A little knowledge!

There are some posts on Watts Up With That (WUWT) that make me realise the merit of the phrase a little knowledge can be a dangerous thing. There is a recent post by someone called R.J. Salvador called Sunspot cycle and the global temperature change anomaly. In this post there are some fairly impressive figures showing a fit to the global temperature anomaly data and a projection into the future suggesting that we are about to enter a phase of cooling.

So, how is this done? Well there is a formula

in which SN is the sunspot number, a, b, c, d, and e are constant and the summation is over the all the previous months. The post actually says,

Each term is calculated by month and added to the prior month’s calculation. The summation stores the history of previous temperature changes and this sum approximates a straight line relationship to the actual Global Temperature Anomaly by month which is correlated by the constants d and e.

Okay, so let’s see. You have a formula that you make up that has 5 unknown constants and has a cosine and power-law dependence on some function of time, SN. You have a data set – the global temperature anomaly. You choose your constants by fitting your function to the known dataset. Okay, I can believe that this has been done correctly. However, it doesn’t mean anything. I could have probably used almost any time series I liked and, with 5 parameters and a suitable choice of function, fitted to the global surface temperature anomaly data. There’s is no physics here whatsoever. It really doesn’t tell us anything at all. It does not mean that the rise in the global temperature anomaly has been driven by the Sun.

The post then goes on to use the Dalton Minimum (a period of low sunspot numbers during the 1800s) to project the analysis forward to 2044 and predict that global temperatures will drop by about 0.6 degrees. Really, there is a suggestion that we may have reduced sunspot numbers in the future, but it is very uncertain. To be fair, the assumptions and analysis have been very clearly defined. I can’t fault the post in that regard. I could, however, probably have done exactly the same analysis using number of cars sold per month as my time series. I could have produced quite a good fit to the global temperature anomaly data and then predicted (based on future car sales) that global temperatures will continue to rise and that it would be due to our increasing use of cars. It would, however, have been equally meaningless. You can’t simply choose some complicated function with a large number of parameters to make predictions about the future evolution of something. You need to base your model on the underlying physics (and chemistry) that is driving the changes in whatever it is that you’re measuring.

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8 Responses to A little knowledge!

  1. To be fair, quite a few of the comments on WUWT are criticising this curve fitting procedure in the same manner that I have. At least some people there recognise that you can’t simply fit a random function to a dataset to make predictions about the future (unless your function has some basis in reality).

  2. Rachel says:

    This reminds me of a blog post I read recently – http://thetaponline.wordpress.com/2013/02/13/there-is-comfort-in-knowing-youre-incompetent/ – about how being unable to recognize your own incompetence can lead to an inflated assessment of your capabilities.

  3. Yes, the possibility of the Dunning-Kruger effect is quite interesting. There does seem to be quite a lot of evidence that there are many who suffer from it. The alternative – that they’re knowingly promoting ideas that are clearly wrong – seems almost worse than the possibility that they just don’t realise how incompetent they are. Of course, one issue with the DKE is that you can never really know if you aren’t suffering from it yourself 🙂

  4. cos(a*SN) essentially generates random numbers, so Σcos(a*SN) is a random walk controlled by the parameter a . It must be a monstrous model to fit as even small changes in a give large changes in the shape of the random walk – any shape curve can be fitted.
    Σb*SN^c generates a trend, convenient for matching the temperature trend since 1880.
    I’ve explored this at http://quantpalaeo.wordpress.com/2013/05/04/von-neumanns-elephant-trunk-wiggles/

  5. Exactly. You’ve done an interesting analysis in your post. As others have pointed out, requiring that your constants have so many significant figures tends to indicate that your fit is very sensitive to those parameters and rather devalues its relevance.

  6. FrankD says:

    Actually, its “a little learning”, which works just as well…

    A little learning is a dangerous thing;
    Drink deep, or taste not the Pierian spring:
    There shallow draughts intoxicate the brain,
    And drinking largely sobers us again.
    Fired at first sight with what the Muse imparts,
    In fearless youth we tempt the heights of Arts ;
    While from the bounded level of our mind
    Short views we take, nor see the lengths behind,
    But, more advanced, behold with strange surprise
    New distant scenes of endless science rise !
    So pleased at first the towering Alps we try,
    Mount o’er the vales, and seem to tread the sky ;
    The eternal snows appear already past,
    And the first clouds and mountains seem the last ;
    But those attained, we tremble to survey
    The growing labours of the lengthened way ;
    The increasing prospect tires our wandering eyes,
    Hill peep o’er hills, and Alps on Alps arise !

    Alexander Pope, 1711.
    (hopefully the line formatting will work)

  7. Very nice, thanks. I assume you meant to type “Alexander” rather than “Alexamber” – which I’ve corrected.

  8. pendantry says:

    one issue with the DKE is that you can never really know if you aren’t suffering from it yourself
    Agreed: however, if you’re aware that it’s a problem, you’re more likely to question your assumptions. “Knowing there’s a trap is the first step in evading it.”

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