Guest Post by Willis Eschenbach
Figure 1 shows their reconstructed decadal averages of sunspot numbers for the last three thousand years, from their paper:
Their claim is that when the decadal average sunspot numbers are less than 21, this is a distinct “mode” of solar activity … and that when the decadal average sunspot numbers are greater than 67, that is also a separate “mode” of solar activity.
Now, being a suspicious fellow myself, I figured I’d take a look at their numbers … along with the decadal averages of Hoyt and Schatten. That data is available here.
I got my first surprise when I plotted up their results …
Figure 2 shows their results, using their data.
The surprising part to me was the claim by Usoskin et al. that in the decade centered on 1445, there were minus three (-3) sunspots on average … and there might have been as few as minus ten sunspots. Like I said, Usoskin et al. seem to have discovered the sunspot equivalent of antimatter, the “anti-sunspot” … however, they must have wanted to hide their light under a bushel, as they’ve conveniently excluded the anti-sunspots from what they show in Figure 1 …
The next surprise involved why they chose the numbers 21 and 67 for the breaks between the claimed solar “modes”. Here’s the basis on which they’ve done it.
Figure 3. The histogram of their reconstructed sunspot numbers. ORIGINAL CAPTION: Fig. 3. A) Probability density function (PDF) of the reconstructed decadal sunspot numbers as derived from the same 106 series as in Fig. 2 (gray-filled curve). The blue curve shows the best-fit bi-Gaussian curve (individual Gaussians with mean/σ being 44/23 and 12.5/18 are shown as dashed blue curves). Also shown in red is the PDF of the historically observed decadal group sunspot numbers (Hoyt & Schatten 1998) (using bins of width ΔS = 10).
The caption to their Figure 3 also says:
Vertical dashed lines indicate an approximate separation of the three modes and correspond to ±1σ from the main peak, viz. S = 21 and 67.
Now, any histogram has the “main peak” at the value of the “mode”, which is the most common value of the data. Their Figure 3 shows the a mode of 44, and a standard deviation “sigma” of 23. Unfortunately, their data shows nothing of the sort. Their data has a mode of 47, and a standard deviation of 16.8, call it 17. That means that if we go one sigma on either side of the mode, as they have done, we get 30 for the low threshold, more than they did … and we get 64 for the high threshold, not 67 as they claim.
So that was the second surprise. I couldn’t come close to reproducing their calculations. But that wouldn’t have mattered, because I must admit that I truly don’t understand the logic of using a threshold of a one-sigma variation above and below not the mean, not the median, but the mode of the data … that one makes no sense at all.
Next, in the right part of Figure 1 they show a squashed-up tiny version of their comparison of their results with the results of Hoyt and Schatten … the Hoyt-Schatten data has its own problems, but let’s at least take a look at the difference between the two. Figure 4 shows the two datasets during the period of overlap, 1615-1945:
Don’t know about you, but I find that result pretty pathetic. In a number of decades, the difference between the two approaches 100% … and the results don’t get better as they get more modern as you’d expect. Instead, at the recent end the Hoyt-Schatten data, which at that point is based on good observations, shows about twice the number of sunspots shown by the Usoskin reconstruction. Like I said … not good.
Finally, and most importantly, I suspect that at least some of what we see in Figure 3 above is simply a spurious interference pattern between the length of the sunspot cycles (9 to 13 years) and their averaging period of ten years. Hang on, let me see if my suspicions are true …
OK, back again. I was right, here are the results. What I’ve done is picked a typical 12-year sunspot cycle from the Hoyt-Schatten data. Then I replicated it over and over starting in 1600. So I have perfectly cyclical data, with an average value of 42.
But once we do the decadal averaging? … well, Figure 5 shows that result:
Note the decadal averages of the upper panel data, which are shown in red in the lower panel … bearing in mind that the underlying data are perfectly cyclical, you can see that none of the variations in the decadal averages are real. Instead, the sixty-year swings in the red line are entirely spurious cycles that do not exist in the data, but are generated solely by the fact that the 10-year average is close to the 12-year sunspot cycle … and the Usoskin analysis is based entirely on such decadal averages.
But wait … it gets worse. Sunspot cycles vary in length, so the error caused by the decadal averaging will not be constant (and thus removable) as in the analysis above. Instead, decadal averaging will lead to a wildly varying spurious signal, which will not be regular as in Figure 5 … but which will be just as bogus.
In particular, using a histogram on such decadally averaged data will lead to very incorrect conclusions. For example, in the pseudo-sunspot data above, here is the histogram of the decadal averages shown in red.
Hmmm … Figure 6 shows a peak on the right, with secondary smaller peak on the left … does this remind you of Figure 3? Shall we now declare, as Usoskin et al. did, and with equal justification, that the pseudo-sunspot data has two “modes”?
In no particular order …
1. The Usoskin et al. reconstruction gives us a new class of sunspots, the famous “anti-spots”. Like the square root of minus one, these are hard to observe in the wild … but Usoskin et al. have managed to do it.
2. Despite their claims, the correlation of their proxy-based results with observations is not very good, and is particularly bad in recent times. Their proxies often give results that are in error by ~ 100%, but not always in the same direction. Sometimes they are twice the observations … sometimes they are half the observations. Not impressive at all.
3. They have set their thresholds based on a bizarre combination of the mode and the standard deviation, a procedure I’ve never seen used.
4. They provided no justification for these thresholds other than their histogram, and in fact, you could do the same with any dataset and declare (with as little justification) that it has “modes”.
5. As I’ve shown above, the shape of the histogram (which is the basis of all of their claims) is highly influenced by the interaction between the length(s) of the sunspot cycle and the decadal averaging.
As a result of all of those problems, I’m sorry to say that their claims about the sun having “modes” simply do not stand up to close examination. They may be correct, anything’s possible … but their analysis doesn’t even come near to establishing that claim of distinct solar “modes”.
Regards to all,
THE USUAL: If you disagree with me or someone else, please quote the exact words that you disagree with. That way, we can all understand just what it is that you object to.