The Elusive ~ 60-year Sea Level Cycle

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,

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

By Googling the title I found the article free on the internet here:

http://www.nc-20.com/pdf/2012GL052885.pdf

I don’t find it any convincing at all. They use the shorter series in the PSMSL sets, and claim to see 64 years oscillations even though the series are only 110 years long.

The article has no Fourier or periodicity analysis of the series.

/Jan

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.

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Greg

April 30, 2014 2:49 pm

Bart : “Yes, it is very clear that the approximately 10, 10.8, 11.8, and 134 year components evident in the SSN data are coming from rectification of processes centered at approximately 20 and 23.6 years.”
Could you elaborate ? Link ?
thx

Latitude

April 30, 2014 2:53 pm

Don’t want to interrupt….just thank you guys for giving us/me an incredible education

1sky1

April 30, 2014 6:46 pm

Willis:
There you go ad hominem again, with your put or shut up meme! Meanwhile, you
remain clueless as to what’s involved in analyzing tidal data for major
constituents. You need HOURLY data for at least a month for LS analysis
(see http://drs.nio.org/drs/bitstream/2264/59/4/Mahasagar_24_1.pdf). And
for a fuller set of tidal constituents, in accordance with Doodson’s
time-honored method, you need at least a year’s worth of hourly data. (see ftp://canuck.seos.uvic.ca/docs/MFTides/heights.pdf)
Nor is your comprehension any better about analyzing MONTHLY sea-level data,
which is a can of worms with all sorts of factors (eustatic and steric
variations, wind set-up, rainfall runoff, etc.) affecting the record even
in geologically stable locations. As your LS fitting of pure sinusoids
to the Cascais record shows, you fail to realize that it’s the presence of a
strong trend that produces your rising values as period increases. And, of
course, the well-established Rayleigh criterion for resolving sinusoids in
a record of finite length remains terra icognita for you. (It specifies
that two sinusoids can be resolved when the spectral peak of one
sinusoidal component falls on the first null of the second frequency in the
record-length dependent spectral window)
As disappointing as the Chambers et al. paper turned out to be (with it’s
simplistic bias + trend + sinusoid conception), at least they had sense
enough to remove the trend in their analysis and use the mean of
the best-fit period to the GMSL. And little is gained by removing the
annual cycle by monthly anomalization, as you do, rather than by their yearly averaging when looking for multidecadal oscillations, which no experienced geophycist would expect to be periodic.

Bart

April 30, 2014 7:27 pm

Greg says:
April 30, 2014 at 2:49 pm
See here.

HenryP

April 30, 2014 9:16 pm

Steven Mosher says
Instead of cheery picking 10 stations, use them all
http://berkeleyearth.lbl.gov/regions/alaska
Henry says
FCirst, I don’t do “cheery” picking
I selected 10 stations, randomly, inland.
I was not interested in looking @sea, now, and I am not interested in results before 1998
(your Berkeley seems to report only from 1990).
If you had followed the whole thread you would know why.
but here is a good method to get a global representative sample:
http://wattsupwiththat.com/2014/04/25/the-elusive-60-year-sea-level-cycle/#comment-1622942
Clearly the Berkeley global data set lacks that balancing,as it reports a (global) warming rate of almost double that of other global data sets, including my own, from 1990.
Otherwise, why don’t you do an anlysis of all the data available from the Elmendorff Army base in Anchorage. It has data from 1942, If you analyse the maximum temperature record there and look at the average change in K/annum from 1972-2014 and from 1942-1972 you should get a part of an a-c wave that looks like the second graph shown here:
http://blogs.24.com/henryp/2012/10/02/best-sine-wave-fit-for-the-drop-in-global-maximum-temperatures/
Clearly there is still some serious cooling coming up in Alaska, Note the difference in the sine wave from Anchorage and the global a-c wave.

HenryP

April 30, 2014 9:53 pm

@steven mosher
I am interested in seeing that calibration record? That must be of a new thermometer? I was talking about re-calibration.
As to error, I have deliberately chosen to look only at the average change from the average over periods of time, i.e. linear regression, in K/annum, which excludes a lot of error, especially calibration and differences between stations. Also, in older records, I trust maximum and minimum temps. more than means as the latter required presence of people and physical work, taking readings during the day.

Steven Mosher

April 30, 2014 11:33 pm

Henry.
Ur method is not BLUE. Its not proven. Its not tested.
Its wrong. Its so bad its not even wrong.
The simplest out of sample test would show you that.
Its an amateur untested flawed unreviewed piece of garbage.
Here is a simple test. Use your 10 stations to predict the 100s you ignore. Then measure your error of prediction.
It will suck. Then use the 100s you ignore to predict the ,10 you “randomly” selected. Note the improvement over
Your boneheaded approach.

Greg

May 1, 2014 12:42 am

1sky1: “As your LS fitting of pure sinusoids
to the Cascais record shows, you fail to realize that it’s the presence of a
strong trend that produces your rising values as period increases.”
The periodic analysis W used fits non harmonic patterns. It’s basically like finding the mean annual “climatology” but with varying window lengths , not just 12mo.
However, your criticism is still valid, It is the upward trend that produces what W showed and reflects his lack of experience and understanding of periodic analysis.
One of the first things to do is to remove the auto-regression and the non stationary mean, which is why the first thing I usually do with this kind of data is work with the first difference not the time-series itself.

Greg

May 1, 2014 2:03 am

Bart says:
April 30, 2014 at 7:27 pm
See here.
http://s1136.photobucket.com/user/Bartemis/media/ssn2.jpg.html?sort=3&o=22
Yes, Isn’t that something I linked you to about six months ago 🙂
I was wondering whether you had found a separate source or had reproduced it.
Oddly that links into the Stockholm temp record that our host has just published about ( comment published in Nature CS). That got me to look at SPD of Stockholm and look what I found:
http://tinypic.com/view.php?pic=lfq5g&s=8#.U2ILc6KBwrQ
I should stress that is hot off the press and unchecked, so caveat emptor.

Greg

May 1, 2014 2:11 am

Sorry is that your reworking of what the other Bart did that was produced on Talkshop?
I think you may have just explained the self convolution, that was one thing I did not get in the original. Nice one.

Greg

May 1, 2014 2:24 am

http://i1136.photobucket.com/albums/n488/Bartemis/PowerAttenuation_zpsb499835e.jpg~original
This is interesting and ties in with something else I’m doing but it’s drifting away from GMSL
Would you like to drop me a comment on my about page and I’ll get back to you?
http://climategrog.wordpress.com/about/

HenryP

May 1, 2014 2:50 am

@steven mosher
why don’t you give me all your Alaska data from Berkeley from 1998, or from 2000, is also OK, if that is more readily available, and we compare that result with the -0.55K/decade I get for Alaska
(I chose 1998 because that was when earth was at its warmest)
Clearly, it is people like you standing in the way of progress,
Progress would be for you to tell the world that we are globally cooling.
.http://www.woodfortrees.org/plot/hadcrut4gl/from:1987/to:2015/plot/hadcrut4gl/from:2002/to:2015/trend/plot/hadcrut3gl/from:1987/to:2015/plot/hadcrut3gl/from:2002/to:2015/trend/plot/rss/from:1987/to:2015/plot/rss/from:2002/to:2015/trend/plot/hadsst2gl/from:1987/to:2015/plot/hadsst2gl/from:2002/to:2015/trend/plot/hadcrut4gl/from:1987/to:2002/trend/plot/hadcrut3gl/from:1987/to:2002/trend/plot/hadsst2gl/from:1987/to:2002/trend/plot/rss/from:1987/to:2002/trend

HenryP

May 1, 2014 7:08 am

@Mr.. Mosher
we are all waiting for you to tell us your (berkeley) result of the amount of cooling taking place in Alaska since 1998 or 2000 in K per decade
If you do not reply we will all know or notice that you are a fake and a fraud, always trying to defend AGW

Bart

May 1, 2014 9:45 am

Greg says:
May 1, 2014 at 2:11 am
There can be only one, true Bart, and that is I.

Willis Eschenbach

Author

May 1, 2014 10:44 am

HenryP says:
May 1, 2014 at 2:50 am

@steven mosher
why don’t you give me all your Alaska data from Berkeley from 1998, or from 2000, is also OK, if that is more readily available, and we compare that result with the -0.55K/decade I get for Alaska

The Berkeley Earth Alaska data is here. Similar to the rest of the planet, the trend doesn’t go positive until you get back to 1992-present, and it doesn’t become significantly positive until you get all the way back to 1973-present … in other words, according to the Berkeley Earth data, there has been no significant warming in Alaska in four decades …
Again according to Berkeley Earth, the trend 1998-present is on average -.47°C/decade, and the trend 2000-present is -1.27°C/decade.
All the best,
w.

HenryP

May 1, 2014 10:58 am

Willis says
Again according to Berkeley Earth, the trend 1998-present is on average -.47°C/decade, and the trend 2000-present is -1.27°C/decade.
henry says
thanks Willis. I appreciate. I am not that much interested in before. Clearly they (berkeley) are a bunch of uninformed government employees, following the masterplan, an orgaisation that has employed or engaged people like Mosher. This helps!! It proves that my estimate of cooling in Alaska of -.55K per decade since 1998 is spot on.
The acceleration to -1.27K/decade from 2000 is somewhat worrying to me. Can it be that much difference? I will check that.

Willis Eschenbach

Author

May 1, 2014 10:58 am

Greg says:
May 1, 2014 at 12:42 am

1sky1:

“As your LS fitting of pure sinusoids
to the Cascais record shows, you fail to realize that it’s the presence of a
strong trend that produces your rising values as period increases.”

The periodic analysis W used fits non harmonic patterns. It’s basically like finding the mean annual “climatology” but with varying window lengths , not just 12mo.
However, your criticism is still valid, It is the upward trend that produces what W showed and reflects his lack of experience and understanding of periodic analysis.

Since I detrended the Cascais record before doing the analysis, all that your bogus long-distance “diagnosis” proves is that once again, you guys are all hat and no cattle. The increasing trend is obviously NOT because of the trend as both of you stupidly claim, because I removed the trend first.
You could have asked me if I’d detrended the data, but noooo, both of you are too smart to do that.
Nice try at discrediting me … unfortunately, the only ones discredited are yourselves. Next time do your homework first. If you had actually run the analysis before opening your mouths, you wouldn’t both look like idiots. Instead, you were so eager to prove me wrong that you both ended up wrong yourselves …
w.

HenryP

May 1, 2014 11:50 am

I checked,
according to my ten sample stations , Alaska cooled by -1.05K/decade since 2000.
That worries me, as it proves my theory that we are cooling from the top, and it is accelerating as times moves on. I can see it from my global tables as well, just adding the results of 2012 and 2013. The cooling is accelerating.Exactly as predicted.
http://blogs.24.com/henryp/2012/10/02/best-sine-wave-fit-for-the-drop-in-global-maximum-temperatures/
Pity that Mr Mosher does not care.

1sky1

May 1, 2014 5:25 pm

Greg:
What W. does with the gap-filled Casais data is LS curve fitting of sinusoids of different periods, not the simple data averaging over different bin-lengths that you presume. What mislead me into thinking that the trend, which always consists of low-frequency components, was not removed was his reference to the previous chart in his write-up. Notwithstanding this mistake, which he conveniently seizes upon to call us both idiots, what he fails to grasp is the irrelevance of such curve fitting to detecting irregular multidecadal oscillations in geophysical data. And he fails to show what happens for periods longer than 80yrs.
BTW, first differencing of data is an effective mean-and-trend-suppressing stratagem, but it also severely attenuates the lowest frequencies. I’m under the gun to finish a technical report this week; I’ll have more to say when I’m finished.

Nicola Scafetta

May 2, 2014 1:42 pm

To Willis (and Anthony)
“Scafetta’s work has been uniformly irreproducible. Unfortunately, he doesn’t give enough information to redo his work, and he has consistently refused to show his data and code.
As a result, what Scafetta does is merely anecdote, not science in any form, and I ignore it completely.”
Anthony, when will you start to correct your guests (Willis and Mosher in primis) about this incorrect statement that my work cannot be reproducible? Holm already let you know that it can be easily reproduced with due scientific knowledge which Willis evidently does not have. Do you understand that the statement has been demonstrated to be false and constitute “defamation” under the civil code?
Said this, about the topic addressed by Willis, as usually he does not seem to understand the issue. In the case of sea level it is caused locally by different phenomena which couple climatic effects such as a changes of the volume of the glaciers, changes in the Earth rotations and changes in the ocean currents.
The phenomenon is quite complex. Let us discuss changes in water current. Water can move from one region to another. This means that in one location the sea level can rise and in another it can decrease and the phenomenon get quite complex depending where you are. Thus the 60-year oscillation is not in phase everywhere nor it is expected to be see everywhere.
In some record it is quite evident in other it is less evident.
As Mosher noted above in my paper
Scafetta is another author showing an ~ 60 year cycle in long sea level data.
Discussion on common errors in analyzing sea level accelerations, solar trends and global warming Pattern Recognition in Physics 1, 37-58.
http://www.pattern-recogn-phys.net/1/37/2013/prp-1-37-2013.pdf
I analyze the record from New York and this long record (since 1860) show it quite clearly.
See my figure 3.
However, Mosher did not noticed that In my paper I have not analyzed only the record from NY but in Figure 2 I have analyzed the global sea level reconstruction by
Jevrejeva, S., Moore, J. C., Grinsted, A., andWoodworth, P. L.: Recent global sea level acceleration started over 200 years ago?, Geophys. Res. Lett., 35, L08715, doi:10.1029/2008GL033611, 2008.
ftp://soest.hawaii.edu/coastal/Climate%20Articles/Jevrejeva_2008%20Sea%20level%20acceleration%20200yrs%20ago.pdf
This global reconstruction of sea level does show a quasi 60 year oscillation. since 1700.
Note that in their paper Jevrejeva et al wrote:
“Superimposed on the long-term acceleration are quasiperiodic fluctuations with a period of about 60 years. ”
The issue, now, is to see whether the patter is an artifacts of the data. To show this one needs to compare with other records since 1700.
This was done in
Scafetta N., 2013. Multi-scale dynamical analysis (MSDA) of sea level records versus PDO, AMO, and NAO indexes. Climate Dynamics. in press.
http://people.duke.edu/~ns2002/pdf/10.1007_s00382-013-1771-3.pdf
See figure 10 where the there is comparison with the NAO index since 1700, and this index shows the same quasi 60-year oscillation.
This is enough to respond to Willis both about the merit of the 60-year oscillation in the SL and the reproducibility of my work.

Willis Eschenbach

Author

May 2, 2014 6:34 pm

1sky1 says:
May 1, 2014 at 5:25 pm

Greg:
What W. does with the gap-filled Casais data is LS curve fitting of sinusoids of different periods, not the simple data averaging over different bin-lengths that you presume. What mislead me into thinking that the trend, which always consists of low-frequency components, was not removed was his reference to the previous chart in his write-up.

You and Greg both claim that your failure to read what I wrote is my fault. Gotta love it, both you guys claiming that I’m in charge of your eyeballs.

Notwithstanding this mistake, which he conveniently seizes upon to call us both idiots, …

Hold up there, cowboy. You seized upon what you thought was my mistake and used it to try to hammer me over the head.

Nor is your comprehension any better about analyzing MONTHLY sea-level data, which is a can of worms with all sorts of factors (eustatic and steric variations, wind set-up, rainfall runoff, etc.) affecting the record even in geologically stable locations. As your LS fitting of pure sinusoids to the Cascais record shows, you fail to realize that it’s the presence of a strong trend that produces your rising values as period increases. And, of course, the well-established Rayleigh criterion for resolving sinusoids in a record of finite length remains terra icognita for you.

You attacked my comprehension and claimed I “fail to realize” something based on nothing more than the fact that you were so eager to prove me wrong that you didn’t bother to read what I said.
So yeah, when you try that kind of nonsense, I will point out your foolishness in big letters.
Doesn’t feel so good when the shoe is on the other foot, does it? Next time, read before you write. Neither of you are acting like savants. If you were, you would read my words very, very carefully before you set out to attack my ideas. That’s generally a mistake even a bear of little brain would avoid, I’m not known to suffer fools gladly.

… what he fails to grasp is the irrelevance of such curve fitting to detecting irregular multidecadal oscillations in geophysical data.

You claim (without a scrap of evidence) that such curve fitting is “irrelevant” to detecting “irregular multidecadal oscillations” … do you really think that an unsupported anonymous opinion swings any weight on WUWT? You may be a pezzonovante in your world. Here, you’re just another popup with a big mouth who claims I’m responsible for what you read. You may be right … but your unsupported word that you are right is a joke. You have no credibility, nobody who posts anonymously does, because you don’t have to stand behind your words. I do, so I’m careful about what I say. You, on the other hand, can make any claim you want and never have to back it up. You can disappear and reappear as “2sunthree” and never take responsibility for every and anything you’ve said. As a result, your unsupported claims have no weight at all.
Note that I’m note saying it’s wrong that you are anonymous. Many people are, some for valid and good reasons, some just to cause mischief and avoid responsibility. But the motives don’t matter, I’m talking about results. I’m just pointing out that anonymous unsupported opinion is valueless, so if you choose to be anonymous, you have to live with that.
But in any case, since detecting irregular oscillations is not what I was using the method for, so what? I wasn’t looking for irregular oscillations. I was looking at whether the claimed regular 55-year signal was or wasn’t present in the data.

And he fails to show what happens for periods longer than 80yrs.

Two reasons. First, as I said above, I was looking for a 55-year cycle, the one that the authors claimed to find. As such, the 80+ year data has no probative value either way, so it was ignored.
Second, unlike some people, I won’t speculate on any cycles longer than half the length of the dataset … that’s just numerology in my book. I don’t even like cycles that long, my rule of thumb is to not believe anything with less than three cycles … and even that is often not enough, as I discussed above. Let me repeat what I said, it’s important:

I have no doubt that for the kind of analysis that you are used to doing, one cycle may be adequate. However, climate is another kettle of fish entirely.
For example, for about three sunspot cycles in the second half of the 20th century, the sea level varied pretty much in parallel with the sunspots … and since the period of the sea level cycle is was hypothesized to be ~11 years from the sunspot period, then according to you only one 11-year cycle would be required to confirm the hypothesis, and three cycles would establish it beyond doubt..
However, when we look at the full record, within a few cycles in either direction the sea levels and the sunspots are way, way out of phase. It turns out the relationship is entirely spurious. The relationship appears, lasts for three good cycles, then the relationship vanishes. Go figure.
In Summary: Not only is one cycle far, far from enough to do what we want to do, to establish that a cycle exists in some climate variable.
In cases like the one I mention, even my recommended three cycles of data are still not enough to establish that a cycle exists.

So I’ll leave you to speculate on an 80-year cycle in a 120-year dataset, 1sky1. Me, I’ll pass.
Finally, I note again that all you do is complain about my methods … if you’re so smart, if you know the right method for what I’m doing, then how come you can’t find the purported 55-year signal?
w.

Willis Eschenbach

Author

May 2, 2014 10:34 pm

Nicola Scafetta says:
May 2, 2014 at 1:42 pm

To Willis (and Anthony)

“Scafetta’s work has been uniformly irreproducible. Unfortunately, he doesn’t give enough information to redo his work, and he has consistently refused to show his data and code.
As a result, what Scafetta does is merely anecdote, not science in any form, and I ignore it completely.”

Anthony, when will you start to correct your guests (Willis and Mosher in primis) about this incorrect statement that my work cannot be reproducible? Holm already let you know that it can be easily reproduced with due scientific knowledge which Willis evidently does not have. Do you understand that the statement has been demonstrated to be false and constitute “defamation” under the civil code?

Nicola, welcome back. I haven’t a clue who Holm is. And sadly, my statement is in fact true. Without data and code, your work is anecdote, not science.
When you are willing to supply your code and your data, at that point your work can be checked for errors. Until then, it can’t be done, so your work can’t be falsified. You have been asked for code and data many times, by Steve McIntyre, by Steven Mosher, and by myself.
Your response, shockingly to me at least, has been the same response that Michael Mann gave, and the same response that Phil Jones gave, which is that your meagre explanations of what you have done are quite sufficient, and that you are under no obligation to reveal either your methods or your data. In other words, you spit on the idea of scientific transparency, you hide your code and your data from public view … and you want to be treated as a scientist?
That excuse was nonsense when Mann and Jones said it back in the day. You should be ashamed to be trying to sell us the same line of nonsense a decade later.
To me, it’s simple, and Mosher said it best. If you don’t provide code and data, it’s not science—it’s just an advertisement. I say it a bit differently—no code, no data, no science.
So, let us know when you want to become a scientist and reveal your code and data, Nicola. Until then, your advertisements are fascinating but unsatisfying …

Said this, about the topic addressed by Willis, as usually he does not seem to understand the issue. In the case of sea level it is caused locally by different phenomena which couple climatic effects such as a changes of the volume of the glaciers, changes in the Earth rotations and changes in the ocean currents.

Nicola, perhaps you didn’t understand what I’m doing here. I’m not trying to analyze the global sea level as you seem to assume. I’m not trying to understand the causation of the changes in sea level like glaciers and stuff. That’s all immaterial to what I’m doing here.
I am doing one thing, and one thing only—attempting to establish the truth value of the authors’ statement that:

… there is a significant oscillation with a period around 60-years in the majority of the tide gauges examined …

So far, I have found very little evidence of such a cycle. Nor have you provided any such evidence.
You go on to say:

The phenomenon is quite complex. Let us discuss changes in water current. Water can move from one region to another. This means that in one location the sea level can rise and in another it can decrease and the phenomenon get quite complex depending where you are.

Again, the complexity of the phenomenon and the water currents are not of interest in this instance. I’m just looking for the 55-year cycle, not trying to explain it, so the causes are immaterial.

Thus the 60-year oscillation is not in phase everywhere nor it is expected to be see[n] everywhere.

Yes, Nicola, according to the authors the 60-year cycle IS expected to be seen everywhere. They claim it is present in “the majority of the tide gauges”. That’s what I didn’t believe when I first read it, and what I’m trying to determine. So far, very few of the tide gauge datasets show such a cycle.

In some record it is quite evident in other it is less evident.
As Mosher noted above in my paper
Scafetta is another author showing an ~ 60 year cycle in long sea level data.
Discussion on common errors in analyzing sea level accelerations, solar trends and global warming Pattern Recognition in Physics 1, 37-58.
http://www.pattern-recogn-phys.net/1/37/2013/prp-1-37-2013.pdf

Yeah, I tried reading that. I got as far as this:

However, Sa2012’s result does not appear robust because, as I will demonstrate below, the geometrical convexity observed in the NYC tide gauge record from 1950 to 2009 was very likely mostly induced by a quasi 60 yr oscillation that is already known to exist in the climate system.

I’m sorry, but saying that something is “very likely mostly induced by a quasi 60 year oscillation” is not science in my book. “Very likely mostly induced by a quasi …” is just waffle words. It’s handwaving to try to cover up the fact that you have no physical mechanism and are just blowing wind.
Indeed, you used the word “quasi” no less than thirty times in your paper. You have “quasi 60 year oscillations”, for example … what does that mean? Is an oscillation with a 40-year period a “quasi 60 year” oscillation? How about a 50-year period? How about a 70-year period? You never say what a “quasi 60 year” oscillation is, which makes your claims unfalsifiable.
Then you have “quasi-secular oscillations”, and a “quasi-millennial solar/climate cycle”.
“Quasi-secular”?
Of course, we mustn’t forget this gem “Finally, the alternating quasi regular large green and red areas evident at scales from 30 to 110 yr indicate a change of acceleration (from negative to positive, and vice-versa) that reveals the existence of a quasi 60–70 yr oscillation since 1700.”
Your claim is that quasi regular 20 to 110 year changes in sea level acceleration reveal a quasi 60-70 year oscillation? Really?
Does that kind of claim really pass for science on your planet, Nicola? Because around here, that dog won’t hunt …
In any case, here’s what you claim is caused by a 60-year oscillation, Fig. 1a from your paper:

What you show is the change in tides as a slow quadratic curve (which you call a geometric convexity above). Say what? At no time can you use a quadratic curve to represent tides. Quadratic curves go to infinity at both ends, hardly a characteristic of the tides.
That’s enough of a problem, but the real problem comes when you try to explain said quadratic curve as the result of a 60-year sine wave … so I can see why you say the quadratic curve is “very likely mostly induced by a quasi 60 yr oscillation”.
Because it would be very hard to explain mathematically how a 60-year sine wave would create a 60-year section of a quadratic curve … try fitting the two together sometime.

I analyze the record from New York and this long record (since 1860) show it quite clearly.
See my figure 3.

I saw your Figure 3. It says very clearly at the top “PS of Sea Level Rise in New York (1893-2011)”. In your comment above, on the other hand, you claim that the data in Figure 3 goes back to 1860 … you see why without the data and code your work is just anecdote? Without the data and code there’s no telling what dataset you used for Figure 3. I suspect that the note on the graph itself is correct, and that you have discarded the earlier data … but without your data and the code there’s no way to know.

However, Mosher did not noticed that In my paper I have not analyzed only the record from NY but in Figure 2 I have analyzed the global sea level reconstruction by
Jevrejeva, S., Moore, J. C., Grinsted, A., andWoodworth, P. L.: Recent global sea level acceleration started over 200 years ago?, Geophys. Res. Lett., 35, L08715, doi:10.1029/2008GL033611, 2008.
ftp://soest.hawaii.edu/coastal/Climate%20Articles/Jevrejeva_2008%20Sea%20level%20acceleration%20200yrs%20ago.pdf
This global reconstruction of sea level does show a quasi 60 year oscillation. since 1700.

Well, I found the Jevrejeva dataset here.
Before looking at it, let me quote a bit from the Jevrejeva paper and discuss how they constructed a tide record back to 1700:

[4] The ‘‘virtual station’’ GSL calculated from 1023 tide gauge records [Jevrejeva et al., 2006], optimally solves the sampling problem of station locations. Detailed descriptions of these time series are available from http://www.pol.ac.uk/ psmsl. All data sets were corrected for local datum changes and glacial isostatic adjustment (GIA) of the solid Earth [Peltier, 2001]. The reconstruction preserves volcanic signatures [Grinsted et al., 2007] and also has published standard errors [Jevrejeva et al., 2006], available from http://www.pol.ac.uk/psmsl/author_archive/jevrejeva_ etal_gsl/.

Gotta admit, I get nervous when someone claims to have “optimally solved” a problem involving the average of an intensive quantity like sea level.
I’m also not impressed by a claim that the method “preserves volcanic signatures”, as I’ve never seen any evidence that volcanoes had the slightest effect on sea level. In any case, they continue:

[5] We extend the record backwards from 1850 using three of the longest (though discontinuous) tide gauge records available: Amsterdam, since 1700 [Van Veen, 1945], Liverpool, since 1768 [Woodworth, 1999] and Stockholm, since 1774 [Ekman, 1988]. We remove the linear part of each record, which contains the land movement component, by comparing each time series with the existing GSL for the period of overlap. In order to estimate the global sea level from these three stations, we assume implicitly that the mean trend from the three records is the same as that globally for the 18th century. And one notes that geological evidence supports relatively stable global sea level over the last 2 millennia [Lambeck et al., 2004]. By far the major source of error when using the three stations as an extended record of GSL is how representative tide gauges from a single ocean basin can be of global sea level; we estimate this error to be ±6 cm from jack knife error estimates when global data are available [Jevrejeva et al., 2006].
[6] We provide a solution for the problem associated with decadal and multi-decadal variability using a method based on the Monte Carlo Singular Spectrum Analysis (MC-SSA). We remove 2–30 year variability, determine the time variable trend and examine temporal variability in acceler- ation in global sea level during the past 300 years.

OK, so they have 150 years of tidal station data that has been carefully analyzed. It has been GIA corrected, and local discontinuities have been removed.
And on the front end of that, they’ve spliced an altered 3-tide-station average …
Now, I might use that result for something simple, or for a rough estimate of historical rates of sea level rise, Nicola. I’d never use it for an analysis of the cycles. I can’t begin to list the number of simplifying assumptions made in there. They assume that land movement is linear, probably justified. They assume that the mean trend of Amsterdam, Liverpool, and Stockholm is equal to the global trend not only in the long run but in the short run, probably not justified. They assume that they can simply spice their three-station average on the early end of an actual global average and analyze it like it were a single dataset. They assume that their “optimum solution” is optimum. They assume that there is one “best” method for averaging intensive data. They assume that there is a “signature” of volcanoes in the sea level, and whatever that signal might be, they’ve designed their analysis to preserve it (with unknown side effects). They assume that their GIA adjustments are not causing any long-term fluctuations in the results. And there are likely more assumptions I’ve overlooked.

Note that in their paper Jevrejeva et al wrote:
“Superimposed on the long-term acceleration are quasiperiodic fluctuations with a period of about 60 years. ”

I did note that. Since Jevrejeva provides no evidence for these “quasiperiodic fluctuations”, whatever that might mean, I fail to see how his bald claim qualifies as science. He provides no Fourier or other analysis of the results. As far as I can tell he looked at the data and said yep, definitely quasiperiodic fluctuations … and you got all impressed. I see nothing in his claim to back up that analysis.
Me, I just went and checked his data in the easiest manner. I compared the cyclical components of the first half of the data (the average of 3 tide gauges) with the second half of the data. If his reconstruction is valid, we should find the same cycles in the two halves … guess what. We don’t. In fact, the cycles in the two halves of the Jevrejeva data are different at most cycle lengths. This is the simplest of tests, and the one test that folks like yourself tend to overlook …

The issue, now, is to see whether the patter[n] is an artifacts of the data. To show this one needs to compare with other records since 1700.

Nope. To do this, one only needs to show that the two halves of the data have very different cycles. If they do, then the cycles are artifacts which are not representative of the entire dataset. Here’s that analysis:

If the first 150 years of the average of the three tide gauges were a valid proxy for the cyclical nature of the next 150 years of global sea level, the first 150 years of data would contain the same cycles as the last 150 years. However, the cycles are nothing like the same.
Q.E.D.
Can’t say that the Jervrejeva paper was impressive or convincing, Nicola. Doubling the length of the tide record by using three individual tide gauge records? That seems … well, like a big stretch. For example, suppose some climate alarmist tried to extend the HadCRUT global temperature data back to 1700 by using three temperature records … how much weight would you put on that?
Me, not much … but that’s what Jevrejeva’s done. And even if it is somewhat valid as a rough guide, finding cycles in it is meaningless.

This was done in
Scafetta N., 2013. Multi-scale dynamical analysis (MSDA) of sea level records versus PDO, AMO, and NAO indexes. Climate Dynamics. in press.
http://people.duke.edu/~ns2002/pdf/10.1007_s00382-013-1771-3.pdf
See figure 10 where the there is comparison with the NAO index since 1700, and this index shows the same quasi 60-year oscillation.
This is enough to respond to Willis both about the merit of the 60-year oscillation in the SL and the reproducibility of my work.

Your last citation provides as a reference the very paper we are discussing here … which I’ve shown above to be using a flawed method to make their claim.
In addition, they are not using “the NAO [North Atlantic Oscillation] index since 1700”. They are using a reconstruction of that index back to 1675 based on “pressure, temperature and precipitation measurements and proxy data”. They say of the reconstruction that “Predictive skill varied for different sub-periods depending on data availability.” This alone would invalidate any cyclical analysis of the data, but there’s more. They say that predictive skill “was highest for autumn and winter and was generally better for the EU than for the NAO index.” And there’s more: “Wavelet analysis suggested significant low-frequency variability, especially for the spring, summer and annual averaged indices.”
As a result, the cyclical components of that reconstruction due to the incorporation of a host of other datasets, each of which contains its own characteristic oscillations, means that the reconstruction is totally unsuitable for the kind of Fourier analysis you show in your paper.
You also are way into “quasi” in that paper as well, with “quasi 20-year and 60-year oscillations”, a “quasi 60–70 year natural oscillation”, “quasi secular-long records”, “quasi decadal, bi-decadal and 50–90 year oscillations”, “quasi-predictable variability of the ocean–atmosphere system”, “quasi periodic oscillations are observed, as indicated by the quasi-periodic shifts”, “synchronous quasi bi-decadal oscillations”, “quasi uniform accelerations”, “repeat quasi- periodically for three hundred years”, and the “quasi millennial oscillation typically found in numerous climatic and solar indexes”.
With your planet containing “quasi oscillations” at decadal, bi-decadal, 50, 60, 70, 90, and 1000 years … I’m quite sure that you can find a quasi oscillation at any cycle length you might choose. As I said in my most recent post:

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

This holds for undefined “quasi oscillations” as well. That’s just handwaving.
For example, suppose in some tidal dataset there is no visible oscillation with an 11 year period for 30 years. Then for thirty years such an oscillation emerges and persists, only to disappear again for the last ten years of the record.
Is that a “quasi 30-year oscillation” or not?
And if so, what if it only appears after 100 years, and then disappears after 30 years and is not seen again in the record … is it still a “quasi 30-year oscillation” or not? What if it only appears for one clearly defined cycle … quasi 30-year oscillation or not?
I’m sure you see the problem. We have no idea what you mean by “quasi”. If you don’t see the problem, here’s another example. In the Jevrejeva data, the first half has a strong cycle at 25 years. The second half has no such cycle. Is that a “quasi 25-year cycle” or not? If you answer no, then what if it was present in the first and last thirds of the record? Or present in the first half and last quarter of the record but not in the third quarter? Still not a “quasi 25-year cycle”.
As a result, your statements are absolutely not falsifiable. With no definition of what a “quasi oscillation” might be, or what a “quasi 20-year cycle” might exclude or include, there is no way to show that your statements are wrong …
And of course, that means that your statements are not science in any sense of the world. Science is concerned with falsifiable statements. If a statement is not falsifiable, it’s not part of the realm of science. The statement “The Buddha was enlightened” is not falsifiable, for example, so it’s not part of science. Doesn’t make it bad or wrong, it’s just not falsifiable, so science can say nothing about it.
The same is true about all of your statements about “quasI’ periods and “quasi” oscillations and “quasi secular-long records”. None of those statements are falsifiable, so none of them have anything to do with science.
Nicola, you need to understand something. Until you come up with data and code, I and others are under no obligation to treat your results as anything more than advertisements for your claimed brilliance.
Now, you may not like that. And you may have gotten away with much less in the past, as many other scientists have.
But this is 2014, and the rules have changed. Scientists have recognized that the English language is inadequate to describe what your computer program does. To truly check what you’ve done, we have to look at your code and data. Even if you describe in detail what you think you’ve done, your description of your procedures doesn’t mean that you have successfully implemented them in computer language in the way that you think you have. A detailed description also can’t demonstrate that there are no bugs in the code. To determine that, we have to see the code and data. It’s called “scientific transparency”. Unless you give us your code and data, we can’t determine if your computer code contains bugs … so we are under no obligation to believe a word you say.
Now, you may not like that, but that’s how it is. Until you depart the company of Mssrs Mann and Jones and you reveal your data and code, most modern scientists will treat your results as just advertisements. Oh, you can hang out at Tallbloke’s and bask in the adulation of those that can’t tell anecdote from science … but around here, you won’t get any traction without data and code.
That’s what I meant when I said:

“Unfortunately, he doesn’t give enough information to redo his work, and he has consistently refused to show his data and code.
As a result, what Scafetta does is merely anecdote, not science in any form, and I ignore it completely.”

It’s not complex. Science absolutely requires transparency. You insist on keeping your code and data totally opaque. You can tell me the logical conclusion of those two true statements.
My best to you,
w.

Greg

May 4, 2014 2:55 am

1sky1: “BTW, first differencing of data is an effective mean-and-trend-suppressing stratagem, but it also severely attenuates the lowest frequencies. I’m under the gun to finish a technical report this week; I’ll have more to say when I’m finished.”
Which is exactly what red-noise, random walks and auto-regression is all about.
It is the auto-regression that creates a lot of the long term variability. That does not make the variability less real but working with first diff puts any random noise back into a “white noise” spectrum.