Guest Post by Willis Eschenbach
Dr. Nir Shaviv and others strongly believe that there is an ~ 11-year solar signal visible in the sea level height data. I don’t think such a signal is visible. So I decided to look for it another way, one I’d not seen used before.
One of the more sensitive signal analysis tools in our arsenal is the Fourier transform. If we have a complex signal, like say the sunspot signal, Fourier analysis allows us to see just how strong the different frequencies are that make up the signal. To start with, Figure 1 shows the sunspot record.
As you can see, there is a clear cyclical signal. However, the cycles vary in length. A Fourier periodogram reveals the strength of the various underlying signals:
As you can see, most of the power is in the 11-year and nearby cycles. There is cycle strength out to twelve years or so. There is also a second smaller group of cycles with a period of ten years, of about half the strength of the 11-year cycle.
Now, if there is actually a solar cycle in the sea level height as Dr. Shaviv believes, then it should peak somewhere around 11 years. To look for such a cycle, I decided to look at the sea level records from the tidal stations of the world. These are available from the Permanent Service for the Mean Sea Level. For your convenience in investigating the question, I’ve collated them as an Excel worksheet here.
I like to have an absolute minimum of three cycles of data to use for my longest term analysis. So I started by selecting all of the tide station datasets that have sixty years or more of data, to allow me to look at cycles up to about twenty years. There were 199 such records. Here are some sample periodograms of four of these longest tide records.
Figure 3. Four periodograms of long-term tidal records. Shortest period shown is four months. The scale on the left is the range (maximum minus minimum) of the fitted cycle as a percentage of the range of the underlying tide data.
The largest period in the tidal records, as we might expect, is a one-year cycle. There is also a smaller cycle visible at half a year (six months). However, as you can see, there is no readily apparent strong 11-year cycle, although Swinoujscie (top right) has a small hint of an 11-year cycle … or it may be a random fluctuation.
Now, the averaging of tidal data has some large problems. The different locations have widely varying tidal amplitudes, so the large swings tend to swamp the averages. As a result, I decided to average the periodograms rather than averaging the data. Since all of the periodograms are expressed in scaled units as percentages of the range of their individual underlying datasets, they are directly comparable. And since the random variations would average out, I figured that averaging them should reveal even small signals. Figure 4 shows the 199-periodogram average:
Figure 4. Average of the periodograms of the 199 long-term tidal station records. Note that the error bars are not the error of the mean, which is much narrower. Instead, they reflect the spread of the underlying individual results.
As with the four individual periodograms, the average clearly shows the one-year and the six-month cycles. And as expected, the averaging of so much data allows us to see even very small cycles. I note, for example, a cycle of a bit more than three and a half years. I’ve noticed this same signal before in other natural datasets, and I’ve never discovered its origin.
There is also a similar-sized small peak visible at about six and a quarter years, also of unknown origin.
But the purported ~ 11-year solar-related cycle? Nowhere to be seen. Not a hint, not a twitch.
Conclusion? If there is any ~ 11-year signal in the sea level height, it is so small as to be lost in the noise.
That was a main problem that I had with Dr. Shaviv’s study. He stated that there appeared to be a cycle in the short satellite sea level height data, and he claimed it was a solar cycle … but for me that’s backwards. For me, the starting point for investigation has to be noticing some verified unexplained anomaly in the actual observational records. First we have to find something unusual, then we can speculate as to its causes and consequences. For example, just what is the odd 3+ year cycle in Figure 4? Now that we know that cycle is real, we can speculate and investigate its origins.
So for me, until there is evidence of an actual ~11 year cycle in the sea level height, any speculation as to the possible solar nature of said unobserved cycle is wildly premature.
And that’s the story of the missing ~ 11-year cycle.
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