Nicola Scafetta has published yet another paper about his theory that the (probably tidal) influence of Jupiter and Saturn is responsible for long-term changes in solar output, and that these cycles are responsible for climate change on earth. You can read about it on WUWT. It doesn’t surprise me that the paper is due to be published in a journal which seems to me to be sinking further and further into disrepute, the Journal of Atmospheric and Solar-Terrestrial Physics. Nor does it surprise me that there’s really no physics in the paper, just mathturbation.
Scafetta begins by claiming that the distribution of lengths of the solar cycle is bimodal. He bases this claim on estimates of the lengths of individual cycles. To estimate the pdf (probability density function) of cycle length, he applies a kernel density estimator using a normal-distribution kernel. That method requires a parameter, sometimes called the “bandwidth,” which controls how much the estimated pdf is smoothed. More data allows for a smaller bandwith, sparse data do not. If your bandwidth is too small you’ll get too many “wiggles” in your estimated pdf.
Scafetta tries two different bandwidths, and , which give these estimates of the pdf for solar cycle lengths:
On this basis, Scafetta argues that not only is the solar cycle length bimodal, but that:
If is used, two peaks appear close to about 10 and 12 years. This double-belled distribution is physically interesting because it reveals that the solar cycle dynamics may be constrained by two major frequency attractors at about 10 and 12 year periods, respectively. Thus, the solar cycle length does not appear to be just a random variable distributed on a single-belled Gaussian function centered around an 11-year periodicity (as typical solar dynamo models would predict), but it appears to be generated by a more complex dynamics driven by two cyclical side attractors.
His choice of bandwidth 0.5 is entirely arbitrary, you can always choose a bandwidth which will make the estimated pdf multimodal, whatever the true underlying distribution. My theory: Scafetta went with the low bandwidth value because it gave him a bimodal pdf estimate.
There is a formula for an “optimal” bandwidth when using a normal-distribution kernel. Using that choice gives the estimated pdf shown as the black line here:
Note that the estimate using the optimal bandwidth is not bimodal. That doesn’t prove the underlying distribution in unimodal (any more that using Scafetta’s arbitrary bandwidth proves it’s bimodal), but it does show how weak is Scafetta’s evidence, and how poorly thought out is his argument.
Scafetta also notes that there are no cycles with estimated lengths between 10.55 and 11.25 years, and argues that this confirms the bimodal distribution of cycle lengths:
The bottom of Fig. 2 shows in circles the 23 actual sunspot cycle lengths used to evaluate the two distributions. No Schwabe solar cycle with a length between 10.55 and 11.25 years is observed. The existence of this gap reinforces the interpretation that solar cycle dynamics may be driven by two dynamical attractors with periods at about 10 and 12 years. In fact, the area below the single-belled distribution within the interval 10.55 and 11.25 is 0.17. It is easy to calculate that the probability to get by chance 23 random consecutive measurements from the single-belled probability distribution depicted in Fig. 2 outside its central 10.55–11.25 year interval is just %, which is a very small probability. Thus, the solar cycle length does not appear to be just a random variable of a single-belled distribution.
This is just a logical fallacy. It may be unlikely to have no estimates (out of 23) in that particular range, but that range was only chosen because it contained no observed values. It’s much more likely to have no estimates in some range with equal total probability.
In fact Scafetta has failed to provide any evidence at all that solar cycle lengths don’t follow the plain old normal distribution. There is a very sensitive test for normality of the underlying distribution, known as the Shapiro-Wilk test. It gives a p-value of 0.67 — not even a hint that the distribution isn’t normal. This isn’t rocket surgery — it should be the first thing you do if you want to make claims about the distribution of a small sample of data. If you want to claim that a distribution is not normal, you should at least apply the most basic and powerful test! And if you can’t even muster evidence that the distribution isn’t normal, then you certainly have no evidence that it’s bimodal.
Scafetta’s argument about solar cycle lengths following a bimodal distribution is truly sloppy work. But that’s just the beginning. His entire paper would make a fine tutorial in how to “prove” a preconceived notion by abandoning any shred of real scientific skepticism. Unfortunately, that’s what we have to put up with from fake skeptics on a regular basis. They do this all the time — support nonsensical theories with shoddy, incorrect analysis.
I’m sick and tired of the amount of garbage that passes for science from fake skeptics. Frankly, it pisses me off that again and again, I have to understand their crappy theories better than they do. And it pisses me off that even though most of the readers of this blog will “get it” with ridiculous ease, the general public isn’t sufficiently math-savvy for me to persuade them of what’s bloody obvious to you.
Almost as much as it pisses me off that the “throw some garbage at the wall and see what sticks” strategy has so confounded the voting public that we’re playing Russian Roulette with the next generation’s supply of food and water.