM, at least for small gJ/gS and small (rCMrS)/rS

    So *if* the Earth’s orbit could be approximated as about a single point between Jupiter and the Sun, assuming the above can be used as guidance, it would be ~ 63 to 215 times closer to the sun than to the Jupiter-Sun barycenter. Thus, rather than changing the Earth-sun distance by ~ +/-0.5 % and thus solar TSI by ~ +/-1 % from average, it would change it by two orders of magnitude less (with the annual average effect perhaps smaller still, although varying with Jupiter’s alignment with the semimajor axis, etc.). Etc. for Saturn et al.

    Comment by Patrick 027 — 5 Sep 2011 @ 4:50 PM

  77. A related but different matter: I’m curious what anybody thinks of these:

    “Possible forcing of global temperature by the oceanic tides”
    Charles D. Keeling, Timothy P. Whorf

    “The 1,800-year oceanic tidal cycle: A possible cause of rapid climate change”
    Charles D. Keeling* and Timothy P. Whorf

    for a little background:
    (PS I recall elsewhere reading that wind, plankton, and tides contribute similarly to oceanic mixing. But is that just in the mixed layer (or entrainment into it) or in the deep ocean, and does this include upwelling with subsequent mixing or merging with the mixed layer via heating, etc.? Also, deep ocean mixing by tides may be through breaking of internal gravity waves – something about submarine ridges or seamounts rings a bell).

    I read through some portion of the first paper, the second I looked at a little. I couldn’t find any mention of the variation of the eccentricity of the Moon’s orbit, and I don’t understand why the parameter γ should be the best for rating the tides. It would be helpful to see a graph of how the tidal amplitude varies – how much variabiligy remains outide of the spring-neap and other short-term cycles?

    And as long as someone would consider such (small?) variations in tide amplitude to be important for oceanic mixing, what about deep mixing (time delay effects?), or if it is important how much tidal energy is dissipated in the diurnal cycle vs the semidiurnal cycle (if my understanding is correct, the equilibrium tide height is zero at the equator and pole and maximum at midlatitudes for the diurnal cycle and zero at the pole and maximum at the equator for the semidiurnal). Or what if stronger tides increased glacial flow or calving at the coasts, or tidal currents openned up gaps in sea ice covering by piling sea ice against islands, thus affecting albedo and surface heat fluxes? (The mechanism proposed by the authors sounds a bit like tidal variations forcing a sort of ENSO-like effect – not the specific geographical effects but the general vertical redistribution of heat in the ocean. If the tides were turned off completely, presumably there would be some global warming, which would then decay with time as it would cause a radiative disequilibrium.)

    I haven’t checked with google scholar but the papers themselves don’t seem to list any other work citing them that really pertains to the hypothesis – unless I missed something.

    Comment by Patrick 027 — 5 Sep 2011 @ 5:58 PM

  78. 75, Gavin: They may as well have correlated temperature to the number of Tibetan monks for all the insight their work provides. – gavin]

    The calculation of climate sensitivity by Pierrehumbert (whose book supports a figure of 2K) assumes that it is constant (an untestable assumption, at least now) and ignores the effects of cloud formation and dissipation (there are other approximations/simplifications to what is known, but those 2 will do for now.) Loehle and Scafetta assume a persistent periodicity, a persistent linear trend, and an additional more recent (but persistent) linear trend attributable to CO2. Both sets of assumptions are deficient. Either or neither may be shown by 2020 (or 2030) to be sufficiently accurate for predicting the global mean temperature in 2050 (or accurate scenarios depending on the accumulation of CO2.)

    If you like assigning numbers to represent degrees of belief, each should get a low number. If you are thinking of public policy, you/we should formulate a public policy for the next ten years that will not be too bad no matter which is best supported by evidence available then.

    I think that your invocation of the Tibetan monks was a poor rhetorical flourish. If their number did correlate with some climate statistic, however, that would be intriguing.

    Comment by Septic Matthew — 5 Sep 2011 @ 8:33 PM

  79. > I haven’t checked with google scholar but the papers themselves
    > don’t seem to list any other work citing them ….

    Papers citing those papers were only published later; each those web pages have links (which only work from the article page): look for and click on
    View citing article information
    Citing articles via CrossRef
    Citing Articles via Web of Science (55)
    Articles citing this article

    Comment by Hank Roberts — 5 Sep 2011 @ 9:07 PM

  80. Here’s one such link — you’ll find familiar names among the authors:

    Comment by Hank Roberts — 5 Sep 2011 @ 9:09 PM

  81. I think that your invocation of the Tibetan monks was a poor rhetorical flourish. If their number did correlate with some climate statistic, however, that would be intriguing.

    Considering Chinese activity wrt Tibet, I wouldn’t be at all surprised if the number of monks showed a decline well correlated to the decadal increase in global temperature. ;)

    Comment by flxible — 5 Sep 2011 @ 11:57 PM

  82. 81, flxible, That was cute — sincerely. But we already know of the correlation with the growth of Chinese industry. So we’d need some sort of (or sorts of) multivariate time series analysis.

    Raymond Pierrehumbert’s book is a treasure trove of information. Because the author is so complete in describing the limitations and approximations in his derivations, it could be called “The AGW Skeptic’s Handbook”. If the so-called “denialists” weren’t so narrow-minded (some are for sure), they’d publish “Annotations” or “A Reader’s Guide” companion explicating the justifications for a skeptical or “lukewarm” assessment of AGW.

    Comment by Septic Matthew — 6 Sep 2011 @ 11:11 AM

  83. Re 79,80 Hank Roberts – thanks.

    Comment by Patrick 027 — 6 Sep 2011 @ 4:02 PM

  84. Re #82

    If the so-called “denialists” weren’t so narrow-minded (some are for sure), they’d publish “Annotations” or “A Reader’s Guide” companion explicating the justifications for a skeptical or “lukewarm” assessment of AGW.

    Or “How to cherry pick factoids you like from a barely understood text book you have just skimmed, without really having thought about working through thoroughly”

    Ok, probably too long

    All the best,

    Comment by Marcus — 9 Sep 2011 @ 3:42 AM

  85. 84, Marcus

    “Cherry picking” hardly does this justice, it’s more like harvesting cherries by the bushel.

    I suppose you’d have considered the inability to correctly model the precession of the perihelion of Mercury a “cherry picked factoid”. That error was far less than the errors to date in predicting climate change.

    A lot of you don’t seem to understand that the models of climate science are approximations, and that in most cases they do not have demonstrated precision better than 3%. Even if Earth truly were a flat disk without terrain, and even if the energy transfer processes were linear, and even if the system were in steady-state, the models would not be accurate enough to make a long-term forecast of the effects of doubling CO2 because the models can not even predict changes in cloud cover.

    Comment by Septic Matthew — 9 Sep 2011 @ 8:33 AM

  86. Septic Matthew,
    If the models were all we have, or if the purpose of the models were to make long-term predictions, I might agree. But neither of these assertions is true. We have mountains–both literal and figurative–of evidence that the planet is warming in a manner consistent with the output of the models–imperfect though they are.

    And the purpose of the models is NOT to provide detailed predictions of every behavior the climate may exhibit, but rather so we can compare qualitative and quantitative trends in nature and in the models.

    See, Matthew, here’s the deal. We know with near 100% certainty that CO2 is a greenhouse gas and that greenhouse gasses warm the climate. We know with better than 95% confidence that doubling CO2 in the atmosphere will raise the planet’s temperature by an average of greater than 2 degrees. We also know that MOST of the uncertainty, by far, is on the high side of that sensitivity confidence curve–that is it’s a whole helluva lot more likely that sensitivity is 6 degrees than it is that it’s 1 degree. If it’s 2 degrees, we might just barely manage if we act soon. If it is 6 degrees, we are cooked. And if you toss out the models, you further increase that high-side probability

    So, I have to say, I’m a little perplexed by denialists like you taking comfort in the “lack of precision” of the models. Uncertainty is NOT the friend of complacent.

    Comment by Ray Ladbury — 9 Sep 2011 @ 10:44 AM

  87. Dear Matthew,

    You can always suspect that I myself do not know sufficiently what a model is and what restrictions it has, as You don’t know what I know… But if You blame the pros here for such a thing You fall victim to the Kruger Dunning fallacy.

    As I understand projections are of course made on the basis of what is known today, which comprises that greenhouse gases force the climate system due to a well understood mechanism of radiative heat transfer, generating models that well explain what is observed and measured today. This is knowledge surely persisting albeit there are model deficiences and open questions.

    Of course always surprising things can happen the next 20 years, maybe Taminos mid atlantic leprechauns take over… not a consideration due to occams razor, though


    Comment by Marcus — 9 Sep 2011 @ 12:14 PM

  88. Re my 76 – of course, the sun is also accelerating toward Jupiter by a similar amount and direction, which would make the Earth’s orbit even closer to being about the Sun (or the Earth-Sun barycenter).

    Comment by Patrick 027 — 9 Sep 2011 @ 12:50 PM

  89. 86, Ray Ladbury: So, I have to say, I’m a little perplexed by denialists like you taking comfort in the “lack of precision” of the models. Uncertainty is NOT the friend of complacent.
    There are too many risks for everyone to “complacently”, so to speak, focus on one to the exclusion of others.

    88, Marco: As I understand projections are of course made on the basis of what is known today, which comprises that greenhouse gases force the climate system due to a well understood mechanism of radiative heat transfer, generating models that well explain what is observed and measured today. This is knowledge surely persisting albeit there are model deficiences and open questions.

    Radiative heat transfer is not the only mechanism, and some of what is observed today is not explained: on another thread is a discussion of clouds.

    Comment by Septic Matthew — 9 Sep 2011 @ 8:06 PM

  90. I recall more than one guest lecture at our physics department’s Centre for Global Change Studies displaying a graph of spectral analysis of temperature histories, with data from multiple time scale sources including thermometer records, ice core data, etc. Separate sources are color coded and aligned to scale.
    The spectrum shows really strong peaks at one day and one year, obviously. The other peaks are the interesting bits. There is a small peak around a couple of days, apparently tied to weather such as pasage of warm and cold fronts. IIRC, any peak at 11 or 22 years for sunspot cycles is not at all strong. Much farther down the curve, there are some peaks for Milankovich frequencies in the ice core data segment.
    I’m limited to working from memory in this, as I’ve searched several times without managing to find the original sources for these graphs. erhaps someone here is familiar with such sources. If so, please post any references you can offer. I”d really like to see these in context and study them more closely, along with the author’s discussion.

    [Response: Here is a relevant reference, perhaps the one you are thinking of: Huybers and Curry, 2006. –eric]

    Comment by Jim Prall — 10 Sep 2011 @ 6:53 AM

  91. For those who’d rather not spend $32 for Huybers and Curry, 2006, linked in eric’s response to #90 there is this:

    It’s free, there.
    (Not sure how to post URLs in any fancy way.)

    Comment by Jon Kirwan — 12 Sep 2011 @ 10:27 AM

  92. Septic Matthew, could you include antecedents to the pronouns you have used in your #89. I’m not sure what “one” is referring to, and I don’t see how it relates to what I posted.

    Comment by Ray Ladbury — 12 Sep 2011 @ 11:34 AM

  93. > some of what is observed today is not explained

    You’re a statistician, you say? In what field?

    Comment by Hank Roberts — 12 Sep 2011 @ 12:39 PM

  94. 89, Septic Matthew: There are too many risks for everyone to “complacently”, so to speak, focus on one to the exclusion of others.

    There are too many risks for anyone to “complacently”, so to speak, focus on one risk to the exclusion of other risks .

    No none is complacent. Most people in this debate are balancing multiple risks.

    Comment by Septic Matthew — 12 Sep 2011 @ 12:42 PM

  95. 93, Hank Roberts: You’re a statistician, you say? In what field?

    Nonstationary multivariate biological time series.

    Comment by Septic Matthew — 13 Sep 2011 @ 11:30 AM

  96. MJD, vukcevic is apparently a bit of a stirrer – if you look closley at the region around 10’oclock, and 1/3 in from the edge on the sum image, you will discover an example of the ubiquity of pi.

    Comment by NHH — 28 Sep 2011 @ 6:08 PM

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