The Danger Of Short Datasets

From Watts Up With That?

Guest Post by Willis Eschenbach

A couple of months ago, I came across another claim that the solar sunspot cycle affects weather down here at the earth’s surface, in particular, ocean temperatures in the El Nino region of the tropical Pacific Ocean.

The paper is called Evidence of solar 11-year cycle from Sea Surface Temperature (SST), by Mazza and Canuto, hereinafter MC2021. I wrote about it in my post “CEEMD Versus Joe Fourier”. In this post, I thought I’d expand my analysis a bit and clarify one of the reasons why the MC2021 claims are not true.

Now, folks who read my work may be aware that I started out as a true believer in the idea that sunspots affect surface weather. As a kid, I’d read about William Herschel’s 1801 claim that sunspots affected wheat prices in England. So I thought it would be very easy to find evidence that the variations in solar energy caused by sunspots actually changed surface weather.

But when I first went to actually look at the data, I found … nothing. So I kept looking. Since then I’ve looked at dozens and dozens of claimed correlations and found … nothing. Well, that’s not exactly true. I did find a scientific paper called “On The Insignificance Of Herschel’s Sunspot Correlation“, wherein the author looked for hard evidence to back up Herschel’s claim and found …


So, I was interested in the MC2021 paper. It says:

After having downloaded and analysed hundreds of temperature records of the earth surface, eventually, we found clear evidence for the sun’s 11-years cycle signature in some few cases, while for the vast majority of the others this wasn’t detectable, buried under other oscillations (seasonal or El-Nino related) or noise. We found that two conditions are the most favourable in finding the proper sun’s signature in temperature records: as a rule of thumbs:

Focus on the sea surface tropical temperatures, in the range 5°N – 5°S. This is not surprising, there solar rays transfer their energy to surface waters with less reflection or scattering and with an optimum incidence angle.

Forget anomalies or indices of whatever type; for our goals this is only data jamming.Look whenever possible to real sea surface temperatures (SST).

After careful analyses of the many temperature records of the whole earth surface temperature, as well as of selected regions, we identified two regions as the most affected by the 11-year solar cycle. Both of them refer to ocean equatorial regions, known to climatologist as El-Nino-3 and El-Nino-3-4.

Hmm, sez I … here’s their money graph showing the claimed relationship:

Figure 1. Figure 4 from MC2021, showing the relationship between sunspots and the cycles in the El Nino regions.

Hmmm, sez I … so I went to see if I could replicate their findings. Instead of just using the Nino4 and Nino34 indexes, I also used the Multivariate ENSO Index (MEI) and the Southern Oscillation Index (SOI). All of these are known to correlate in some strong manner with the El Nino/La Nina oscillation in the tropical Pacific. (I have not used the NINO3 Index as they did, because it does not correlate with the others.) Here’s that result, starting in 1979, which is the start of the MEI dataset.

Figure 2. A comparison of the underlying ~ 11-year cycles in the sunspots and the tropical Pacific Ocean. Cycles have been determined using Complete Empirical Ensemble Mode Decomposition.

Hmmm, sez I … one thing is for sure. The Nino4, Nino34, MEI, and SOI are all clearly different measures of the same underlying phenomenon. In each dataset, you can see the recent very long La Nina conditions at the right side of the graph, and the datasets agree well with each other throughout.

And all of them line up quite well with the sunspots, with a lag of a couple of years between the sunspots and the tropical ocean indexes.

So what’s not to like?

Well, what’s not to like is that the data is very short. My rule of thumb is that you can’t tell much with only three cycles of some phenomenon, and I’ve been fooled more than once by even five cycles. And here we have only four cycles.

Fortunately, although the MEI only goes back to 1979, the other three indices go back much further. Here are the full datasets, starting in 1870.

Figure 3. A comparison of the post-1870 underlying ~ 11-year cycles in the tropical Pacific Ocean. Cycles have been determined using Complete Empirical Ensemble Mode Decomposition.

Since there is reasonably good agreement between the timing of the cycles of the three datasets, let me use their average to represent the long-term conditions in the tropical Pacific, and compare that to the sunspot data.

Figure 4. A comparison of the post-1870 sunspots and the average underlying ~ 11-year cycles in the tropical Pacific Ocean. Cycles have been determined using Complete Empirical Ensemble Mode Decomposition.

I’m sure you can see the difficulty. Prior to about 1945, the ocean is way out of phase with the sunspots. And the further back you go, the greater the disagreement between the two datasets. In addition, the envelopes of the signals are very dissimilar. You’d expect that if the solar signal is strong, the temperature should be strong also … but that’s not the case at all.

You can see this via Fourier analysis as well. The more recent post-1960 part of the ENSO record has a clear 12-year cycle (not 11 but 12 years, blue line, right panel) … but when you look at the full dataset back to 1870 (red line, right panel), that cycle disappears down into the noise and changes to a 13-year cycle. Note that this doesn’t happen with the sunspot data (left panel). There, the 11-year cycle is always clearly above the noise and remains steady at 11 years.

Figure 5. Fourier periodograms of the full-length (red) and post-1960 sunspots (left panel), and Nino4 index(right panel).

Unfortunately for those of us studying climate science, we’re looking at a hugely complex system. The climate is composed of six major subsystems—the atmosphere, biosphere, hydrosphere, cryosphere, lithosphere, and electrosphere. Each of these subsystems has internal resonances and cycles occurring at a variety of timescales from milliseconds to millions of years. Not only that, but all the subsystems are exchanging energy on a variety of regular, intermittently regular, and random intervals on the same timescales. Finally, the system is fueled by a constantly varying source of energy.

Even the IPCC acknowledges that this system is totally chaotic, chaos that has existed for millions of years. And as a result, we often see what I call “pseudocycles”. These are cyclical variations in some given datasets. However, they are not true cycles—they appear without warning, last for some time, and then fade away and disappear, replaced by some other pseudocycles.

This problem is exacerbated by the fact that so many of our weather-related datasets are so short, often shorter than one human lifetime. The MSU dataset of the lower troposphere temperature is only 44 years of data, shorter than most lives. Same for the Multivariate Enso Index. Same for the post-1970 data used in the paper under discussion, MC2021.

And this intersection of short datasets and pseudocycles leads to lots of claims of cyclical behavior in surface temperature datasets, particularly regarding sunspots, where no true, unchanging cycles actually exist.

There’s a final problem. This has to do with the fact that natural weather datasets are often what’s called “autocorrelated”. This means that today’s temperature is often related to yesterday’s temperature, and this month’s temperature is often related to last month’s temperature.

The problem is that autocorrelated data often includes cycles … cycles that may or may not mean something. For example, here’s a random autocorrelated dataset, of a type called “Fractional Gaussian Noise” or “FGN”. As the name implies, it’s just noise, no meaningful signals. Note how closely it resembles say a natural temperature dataset.

Figure 6. An example of random fractional gaussian noise (FGN).

And here’s the CEEMD decomposition of that same FGN dataset. Remember, this is just noise, no actual signals present.

Figure 7. CEEMD analysis of an example of random fractional gaussian noise (FGN).

So … what are we looking at here? Well, the left panel shows the individual signals resulting from the decomposition of the FGN noise. As you can see, there are signals at a variety of frequencies, with a residual showing what’s left after all the regular signals are removed.

The right panel, on the other hand, shows “periodograms” of each of the signals in the left panel, with corresponding colors. The periodograms show what the strongest cycles are in the decomposed signals. As you can see, the strongest cycle is at 10 years, shown in green. You can see that signal on the left panel. Must be from sunspots! … oh, wait, it’s just random Gaussian noise …

However, the ten-year cycles are far from a regular signal. Both the amplitude and the cycle length are constantly changing, as can be seen in the green line of the left-hand panel. It’s also revealed by the smaller peaks in the green line on the right-hand panel.

That, dear friends, is what I have termed a “pseudocycle”. It’s “pseudo” because it is not an unchanging, persistent cycle. Instead, it’s just one of the many cycles that we find in all autocorrelated data, meaningless cycles that appear, change, and disappear.

Notice also that the FGN noise contains a persistent trend, the black line at the bottom right of the left panel. This is the result of the same thing, autocorrelation. As discussed in the AGU article “Nature’s Style: Naturally Trendy“, trends in natural datasets may mean just as little as the trend displayed by this FGN data.

And this is why in climate science folks must always, each and every time, adjust their statistical claims for autocorrelation … for example, without adjustment for autocorrelation, the statistics of the FGN signal shown above say the trend is very meaningful, with a p-value of <2e-16.

But once we adjust for autocorrelation and use the Bonferroni calculation to adjust for the fact that I looked at 5 FGN datasets to find that one, it turns out that it’s not statistically significant at all, with an autocorrelation and Bonferroni adjusted p-value of 0.075 … just random noise after all.

Climate science. Hidden potholes everywhere.

My best wishes to all,


The Usual Request: Quote the exact words you are discussing. I can defend my words. I can’t defend your (mis) understandings of my words. Thanks.

Further Readings: Most of my prior sunspot investigations …

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