A demonstration of Chladni Patterns

Post submitted by John A.

antarctic-10pc-trend-plot

Readers of Climate Audit will have noted Steve McIntyre  mentioning Chladni patterns in respect to the results of some climate reconstructions which exhibit spacial autocorrelation – which means that the data points are related to each other depending on how far away from each other they are, and thus by the shape of the area which contains the data points.

The notable example being Steig, Mann et al 2010 which purported to reconstruct temperatures in Antarctica and demonstrate a warming of West Antarctica. That study turned out to be caused by the poor modelling and worse statistical analysis, as shown by O’Donnell et al 2011. (Who would have expected a piece of statistical analysis to be so flawed when done by Michael Mann? I was as shocked as the rest of you).

Steve noted (but it didn’t survive the Steig-acting-as-a-conflicted-peer-reviewer cut) that the eigenvector patterns that were supposed to reflect temperature changes were in fact patterns which arise from autocorrelated noise.

The Chladni patterns can be shown easily using a square metal plate which has rice scattered on it, sitting on top of an amplifier. The amplifier sends a pure frequency sound to the metal plate, and in the demonstration below, that frequency is slowly increased. The patterns change dramatically as the signal frequency is slowly changed.

I think its a cool video. Enjoy.

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25 thoughts on “A demonstration of Chladni Patterns

  1. John A.wrote
    The Chladni patterns can be shown easily using a square metal plate which has rice scattered on it, sitting on top of an amplifier. The amplifier sends a pure frequency sound to the metal plate, and in the demonstration below, that frequency is slowly increased. The patterns change dramatically as the signal frequency is slowly changed

    Same thing seems to apply the Alarmist predictions.
    The more the real world observations tell/show us global warming is not happening the way the models/they predicted. The more garbage science they put out and at a increased frequency,

  2. Another deceptive map, check out the chloropleth legend. Most people will assume that white = no change where as white is slight cooling and orange is slight warming. Of course the orange pops out much more prevelantly than the white.

  3. lol, it is nice to revisit a bit of climatology history. What’s difficult for me, and probably most mere mortals, is discerning the difference between noise patterns and patterns from data. Weather and climate being especially difficult for me, because I expect patterns.

    Great video illustrating the patterns and the difficulty.

  4. I understand that the nodal pattern is partly dependent upon the shape of the plate and the way the plate is constrained, and that the shape correlates to the shape of the area being studied for temperature change. Is there a physical parameter in the temperature study which correlates to the frequency dependence of the nodal pattern on the plate?

  5. Forgive me, but although it is a cool video, how does it connect to temperture data? I don’t see how rice being bounced around on plate can have anything to do with temperture studies? Not a troll, just lack understanding.

  6. Thank you, ‘Pull My Finger’, I hadn’t noticed that. Well spotted. White on that map is slight cooling, this makes the map appear deceptively warm when glanced at, but when you notice the scale at the bottom, there is nowhere near as much warming as appears in the map at first glance.

  7. “It doesn’t take a majority to win, just a tireless minority that will keep starting
    brush fires in the mind and hearts of their fellow men.” Samuel Adams

    The video is impressive. Take us back to effectual science.

    As for the gloomydoom-meisters of AGW, just repeat the quote from our friend Samuel Adams.

  8. I am having difficulty seeing how this relates to temperature measurements.

    The patterns shown in the video are caused by standing waves on the plate surface. These are a result of reflection of energy from the discontinuity of the edges of the plate, and constructive/destructive interference of the reflected energy.

    I find it difficult to believe that there is ANY correspondence between the physics here and temperature measurements across a continent.

  9. Interesting video – TBH I have forgotton more than I care to remember regarding the subject of sound, harmonics and resonance, but aren’t these patterns generated by the ‘resonance nodes’ of the plate? and have nothing to do with the rice (which just ‘align’ to the positions of least movement). Something seems to tell me this is simply to do with the resonant frequecies of the material of the plate, thickness, etc….

  10. Great video and a good example of how lack of data can result is some strange conclusions.

    The Nyquist sampling theorem show how lack of data points can produce artifacts too.

    This video shows a strange effect caused by the camera creating the image one scan-line at a time, and the blade of the prop having moved in the time it takes to have started on the next scan-line, which produces the video aliasing artefacts seen…

  11. Pull My Finger-I think the number labels are shifted slightly to the right of what they actually are labeling. Not sure but I doubt there was anything intentional about the scale meant to mislead. Anyway it makes little difference as far as I can tell. The main point is the presence of spurious patterns, not where zero is.

  12. For whatever it is worth, the New Testament, John 1 says the world and the life in it was created this way.

  13. Matthew W @ 8:21 am OK, I have to ask “What does it mean”?

    It’s a bit subtle and has to do with “orthogonal” functions. Any vibration pattern on the plate can be decomposed into a weighted sum of the Chladni patterns. Your ability to reproduce an arbitrary vibration pattern is determined by how many terms and which ones you keep in the sum. Not enough terms or the wrong ones and your mathematical description is not a good fit to reality.

    For example, suppose the vibration wasn’t a pure tone but some complicated sound that made the rice pile up in an off center mound. It would be composed of a weighted sum of all the patterns you saw. If you only kept the lowest order pattern, the pin cushioned square with the circle inside, that would be a poor approximation to an off center mound.

    In the case of Steig et. al., the Chladni patterns for Antarctica are not nearly so pretty, but the same caveat applies. They didn’t keep enough patterns and that’s where they went wrong.

  14. I, too, would like to see a deeper explanation of how the Chladni patterns apply.

    I had imagined that it was something like: we have very sparse data combined with aliasing from PCA analysis that results in Chladni-like patterns, with the PCs being analogous to frequencies and the data points being analogous to “shape” (or perhaps nodes). Paul Linsay’s explanation is different from this, though the graph retains 20 PCs so I’m not sure if it’s the more correct explanation or not.

    (I’m neither an expert in PCA nor Chladni patterns, so my imagined explanation is probably incorrect.)

  15. I’m with Philip Peake on this one. This looks like a demonstation of interference patterns to me.

    On a related note, I’ve been wondering if interference patterns show up in the annual signal of heat transferrence into the oceans. I say this because of a few plots I produced using ARGO Climatology data. For each latitude and depth, a sine curve was fitted to the 12 months of mean temperature data to get the amplitude, phase, mean, and R^2 stat. I then produced the corresponding plots.

    As expected, there was a weak signal around the equator, presumably due to the bi-annual frequency there. However, I thought that there might be a legitimate interference pattern at other latitudes.

    Here’a plot of the R^2 verification statistic by latitude and depth:

    Here’a plot of the amplitude signal, scaled by standard deviations of the depth:


  16. “…
    (Who would have expected a piece of statistical analysis to be so flawed when done by Michael Mann? I was as shocked as the rest of you).
    …”

    Chuckle! Careful there, you may hurt yourself with your tongue so far out in your cheek.

  17. It would seem that Chladni Patterns can occur in nature as demonstrated by the plate and the rice.

    Are we sure that that the patterns are an artifact of Steig’s methods and not real and naturally occurring?

  18. John A.wrote ‘The Chladni patterns can be shown easily using a square metal plate which has rice scattered on it, sitting on top of an amplifier.’ Some partial clarification folows.
    John A., did you mean not an amplifier, but a sine wave or other type of signal generator whose bandwidth is narrow and variable at will? Our cat sits on our amplifier in Winter, but not on the speakers it feeds. A few rare CDs have an equipment check that ramps up the frequency of an audio signal. I’m going to try it on a horizontal speaker later today because it looks cool.
    In the context of the Antarctic, i think it correct that the analogy with the rice plate is to the mathematical analysis. I do not think it is intended to mean that the Antarctic Ice Sheet vibrates and resonates and physically causes cooler regions.

  19. Paul Linsay says: June 7, 2011 at 10:30 am
    Wayne says: June 7, 2011 at 11:15 am

    I pretty much agree with Paul. They are just basis functions, in any scheme. Doesn’t say anything good or bad about Steig, except that he retained three which he acknowledges was too few. Four to six seems to be a better range.

    The eigenfunctions of wave equations (Chladni) and spatial correlation matrices are closely related.

  20. Nick,
    So it comes down to a lack of confidence in which computation is optimum “Four to six SEEMS to be a better range”. What I have not seen is a proper estimate of bias and precision for most of the combinations. The bias would have to enclose all computations/maps shown above, from which it is logical to deduce that the data are too noisy for analysis of this sophistication.
    There is a difference between “best computational method” and “best approach to actual temperature.”

  21. Nick Stokes said: June 7, 2011 at 5:45 pm
    “Doesn’t say anything good or bad about Steig, except that he retained three which he acknowledges was too few”
    Not quite. Steig also put an unwarranted physical interpretation on what were, in reality, just Chladni patterns:
    “The first three principal components are statistically separable and can be meaningfully related to important dynamical features of high-latitude Southern Hemisphere atmospheric circulation, as
    defined independently by extrapolar instrumental data. The first principal component is significantly correlated with the SAM index (the first principal component of sea-level-pressure or 500-hPa geopotential heights for 20u S–90u S), and the second principal component reflects the zonal wave-3 pattern, which contributes to the Antarctic dipole pattern of sea-ice anomalies in the Ross Sea and
    Weddell Sea sectors.”

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