Guest Post by Willis Eschenbach
[UPDATE] In the comments, Nick Stokes pointed out that although I thought that Dr. Shaviv’s harmonic solar component was a 12.6 year sine wave with a standard deviation of 1.7 centimetres, it is actually a 12.6 year sine wave with a standard deviation of 1.7 millimetres (5 mm peak to peak) … I got 1.7 cm into my head and never questioned it because mm seemed way too small … but there it is. My thanks to Nick for pointing out my error.
So … in answer to the question, is a sine wave with a standard deviation of just under 2 mm detectable by Fourier analysis of the tidal station data … the answer is no. I’ve struck out the incorrect conclusions below.
I got to thinking about whether the Fourier analysis I used in my most recent post was sensitive enough to reveal the putative “harmonic solar component” which Dr. Shaviv claims to have measured. He said that he’d found a sine wave signal with a standard deviation of 1.7
cm mm in the satellite sea level record. So I added a solar signal with a standard deviation of 1.7 cm to the same 199 long-term climate records. [Ten times the size of Dr. Shaviv’s signal.] Note that unlike Dr. Shaviv’s so-called “harmonic solar component”, which was actually just a sine wave, I have used the actual sunspot record, and I scaled it to give it the same standard deviation (signal strength) as Dr. Shaviv’s sine wave. Figure 1 shows the “before” graph of the 199 tide station records from my last post.
Figure 1 shows the actual tide station data. Notice that there is no signal at around 11 years. And here’s what it looks like with an added solar (sunspot) signal with a standard deviation of 1.7 cm, a mere 3/4 of an inch, the size of Dr. Shaviv’s claimed signal.
Figure 2. Average of the periodograms of all tidal stations with records longer than 60 years, to each of which have been added a copy of the sunspot signal scaled to a standard deviation of 1.7 cm. This gives a signal (sunspot data) to noise (tidal data) ratio of one part signal, seven parts noise.
So in answer to the question, can my method detect a signal of the strength claimed by Dr. Shaviv mixed into the maelstrom of the individual tide station records, the answer is clearly yes, no problem. It is quite visible.
Ah, but Willis, I hear you say … surely all of these tide stations wouldn’t be affected by the solar changes at the same time. And that is true, there might be lags that differ on the order of months, seasons, or perhaps even years between the forcing change and the response in a given location. But that is the beauty of my method of averaging the periodograms. The periodogram finds the signal regardless of the phase. The phase of the signal doesn’t matter in the slightest—if the signal is there, the Fourier analysis will reveal it. As a result, the lag at any individual tidal station is immaterial.
Let’t push it further. Let’s see if we can do twice as well, say a signal to noise ratio of one part signal to fifteen parts of tidal noise. That would mean a tiny signal with a standard deviation of 0.8 cm … bear in mind what I’m doing. I’m adding a tiny duplicate of the solar signal to the monthly tide data, with a standard deviation of only eight freakin’ millimetres, less than half an inch. None of the tidal records cover exactly the same time span, and many have gaps. So each record gets a different chunk of the sunspot data. So the question is … can the periodogram find a solar signal at fifteen parts noise to one part signal?
OK, here’s that graph.
Yes, I can still see the signal. It’s clearest at the lower edge of the black error bar lines behind the gold graph line. But I’d say we’ve reached the detection limit for this size of signal in this size of dataset … one part signal to 15 parts noise, a detectability limit of a signal strength of 0.8 cm. Not bad.
Conclusions? Well, I’d say that if there is a solar signal in the sea levels, it is vanishingly small.
And I’d also say that Dr. Shaviv’s claimed signal with a 1.7 cm standard deviation is large enough to be found if it actually existed … see Figure 1 and 2 to decide if you think it exists.
And finally, I hope that this puts an end to the claim that Fourier analysis can’t find solar signals because they have different periods from nine to thirteen years. It not only can do so, it can do so in the face of stacks of noise and with the solar data covering different periods and often broken by gaps in individual tide station records. Consider that some of the records look like this …
Figure 4. Detrended monthly tidal data, Sheerness.
Despite the gaps, we can find a signal with a standard deviation of 8 mm in the midst of tidal data like that if we have enough tide stations … not bad.
Regards to all,
For Clarity: If you disagree with someone, please quote the exact words that you disagree with. That way we can all understand what you are objecting to.