Guest Post by Willis Eschenbach
In my last post on the purported existence of the elusive ~60-year cycle in sea levels as claimed in the recent paper “Is there a 60-year oscillation in global mean sea level?”, I used a tool called “periodicity analysis” (discussed here) to investigate cycles in the sea level. However, some people said I wasn’t using the right tool for the job. And since I didn’t find the elusive 60-year cycle, I figured they might be right about periodicity analysis. In the process, however I found a more sensitive tool, which is to just fit a sine wave to the tidal data at each cycle length and measure the peak-to-peak amplitude of the best-fit sine wave. I call this procedure “sinusoidal periodicity”, for a simple reason—I’m a self-taught mathematician, so I don’t know the right name for the procedure. I’m sure this analysis method is known, but since I made it up I don’t know what it’s actually called.
I like to start with a look at the rawest view of the data. In this case, here’s the long-term Stockholm tide gauge record itself, before any further analysis. This is the longest complete monthly tidal gauge record I know of, at 200 years.
Figure 1. Stockholm monthly average sea level. This is a relative sea level, measured against an arbitrary zero point.
As you can see, Stockholm is (geologically speaking) rapidly leaping upwards after the removal of the huge burden of ice and glaciers about 12,000 years ago. As a result, the relative sea level (ocean relative to the land) has been falling steadily for the last 200 years, at a surprisingly stable rate of about 4 mm per year.
In any case, here’s what the sinusoidal periodicity analysis looks like for the Stockholm tide data, both with and without the annual cycle:
Figure 1a. “Sinusoidal Periodicity” of the Stockholm tide gauge data, showing the peak-to-peak amplitude (in millimetres) of the best-fit sine wave at each period length. Upper panel shows the data including the annual variations. In all cases, the underlying dataset is linearly detrended before sinusoidal periodicity analysis. Note the different scales of the two panels.
Now, I could get fond of this kind of sinusoidal analysis. To begin with, it shares one advantage of periodicity analysis, which is that the result is linear in period, rather than linear with frequency as is the case with Fourier transforms and spectral analysis. This means that from monthly data you get results in monthly increments of cycle length. Next, it outperforms periodicity analysis in respect of the removal of the short-period signals. As you can see above, unlike with periodicity analysis, removing the annual signal does not affect the results for the longer-term cycles. The longer cycles are totally unchanged by the removal of the annual cycle. Finally, I very much like the fact that the results are in the same units as the input data, which in this case is millimetres. I can intuitively get a sense of a 150-mm (6 inch) annual swing in the Stockholm sea level as shown above, or a 40 mm (1.5 inch) swing at both ~5.5 and ~31 years.
Let me start with a few comments on the Stockholm results above. The first one is that there is no significant power in the ~ 11-year period of the sunspot cycle, or the 22-year Hale solar cycle, as many people have claimed. There is a small peak at 21 years, but it is weak. After removal of the annual cycle, the next strongest cycles peak at ~5.5, 31.75, and 15 years.
Next, there are clearly cycle lengths which have very little power, such as 19.5, 26.5, and 35 years.
Finally, in this record I don’t see much sign of the proverbial ~60 cycle. In this record, at least, there isn’t much power in any of the longer cycles.
My tentative conclusion from the sinusoidal analysis of the Stockholm tide record is that we are looking at the resonant frequencies (and non-resonant frequencies) of the horizontal movement of the ocean within its surrounding basin.
So let me go through all of the datasets that are 120 years long or longer, using this tool, to see what we find.
So lets move on to the other 22 long-term tidal datasets that I linked to in my last post. I chose 120 years because I’m forced to use shorter datasets than I like. Normally, I wouldn’t consider results from a period less than three times the length of the cycle in question to be significant. However, there’s very few datasets that long, so the next step down is to require at least 120 years of data to look for a 60-year cycle. Less than that and you’re just fooling yourself. So without further ado, here are the strengths of the sinusoidal cycles for the first eight of the 22 datasets …
Figure 2. Sinusoidal amplitude, first eight of the 22 long-term (>120 year) datasets in the PSMSL database. Note that the units are different in different panels.
The first thing that strikes me about these results? The incredible variety. A few examples. Brest has lots of power in the longer-term cycles, with a clear peak at ~65 years. Wismar 2, on the other hand, has very little power in the long-term cycles, but a clear cycle at ~ 28 years. San Francisco has a 55-year peak, but the strongest peak there is at 13 years. In New York, on the other hand, the ~51 year peak is the strongest cycle after the annual cycle. Cuxhaven 2 has a low spot between 55 and 65 years, as does Warnemunde 2, which goes to zero at about 56 years … go figure.
Confused yet? Here’s another eight …
Figure 3. Sinusoidal periodicity, second eight of the 22 long-term (>120 year) datasets in the PSMSL database. Note that the units are different in different panels.
Again the unifying theme is the lack of a unifying theme. Vlissingen and Ijmuiden bottom out around 50 years. Helsinki has almost no power in the longer cycles, but the shorter cycles are up to 60 mm in amplitude.. Vlissingen is the reverse. The shorter cycles are down around 15-20 mm, and the longer cycles are up to 60 mm in amplitude. And so on … here’s the final group of six:
Figure 4. Sinusoidal periodicity, final six of the 22 long-term (>120 year) datasets in the PSMSL database. Note that the units are different in different panels.
Still loads of differences. As I noted in my previous post, the only one of the datasets that showed a clear peak at ~55-years was Poti, and I find the same here. Marseilles, on the other hand, has power in the longer term, but without a clear peak. And the other four all bottom out somewhere between 50 and 70 years, no joy there.
In short, although I do think this method of analysis gives a better view, I still cannot find the elusive 60-year cycle. Here’s an overview of all 22 of the datasets, you tell me what you see:
Figure 5. Sinusoidal periodicity, all twenty-two of the long-term tide gauge datasets.
Now, I got started on this quest because of the statement in Abstract of the underlying study, viz:
We find that there is a significant oscillation with a period around 60-years in the majority of the tide gauges examined during the 20th Century …
(As an aside, waffle-words like “a period around 60-years” drive me spare. The period that they actually tested for was 55-years … so why not state that in the abstract? Whenever one of these good cycle-folk says “a period around” I know they are investigating the upper end of the stress-strain curve of veracity … but I digress.)
So they claim a 55-year cycle in “the majority of the tide gauges” … sorry, I’m still not seeing it. The Poti record in violet in Figure 5 is about the only tide gauge to show a significant 55-year peak.
On average (black line), for these tide gauge records, the strongest cycle is 6 years 4 months. There is another peak at 18 years 1 month. All of them have low spots at 12-14 years and at 24 years … and other than that, they have very little in common. In particular, there seems to be no common cycles longer than about thirty years or so.
So once again, I have to throw this out as an opportunity for those of you who think the authors were right and who believe that there IS a 55-year cycle “in the majority of the tide gauges”. Here’s your chance to prove me wrong, that’s the game of science. Note again that I’m not saying there is no 55-year signal in the tide data. I’m saying I’ve looked for it in a couple of different ways now, and gotten the same negative result.
I threw out this same opportunity in my last post on the subject … to date, nobody has shown such a cycle exists in the tide data. Oh, there are the usual number of people who also can’t find the signal, but who insist on telling me how smart they are and how stupid I am for not finding it. Despite that, so far, nobody has demonstrated the 55-year signal exists in a majority of the tide gauges.
So please, folks. Yes, I’m a self-taught scientist. And yes, I’ve never taken a class in signal analysis. I’ve only taken two college science classes in my life, Introductory Physics 101 and Introductory Chemistry 101. I freely admit I have little formal education.
But if you can’t find the 55-year signal either, then please don’t bother telling me how smart you are or listing all the mistakes you think I’m making. If you’re so smart, find the signal first. Then you can explain to me where I went wrong.
What’s next for me? Calculating the 95% CIs for the sinusoidal periodicity, including autocorrelation. And finding a way to calculate it faster, as usual optimization is slow, double optimization (phase and amplitude) is slower, and each analysis requires about a thousand such optimizations. It takes about 20 seconds on my machine, doable, but I’d like some faster method.
Best regards to each of you,
w.
As Always: Please quote the exact words that you disagree with, it avoids endless misunderstandings.
Also: Claims without substantiation get little traction here. Please provide links, citations, locations, observations and the like, it’s science after all. I’m tired of people popping up all breathless to tell us about something they read somewhere about what happened some unknown amount of time ago in some unspecified location … links and facts are your friend.
Data: All PSMSL stations in one large Excel file, All Tide Data.xlsx
Just the 22 longest stations as shown in Figs. 2-4 as a CSV text file, Tide Data 22 Longest.csv .
Stockholm data as an excel worksheet, eckman_2003_stockholm.xls
Code: The function I wrote to do the analysis is called “sinepower”, available here. If that link doesn’t work for you, try here. The function doesn’t call any external functions or packages … but it’s slow. There’s a worked example at the end of the file, after the function definition, that imports the 22-station CSV file. Suggestions welcome.
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Thanks. Fascinating. I’ve often wondered how the “60-year cycle” stands testing.
I get error (400) at dropbox… Thanks.
Edit on error (400) above: Copy the URL, paste it into address, backspace over the space, replace it with another space, and hit enter. The code came up as text.
Willis, I have to admit that I don’t follow exactly what you are doing, but the results make for interesting graphs, and evidently new insights.
So that leads me to ask two questions, neither of which is a criticism.
1) you say you are removing an annual cycle “for clarity”. OK so for just any one example, what does the resultant graph look like if you don’t do that; so we can see the fog fall away ??
2) on a similar vein, since my (now somewhat weak) brain thinks that a linear trend oughta morph into some recognizable “spectral” feature ; what if you just do your mastication on the raw data; what does it look like then. No; just a single example unless you can just dismiss the question on some logical ground that escapes me, at the moment.
Maybe you have found a transform that produces a universal null at 60 years, for any and all input data !!
I wonder why the post doc fellows aren’t doing what you are ?
G
Thanks, Willis. Good try, there is possibly nothing there like you were looking for.
Theory. There is a 60 year cycle.
Tested.
Results. Negative.
Paging dr feynman.
Of course some will come along and suggest different data different methods.
None will explain why a 60 year cycle should be found.
That is explain it with physics.
They might say. It has to because the sun.
One problem with tidal measurements is that it assumes the tidal gage at measuring point “X” is forever stable; i.e., is on land not subject to any rise or fall. What justifies accepting that assumption as true? As both are subject to change no read periodic it is possible.
Ah – But there IS – should I be more negative and say “DOES appear to be” – a recent 60 year cycle in the surface temperature record since 1820: today’s peak between 2015-1998, between 1945 – 1936, at 1880, etc. each superimposed on a longer 900 year cycle down from the Roman Optimum, down to the dark Ages, up from the dark Ages into the Medieval Warm Period, down again into the Little Ice Age and back up towards today’s Modern Warming Period.
Now, I cannot tell anybody what causes that short cycle – nor what other things “might” either co-relate to that cycle, might precede it, or lag after it, but the cycle itself certainly appears visible.
george e. smith says:
May 1, 2014 at 6:51 pm
Suppose we take a sine wave that is say exactly 40 years long. I adjust (“fit”) the phase and the amplitude of the signal until I get the very best fit between the sine wave and the data. I measure the amplitude (peak to peak) of that signal.
Then I do the same thing at every other length from two months to 70 years. The result is what is shown in the graphs above. They show the amplitude (total tidal range) at the various periods.
See Figure 1a which shows the same data before and after removing the annual cycle. The problem is that the annual cycle typically 5-10 times larger than any other cycle, so if we scale the graph to include that, it’s hard to see the details of the smaller, longer-term cycles.
Not sure what you mean by “a linear trend oughta morph into some recognizable “spectral” feature”, sorry.
Since none of the results I show above have a null at 60 years, and instead each one has a different value at 60 years, I don’t understand what you mean.
I sometimes wonder why I do what I do …
Regards,
w.
Steven Mosher says:
May 1, 2014 at 7:34 pm
Tell that to these guys:
Deser, Clara; Alexander, Michael A.; Xie, Shang-Ping; Phillips, Adam S. (January 2010). “Sea Surface Temperature Variability: Patterns and Mechanisms”. Annual Review of Marine Science 2 (1): 115–143.
And to the Pacific salmon fisheries guy who discovered the PDO, no thanks to your lying, trough-feeding, anti-scientific buddies in the pay of Big Government & the windmill & solar panel industries:
Mantua, Nathan J. et al. (1997). “A Pacific interdecadal climate oscillation with impacts on salmon production”. Bulletin of the American Meteorological Society 78 (6): 1069–1079.
Tom Asiseeitnow says:
May 1, 2014 at 7:38 pm
Thanks, Tom. Not sure what you mean. I talked in the head post about how the land under Stockholm is rising. I’m definitely assuming it’s subject to rise or fall, and in this case it’s rising.
That would certainly be true if the uplifting rate of the underlying land were greatly variable. But we’re talking about a 10,000 year adjustment to the loss of the unimaginable weight of the ice age glaciers . So as you can see from the Stockholm data in Figure 1, the uplifting is roughly linear. This definitely allows us to do real periodic analyses.
w.
you tell me whatyou see: Pretty colours. Always love your posts Willis.
My attempt to access the code was unsuccessful: “Error (400) Something went wrong. Don’t worry, your files are still safe and the Dropboxers have been notified.”
no uplift is not linear. Think earth quakes ….. starts and stops and sometimes you get a 8.5 magnitude and then sometimes a 2.1. Why should up lift be linear?
You can get the same result at equally spaced points in frequency by appending zeros to the detrended data and using the fft. Appending zeros is not going to change the sinusoidal optimization if you are doing least squares fits for the optimization. You probably want to plot the amplitude of the result, and the peak to peak will be that divided by the number of original data points. As the number of points increases, the band will be better resolved, so you can also estimate the sum across the band, but that requires divided by the total number of points, including zeros, before the sum. As you can see the total sum will remain approximately equal if you do that since the resolved band width is proportional to the total number of points.
I’ve left out some details. You would probably would want to apodize the data, and phase correct over the band if you use the sum. For this sort of thing, where you might be looking for the best fit with a fixed number of frequencies, maximum entropy or one of its relations might also be a candidate for the method. Not that I think there is much to be gained by these methods, but they will run faster.
” That would certainly be true if the uplifting rate of the underlying land were greatly variable. But we’re talking about a 10,000 year adjustment to the loss of the unimaginable weight of the ice age glaciers . So as you can see from the Stockholm data in Figure 1, the uplifting is roughly linear. This definitely allows us to do real periodic analyses.”sorry I didn’t quote what I disagreed with . Not that I exactly disagree but to my understanding , the earths tectonic processes don’t work in a linear fashion. Perhaps your averaging them out over ten thousand years might lend merit to your statement but then again the very nature of these processes would make them be much more random and nonlinear.
RACookPE1978 says:
May 1, 2014 at 7:46 pm
RA, could I ask you to restrict the issues to the question at hand, that of sea level cycles? There are a million questions about cycles, and we can’t answer them all in one thread.
I want to settle this one question at a time, and for this thread it’s the elusive ~60-year cycle in sea levels.
Thanks,
w.
Got point #1 thanks.
Other was a bit of a chain yank to keep you awake.
thanks.
g
milodonharlani says:
May 1, 2014 at 7:52 pm
Tell what to those guys? They wrote about sea surface temperature. Mosh was talking about ~ 60-year cycles in sea levels. What are you proposing that Mosh should tell them?
w.
Joe Born says:
May 1, 2014 at 8:05 pm
Fixed. Lately wordpress has added spaces at random to the end of my dropbox urls … go figure. Try it again, should work now.
w.
david says:
May 1, 2014 at 8:16 pm
Ummm … because uplift != earthquakes?
w.
Chuck says:
May 1, 2014 at 8:16 pm
Thanks, Chuck. As I mentioned above, I much prefer an analysis that is linear in period to one that is linear in frequency.
w.
Willis Eschenbach says:
May 1, 2014 at 8:57 pm
Thermal expansion from higher SST can’t help but translate into higher MSL, all other factors being equal, can it?
And the reverse for cooler SSTs.
IMO, if we could actually measure MSL changes precisely & accurately, the decadal fluctuations would be obvious. But we can’t, because MSL trend changes are so small.
PS: Even with the questionable data available, PDO contribution to 20-year MSL changes has been detected:
http://onlinelibrary.wiley.com/doi/10.1002/grl.50950/abstract
But then I might be biased, as a North Pacific salmon fisher of five decades’ standing, who has observed these changes personally.
Not really related, but when in remote Indonesia the locals often claim that ocean swells are higher with the full moon and full moon tides.
I know that in some places localised tidal currents greatly affect ocean swells in Lombok and Lembongan, because the tide acts with, or against, the incoming swells between islands, making the swells sizes change dramatically. These currents even affect the shape of the islands. I have seen ocean waves go from 6 inches to 6 feet in 1 hour with the incoming tide, and vice versa as the tide goes out, at Lembongan. I went out an sat in 6 inch waves with my surfboard and just waited because you could predict the swell change like a clock. Half an hour later the waves jumped. So the same could be true out in the deeper ocean.
Not sure if this is relevant to the discussion, but thought Id mention it, because if tidal cycles affect ocean swells, then perhaps ocean phases/temperatures couldn’t affect tidal cycles.