Guest Post by Willis Eschenbach
In a comment on a recent post, I was pointed to a study making the following surprising claim:
Here, we analyze the stream flow of one of the largest rivers in the world, the Parana ́ in southeastern South America. For the last century, we find a strong correlation with the sunspot number, in multidecadal time scales, and with larger solar activity corresponding to larger stream flow. The correlation coefficient is r = 0.78, significant to a 99% level.
I’ve seen the Parana River … where I was, it was too thick to drink and too thin to plow. So this was interesting to me. Particularly interesting because in climate science a correlation of 0.78 combined with a 99% significance level (p-value of 0.01) would be a very strong result … in fact, to me that seemed like a very suspiciously strong result. After all, here is their raw data used for the comparison:
They are claiming a 0.78 correlation between the data in panel (a) and the data in panel (b) … I looked at Figure 1 and went “Say what?”. Call me crazy, but do you see any kind of strong 11-year cycle in the top panel? Because I sure don’t. In addition, when the long-term average of sunspots rises, I don’t see the streamflow rising. If there is a correlation between sunspots and streamflow, why doesn’t a several-decade period of increased sunspots lead to increased streamflow?
So how did they get the apparent correlation? Well, therein lies a tale … because Figure 2 shows what they ended up analyzing.
And wow, that sure looks like a very, very strong correlation … so how did they get there from such an unpromising start?
Well, first they took the actual data. Then, from the actual data they subtracted the “secular trends” (see dark smooth lines Figure 1). The effect of this first one of their processing steps is curious.
Look back at Figure 1. IF streamflow and sunspots were correlated, we’d expect them to move in parallel in the long term as well as the short term. But inconveniently for their theory … they don’t move in parallel. How to resolve it? Well, since the long-term secular trend data doesn’t support their hypothesis, their solution was to simply subtract that bad-mannered part out from the data.
I’m sure you can see the problems with that procedure. But we’ll let that go, the damage is fairly minor, and look at the next step, where the real destruction is done.
They say in Figure 2 that the sunspot data was “smoothed by an 11-yr running mean to smooth out the solar cycle”. However, it is apparent that the authors didn’t realize the effect of what they were doing. Calling what they did “smoothing” is a huge stretch. Figure 3 shows the residual sunspot anomaly (in blue) after removing the secular trend (as the authors did in the paper), along with the 11-year moving average of that exact same data (in red). Again as the authors did, I’ve normalized the two to allow for direct comparison:
Figure 3. Sunspot anomaly data (blue line), compared to the eleven-year centered moving average of the sunspot anomaly data (red line). Both datasets have been normalized to a mean of zero and a standard deviation of one.
Talk about a smoothing horror show, that has to be the poster child for bad smoothing. For starters, look at what the “smoothing” does to the sunspot data from 1975 to 2000 … instead of having two peaks at the tops of the two sunspot cycles (blue line, 1980 and 1991), the “smoothed” red line shows one large central peak, and two side lobes. Not only that, but the central low spot around 1986 has now been magically converted into a peak.
Now look at what the smoothing has done to the 1958 peak in sunspot numbers … it’s now twice as wide, and it has two peaks instead of one. Not only that, but the larger of the two peaks occurs where the sunspots actually bottomed out around 1954 … YIKES!
Finally, I knew this was going to be ugly, but I didn’t realize how ugly. The most surprising part to me is that their “smoothed” version of the data is actually negatively correlated to the data itself … astounding.
Part of the problem is the use of a running mean to smooth the data … a Very Bad Idea™ in itself. However, in this case it is exacerbated by the choice of the length of the average, 11 years. Sunspot cycles range from something like nine to thirteen years or so. As a result, cycles longer and shorter than the 11 year filter get averaged very differently. The net result is that we end up with some of the frequency data aliased into the average as amplitude data … resulting in the very different results from about 1945-60 versus the results 1975-2000.
Overall? I don’t care what they end up comparing to the red line … they are not comparing it to sunspots, not in any way, shape, or form. The blue line shows sunspots. The red line shows a mathematician’s nightmare.
How about the fact that they performed the same procedure on the Parana streamflow data? Does that make a difference? Figure 4 shows that result:
Figure 4. Parana streamflow anomaly data (blue line), compared to the eleven-year centered moving average of the streamflow anomaly data (red line). Both datasets have been normalized to a mean of zero and a standard deviation of 1.
As you can see, the damage done by the running mean is nowhere near as severe in this streamflow dataset as it was for the sunspots. Although there still are a lot of reversals, and turning peaks into valleys, at least the correlation is still positive. This is because the streamflow data does NOT contain the ± eleven-year cycles present in the sunspot data.
Conclusions? Well, my first conclusion is that as a result of doing what the authors did, comparing the red line in Figure 3 with the red line in Figure 4 says absolutely nothing about whether the Parana river streamflow is related to sunspots or not. The two red lines have very little to do with anything.
My second conclusion is, NEVER RUN STATISTICAL ANALYSES ON SMOOTHED DATA. I don’t care if you use gaussian smoothing or Fourier smoothing or boxcar smoothing or loess smoothing, if you want to do statistical analyses, you need to compare the datasets themselves, full stop. Statistically analyzing a smoothed dataset is a mug’s game. The problem is that as in this case, the smoothing can actually introduce totally false, spurious correlations. There’s an old post of mine on spurious correlation and Gaussian smoothing here for those interested in an example.
Please be clear that I’m not accusing the authors of any bad intent in this matter. To me, the problem is simply that they didn’t understand and were unaware of the effect of their “smoothing” on the data.
Finally, consider how many rivers there are in the world. You can be assured that people have looked at many of them to find a connection with sunspots. If this is the best evidence, it’s no evidence at all. And with that many rivers examined, a p-value of 0.05 is now far too generous. The more places you look, the more chance of finding a spurious correlation. This means that the more rivers you look at, the stronger your results must be to be statically significant … and we don’t yet have even passable results from the Parana data. So as to rivers and sunspots, the jury is still out.
How about for sea level and sunspots? Are they related? I can’t do better than to direct you to the 1985 study by Woodworth et al. entitled A world-wide search for the 11-yr solar cycle in mean sea-level records , whose abstract says:
Tide gauge records from throughout the world have been examined for evidence of the 11-yr solar cycle in mean sea-level (MSL). In Europe an amplitude of 10-15 mm is observed with a phase relative to the sunspot cycle similar to that expected as a response to forcing from previously reported solar cycles in sea-level air pressure and winds. At the highest European latitudes the MSL solar cycle is in antiphase to the sunspot cycle while at mid-latitudes it changes to being approximately in phase. Elsewhere in the world there is no convincing evidence for an 11-yr component in MSL records.
So … of the 28 geographical locations examined, only four show a statistically significant signal. Some places it’s acting the way that we’d expect … other places its not. Nowhere is it strong.
I haven’t bothered to go through their math, except for their significance calculations. They appear to be correct, including the adjustment to the required significance given the fact that they’ve looked in 28 places, which means that the significance threshold has to be adjusted. Good on them 1980s scientists, they did the numbers right back then.
However, and it is a very big however, as is common with such analyses from the 1980s, I see no sign that the results have been adjusted for autocorrelation. Given that both the sunspot data and the sea level data are highly autocorrelated, this can only move the results in the direction of less statistical significance … meaning, of course, that the four results that were significant are likely not to remain so once the results are adjusted for autocorrelation.
Is there a sunspot effect on the climate? Maybe so, maybe no … but given the number of hours people have spent looking for it, including myself and many, many others, if it is there, it’s likely very weak.
My best regards to all,
NOTA BENE! If you disagree with something I said, please quote my exact words, and then tell me why you think I’m wrong. Telling me things like that my science sucks or baldly stating that I don’t understand the math doesn’t help me in the slightest. If I’m wrong I want to know it, but I have no use for claims like “Willis, you are so off-base in this case that you’re not even wrong.” Perhaps I am, but we’ll never know unless you specify exactly what I said that was wrong, and what was wrong with it.
So if you want me to treat you and your comments with respect, quote what you object to, and specify your objection. It’s the only way I can know what the heck you are talking about, and I’ve had it up to here with vague unsupported accusations of wrongdoing.
DATA: Digitized Parana streamflow data from the paper plus SIDC Sunspot data and all analyses for this post are on an Excel spreadsheet here. You’ll have to break the links, they are to my formula for Gaussian smoothing.
PS—Thanks to my undersea contacts for coming up with a copy of the thirty-year-old Woodworth study, and a hat tip to Dr. Holgate and Steve McIntyre at Climate Audit for the lead to the study. Dr. Holgate is well-known in sea level circles, here’s his comment on the sunspot question:
Many people have tried to link climate variations to sunspot cycles. My own feeling is that they both happen to exhibit variability on the same timescales without being causal. No one has yet shown a mechanism you understand. There is also no trend in the sunspot cycle so that can’t explain the overall rise in sea levels even if it could explain the variability. If someone can come up with a mechanism then I’d be open to that possibility but at present it doesn’t look likely to me.
If you’re interested in solar cycles and sea level, you might look at a paper written by my boss a few years back: Woodworth, P.L. “A world-wide search for the 11-yr solar cycle in mean sea-level records.” Geophysical Journal of the Royal Astronomical Society. 80(3) pp743-755
You’ll appreciate that this is a well-trodden path. My own feeling is that it’s not the determining factor in sea level rise, or even accounts for the trend, but there may be something in the variability. I’m just surprised that if there is, it hasn’t been clearly shown yet.
I can only agree …