Guest post by Willis Eschenbach

In my last post, The Sun Also Sets, I looked at a study that I’ll continue to call L2021. It claimed a correlation between what they called a “termination” in each sunspot cycle on the one hand, and on the other hand, El Nino/La Nina alterations as shown by the Oceanic Nino Index. Although their claim seemed at least possible, I didn’t think they’d shown it to be valid.

I wanted more data to see what I could find out. We have plenty of sunspot data. But I didn’t have access to any more of their “termination” dates. So I looked at their “terminations”, and they occurred at an average of 15% of the way through the sunspot cycle. Not only that, but the error using 15% was never more than a little over half a year. So I took 15% of the way into the complete sunspot cycle as a good approximation of the time of their “termination”.

Next, I needed more El Nino data. I compared the much longer NINO34 El Nino Index with the Oceanic Nino Index that they’d used, and found extremely good agreement. Here’s the comparison.

Figure 1. Comparison of the ONI and the NINO34 indices of El Nino during the period of their overlap, 1950 to 2020.

In practical terms for what I wanted to do, there’s no difference between the two. This was very good news, since the NINO34 index goes back to 1870.

So here was my plan of attack. I’d standardize all of the 13 sunspot cycles that have occurred since 1870 by adjusting them to be the same length as the average cycle over that period, which is 10.85 years. Then I’d stack them all up and average them.

Then I’d take the NINO34 data for the exact same time periods, set them all to 10.85 years like the sunspots, and average them.

This should show if there is any actual correlation between sunspot cycles (or their “terminations” as described in L2021) and El Ninos. Figure 2 below shows the result, with sunspots in red, NINO34 Index in yellow, and the uncertainty in the NINO34 average in gray.

Figure 2. “Stacked” averages of sunspots and NINO34 El Nino index, all for identical time spans.

Now, this is both interesting and frustrating. It’s frustrating because of the wide size of the gray area that’s showing the uncertainty in the NINO34 averages. The problem is that when the confidence intervals of two values overlap, we can’t say that two are statistically different. And they overlap everywhere. No bueno. Just as in their study, this means we can’t draw any firm conclusions from this analysis.

However, it’s interesting in that there’s indeed a drop in the NINO34 average at the approximate time of the L2021 “termination”. And it’s more interesting that there is an equally large drop in the NINO34 average about 8 years into the average sunspot cycle … which is far from their termination. IF they are real and not an artifact of the short length of the records (only 13 cycles), they most probably are from different causes. Curious.

Finally, it’s interesting in that the gray area showing the uncertainty at about the four or five-year mark is only about half as wide as it is earlier and later in the cycle … again, this may or may not be an artifact of the short data length. I can see no obvious reason for this.

One last analysis. I use a method called Complete Ensemble Empirical Mode Decomposition to reveal the underlying cycles in any time-varying signal. There’s more information about the method here.

So I looked at the CEEMD analysis of both the sunspot data and the NINO34 data. These used the raw underlying data from 1870 to 2020, not the standardized 1970-2020 data in equal-length cycles used in Figure 2 above. Here is that result.

Figure 3. CEEMD analysis, sunspots (black) and NINO34 El Nino Index (red), 1870-2020

Now, the lengths of the sunspot cycles in that time period ranged from 10 years to 12 years 4 months … and looking closely you can see those cycles, along with the CEEMD showing the average of 10.8 years.

But the NINO34 Index data contains nothing of any strength at those lengths.

Here’s another view, this time of just the cycles of Empirical Mode C3 for each of the two datasets.

Figure 4. Underlying cycles that fall into CEEMD Empirical Mode 3 for the sunspot (red) and NINO34 El Nino Index (yellow).

Call me crazy, but I see very little in the NINO34 data (yellow) in the way of regular cycles related to the sunspots … it’s all over the map and it goes into and out of phase with the sunspots.

And that’s about as far as I can take their hypothesis about the “termination” times of sunspot cycles affecting the El Nino … with the small amount of data available there’s nothing certain, but I’m still not seeing it.

My best regards to all, skeptics and others equally,

w.

via Watts Up With That?

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April 7, 2021 at 12:19PM