Guest Post by Willis Eschenbach
I was referred to a paywalled paper called “Is there a 60-year oscillation in global mean sea level?” The authors’ answer to the eponymous question is “yes”, in fact, their answer boils down to “dangbetcha fer sure yes there is a 60-year oscillation”, viz:
We examine long tide gauge records in every ocean basin to examine whether a quasi 60-year oscillation observed in global mean sea level (GMSL) reconstructions reflects a true global oscillation, or an artifact associated with a small number of gauges. 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, and that it appears in every ocean basin.
So, as is my wont, to investigate this claim I got data. I went to the PSMSL, the Permanent Service for the Mean Sea Level, and downloaded all their monthly tidal records, a total of 1413 individual records. Now, the authors of the 60-year oscillation paper said they looked at the “long-term tide records”. If we’re looking for a 60-year signal, my rule of thumb says that you need three times that, 180 years of data, to place any confidence in the results. Bad news … it turns out only two of the 1,413 tidal gauge records, Brest and Swinoujscie, have 180 years of data. So, we’ll need to look at shorter records, maybe a minimum of two times the 60-year cycle we’re looking for. It’s sketchy to use that short of a record, but “needs must when the devil drives”, as the saying goes. There are twenty-two tidal datasets with 120 years or more of data. Figure 1a shows the first eight of them:
Figure 1a. Tide gauge records with 1440 months (120 years) or more of records. These are all relative sea levels, meaning they are each set to an arbitrary baseline. Units are millimetres. Note that the scales are different, so the trends are not as uniform as they appear.
Now, there’s certainly no obvious 60-year cycles in those tidal records. But perhaps the subtleties are not visible at this scale. So the following figure shows the Gaussian averages of the same 8 tidal datasets. In order to reveal the underlying small changes in the average values, I have first detrended each of the datasets by removing any linear trend. So Figure 1b emphasizes any cycles regardless of size, and as a result you need to note the very different scales between the two figures 1a and 1b.
Figure 1b. Gaussian averages (14-year full-width half-maximum) of the linearly detrended eight tide gauge datasets shown in Figure 1a. Note the individual scales are different from Figure 1a.
Huh. Well, once the data is linearly detrended, we end up with all kinds of swings. The decadal swings are mostly on the order of 20-30 mm (one inch) peak to peak, although some are up to about twice that. The big problem is that the decadal swings don’t line up, they aren’t regular, and they don’t have any common shape. More to the current point, there certainly is no obvious 60-year cycle in any of those datasets.
Now, we can take a closer look at what underlying cycles are in each of those datasets by doing a periodicity analysis. (See the notes at the end for an explanation of periodicity analysis). It shows how much power there is in the various cycle lengths, in this case from two months to seventy years Figure 1c shows the periodicity analysis of the same eight long datasets. In each case, I’ve removed the seasonal (annual) variations in sea level before the periodicity analysis.
Figure 1c. Periodicity analysis, first eight long-term tidal datasets.
Boooring … not much of anything anywhere. Top left one, Brest, has hints of about a 38-year cycle. New York shows a slight peak at about 48 years. Other than that there is no energy in the longer-term cycles, from say 30 to 70 years.
So let’s look at the rest of the 22 datasets. Here are the next eight tide gauge records, in the same order—first the raw record, then the Gaussian average, and finally the periodicity analysis.
Figures 2a, 2b, and 2c. Raw data, Gaussian averages, and periodicity analysis, next 8 stations longer than 120 years.
No joy. Same problem. All kinds of cycles, but none are regular. The largest problem is the same as in the first eight datasets—the cycles are irregular, and in addition they don’t line up with each other. Other than a small peak in Vlissingen at about 45 years, there is very little power in any of the longer cycles. Onwards. Here are the last six of the twenty-two 120-year or longer datasets:
Figures 3a, 3b, and 3c. Data, Gaussian averages, and periodicity analysis as above, for the final six 120-year + tide gauge datasets.
Dang, falling relative sea levels in Figure 3a. Obviously, we’re looking at some tidal records from areas with “post-glacial rebound” (PGR), meaning the land is still uplifting after the removal of trillions of tons of ice at the end of the last ice age. As a result, the land is rising faster than the ocean …
How bizarre. I just realized that people worry about sea-level rise as a result of global warming, and here, we have land-level rise as a result of global warming … but I digress. The net result of the PGR in certain areas are the falling relative sea levels in four of the six datasets.
Like the other datasets, there are plenty of cycles of various kinds in these last six datasets in Figure 3, but as before, they don’t line up and they’re not regular. Only two of them have something in the way of power in the longer cycles. Marseille has a bit of power in the 40-year area. And dang, look at that … Poti, the top left dataset, actually has hints of a 60-year cycle … not much, but of the twenty-two datasets, that’s the only one with even a hint of power in the sixty-year range.
And that’s it. That’s all the datasets we have that are at least twice as long as the 60-year cycle we’re looking for. And we’ve seen basically no sign of any significant 60-year cycle.
Now, I suppose I could keep digging. However, all that are left are shorter datasets … and I’m sorry, but looking for a sixty-year cycle in a 90-year dataset just isn’t science on my planet. You can’t claim a cycle exists from only enough data to show one and a half swings of the cycle. That’s just wishful thinking. I don’t even like using just two cycles of data, I prefer three cycles, but two cycles is the best we’ve got.
Finally, you might ask, is it possible that if we average all of these 22 datasets together we might uncover the mystery 66-year cycle? Oh, man, I suppose so, I’d hoped you wouldn’t ask that. But looking at the mish-mash of those records shown above, would you believe it even if I found such a cycle? I don’t even like to think of it.
Ah, well, for my sins I’m a scientist, I am tormented by unanswered questions. I’d hoped to avoid it, so I’ve ignored it up until now, but hang on, let me do it. I plan to take the twenty-two long-term records, linearly detrend them, average them, and show the three graphs (raw data, Gaussian average, and periodicity analysis) as before. It’ll be a moment.
…
OK. Here we go. First the average of all of the detrended records, with the Gaussian average overlaid.
Figure 4a. Mean of the detrended long-term tidal records. Red line shows a 14-year full-width half-maximum (FWHM) Gaussian average of the data, as was used in the earlier Figures 1b, 2b, 3b.
Well, I’m not seeing anything in the way of a 60-year cycle in there. Here’s the periodicity analysis of the same 22-station mean data:
Figure 4b. Periodicity analysis of the data shown in Figure 4a immediately above.
Not much there at all. A very weak peak at about forty-five years that we saw in some of the individual records is the only long-term cycle I see in there at all.
Conclusions? Well, I don’t find the sixty-year cycle that they talk about, either in the individual or the mean data. In fact, I find very little in the way of any longer-term cycles at all in the tidal data. (Nor do I find cycles at around eleven years in step with the sunspots as some folks claim, although that’s a different question.) Remember that the authors said:
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 …
Not able to locate it, sorry. There are decadal swings of about 25 – 50 mm (an inch or two) in the individual tide gauge datasets. I suppose you could call that “significant oscillations in the majority of the tide gauges”, although it’s a bit of a stretch.
But the “significant oscillations” aren’t regular. Look at the Gaussian averages in the first three sets of figures. The “significant oscillations” are all over the map. To start with, even within each individual record the swings vary greatly in amplitude and cycle length. So the cycles in each individual record don’t even agree with themselves.
Nor do they agree with each other. The swings in the various tidal records don’t line up in time, nor do they agree in amplitude.
And more to the point, none of them contain any strong approximately sixty-year signal. Only one of the twenty-two (Poti, top left in Figure 3a,b,c) shows any power at all in the ~ 60 year region in the periodicity analysis.
So I’m saying I can’t find any sign in those twenty-two long tidal datasets of any such sixty-year cycle. Note that this is different from saying that no such cycle exists in the datasets. I’m saying that I’ve pulled each one of them apart and examined them individually as best I know how, and I’m unable to find the claimed “significant oscillation with a period around 60-years” in any of them.
So I’m tossing the question over to you. For your ease in analyzing the data, which I obtained from the PSMSL as 1413 individual text files, I’ve collated the 1413 record tide station data into a 13 Mb Excel worksheet, and the 22 long-term tidal records into a much smaller CSV file. I link to those files below, and I invite you to try your hand at demonstrating the existence of the putative 60-year cycle in the 22-station long-term tidal data.
Some folks don’t seem to like my use of periodicity analysis, so please, use Fourier analysis, wavelet analysis, spectrum analysis, or whatever type of analysis you prefer to see if you can establish the existence of the putative “significant” 60-year cycles in any of those long-term tidal datasets.
Regards to all, and best of luck with the search,
w.
The Standard Request: If you disagree with something someone says, please have the courtesy to quote the exact words you disagree with. It avoids all kinds of trouble when everyone is clear what you are objecting to.
Periodicity Analysis: See the post “Solar Periodicity” and the included citations at the end of that post for a discussion of periodicity analysis, including an IEEE Transactions paper containing a full mathematical derivation of the process.
Data: I’ve taken all of the PSMSL data from the 1413 tidal stations and collated it into a single 13.3 Mb Excel worksheet here. However, for those who would like a more manageable spreadsheet, the 22 long-term datasets are here as a 325 kb comma-separated value (CSV) file.
[UPDATE] An alert commenter spots the following:
Jan Kjetil Andersen says:
April 26, 2014 at 2:38 pm
Thanks much for that, Jan. I just took a look at the paper. They are using annually averaged data … a very curious choice. Why would you use annual data when the underlying PSMSL dataset is monthly?
In any case, the problem with their analysis is that you can fit a sinusoidal curve to any period length in the tidal dataset and get a non-zero answer. As a result, their method (fit a 55 year sine wave to the data) is meaninglesswithout something with which to compare the results.
A bit of investigation, for example, gives the following result. I’ve used their method, of fitting a sinusoidal cycle to the data. Here are the results for Cascais, record #43. In their paper they give the amplitude (peak to peak as it turns out) of the fitted sine curve as being 22.3. I get an answer close to this, which likely comes from a slight difference in the optimization program.
First, let me show you the data they are using:
If anyone thinks they can extract an “~ 60 year” cycle from that, I fear for their sanity …
Not only that, but after all of their waffling on about an “approximately sixty year cycle”, they actually analyze for a 55-year cycle. Isn’t that false advertising?
Next, here are the results from their sine wave type of analysis analysis for the periods from 20 to 80 years. The following graph shows the P-P amplitude of the fitted sine wave at each period.
So yes, there is indeed a sinusoidal cycle of about the size they refer to at 55 years … but it is no different from the periods on either side of it. As such, it is meaningless.
The real problem is that when the cycle length gets that long compared to the data, the answers get very, very vague … they have less than a hundred years of data and they are looking for a 55-year cycle. Pitiful, in my opinion, not to mention impossible.
In any case, this analysis shows that their method (fit a 55-year sine wave to the data and report the amplitude) is absolutely useless because it doesn’t tell us anything about the relative strength of the cycles.
Which, of course, explains why they think they’ve found such a cycle … their method is nonsense.
Eternal thanks to Jan for finding the original document, turns out it is worse than I thought.
w.