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:

all tide records over 120 years 1-8Figure 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.

gauss all tide records over 120 years 1-8Figure 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.

periodicity all tide records over 120 years 1-8Figure 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.

all tide records over 120 years 9-16 gauss all tide records over 120 years 9-16 periodicity all tide records over 120 years 9-16Figures 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:

all tide records over 120 years 17-22 gauss all tide records over 120 years 17-22 periodicity all tide records over 120 years 17-22

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.

mean detrended 22 tide recordsFigure 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:

periodicity mean detrended 22 tide recordsFigure 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

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.

w.

 

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Here are some relevant papers:
http://sealevel.info/papers.html#howlong

Greg

http://climategrog.wordpress.com/?attachment_id=933
Last time I looked at this paper, I concluded there was not enough detail of the method to reproduce it but there seems to be a clear 60 y cycle in the rate of change. It’s a lot less visible in sea level data.

AJ

Willis… if you need some code to import the psmsl data into a single R dataframe, the following might be of interest:
https://sites.google.com/site/climateadj/nh-sea-level-reconstruction

Greg

JJ paper used SSA and some kind of 30 year filter, so very heavily damped.
Perhaps the most signficant bit is that for the last century it’s clearly hovering about 2mm/y , not the 3.4mm/y claimed by satellite altimetry crews.

Kev-in-Uk

Look, it is real simple and obvious to all but the most blind of observers – there is simply no way we have enough accurate data for sea level analysis, land or ocean surface temperature analysis, or basically any other fecking type of analysis one might wish to ‘believe’ one can undertake from current ‘datasets’ – It ain’t happening, and the sooner we realise how little we actually know, the better.. The earth and its biosphere is simply a massive perpetually moving and changing interaction of a bazillion (or more!) different positive and negative effects, all on different periodicities and interactive levels, NONE, I repeat – NONE – of which are known in any great detail ! (I won’t even comment on these bazillion interqctions being condensed into ‘models’! LOL)
When folk finally realises this, the issue (whatever it may be) simply disappears. Willis has easily shown that even the best sea level data cannot be tortured and forced to give up any underlying trend – frankly, I don’t see that ANY of the current climate knowledge and data is any better.

Latitude

Where’s that paper that said 65% of tide gauges either show sea levels falling or no sea level rise at all…

Willis Eschenbach

AJ says:
April 25, 2014 at 3:09 pm

Willis… if you need some code to import the psmsl data into a single R dataframe, the following might be of interest:
https://sites.google.com/site/climateadj/nh-sea-level-reconstruction

Thanks, AJ, your work in R is always of interest, and this is no exception. I’ll need to study it.
On my end, I downloaded the 1413 files, and then read them into a matrix. I find a matrix a bit easier to work with than a data frame, likely my unfamiliarity with the latter. I’ll look to see how you do it.
w.

Roger Dewhurst

Kev-in-UK hits the nail on the head.

Pat Frank

Willis, is it possible that the tide gauge data need to be corrected for any isostatic movement of the land-base?

A guy wearing partially tied sneakers, no belt with his pants dragging down his butt gets a job at a dairy farm.
Day 1
Worker is not trusted with the tender areas of cows gets to clean up around the cows, lays down fresh hay, fills up the feed trough when he notices that his sneakers are a different color and filled with stuff. Has to borrow some twine to try and tie his pants up.
Day 2
Worker shows up with cheap calf high rubber boots. Discovers the manure gutter chain is jammed and spends a couple of hours working in a gutter full of soggy manure. Vomits a couple of times. His new rubber boots were too short and easily filled with the juicy stuff. Decides he really needs better fitting pants and a belt.
Day 3
Worker arrives with the cheapest pair of hip boots sold at the hardware store. Learns from the farmer that the gutter chain is under maintenance and it’s availability is still unknown. Worker spends the day filling a wheelbarrow and moving manure to the crap wagon. Worker falls into the wagon a couple of times trying to successfully dump the manure in the wagon. As often happens the worker learns that rubber boots keep things from leaking out very well. Worker realizes that he hasn’t lost his breakfast all day.
Day 4
Worker arrives at the farm wearing Carhartt overalls with good quality for the price clodhopper work boots. Sets to work without dilly or dallying.
My apologies for the dairy farm worker introduction Willis. Just that I am getting rather amazed that you can open some of these data bases without losing your lunch. Even with repeated exposure it must be hard to keep your cookies where they belong sometimes.
Thank you Willis for opening these cans of worm goo! Sixty year cycle… After living and fishing the Gulf of Mexico for a number of years with it’s odd tides I certainly believe that it is difficult to find common frequencies amongst tidal records.

Willis Eschenbach

Latitude says:
April 25, 2014 at 3:52 pm

Where’s that paper that said 65% of tide gauges either show sea levels falling or no sea level rise at all…

Hang on … OK, here’s the data:

The very high and low values for the rate of sea level rise are almost all from short records. If we restrict it to records longer than 20 years, here’s the result:

Out of that 820 records, about 20% of them show falling levels.
w.

nutso fasst

Any studies on how much sea level rise can be attributed to displacement by post-glacial rebound?

David L. Hagen

Hi Willis
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, doi:
10.5194/prp-1-37-2013, 2013

“(1) multidecadal natural oscillations (e.g. the quasi 60 yr Multidecadal Atlantic Oscillation (AMO), Norther Atlantic Oscillation (NAO) and Pacific Decadal Oscillation (PDO) need to be taken into account for properly quantifying anomalous background accelerations in tide gauge records such as in New York City;”

See Fig. 2, Fig. 3 analyzing New York’s 1893 to 2011 record.
Look forward to your evaluation or testing of his methods.

Greg

power spectrum of Church and White GMSL
http://climategrog.wordpress.com/?attachment_id=935
This is just a quick rough but seems reminiscent of what I found looking at the Jevrejava data last time this came up.
circa 10.x and 20.x possibly suggestive of solar , and 8.82 pretty surely the lunar apsides yet again.
So the same conclusion I’ve been pointing to for a couple of years now: attempts to attibutre the solar signal has phase crisises because there is interference patterns with the close by lunar periodicity.
Until climatology gets a grip on the importance of lunar apsides which seems to crop up anywhere there is the subject of water, they will not find a stable solar signal.
But since that suits them fine and they can pretend it’s all “stochastic noise” + AGW , I don’t suppose they are going to be looking too hard.

Greg

Yeah interesting that median rate of sea level rise is 1.8 mm/y. The same as what i get eyeballing Jevrejava’s rate of rise graph above.
Now if [satellite] alitmetry says 3.4mm/y this it must all be piling up in mid ocean where there are not tide gauges !!

Rob Dawg

Thank you sir. It is so much more difficult to expose the null than it is to imply a trend/cycle. You have done the near impossible.

Latitude

Out of that 820 records, about 20% of them show falling levels
===
Bingo!
Here’s what I was looking for:
Abstract
The location of tide gauges is not random. If their locations are positively (negatively) correlated with SLR, estimates of global SLR will be biased upwards (downwards). We show that the location of tide gauges in 2000 is independent of SLR as measured by satellite altimetry. Therefore PSMSL tide gauges constitute a quasi-random sample and inferences of SLR based on them are unbiased, and there is no need for data reconstructions. By contrast, tide gauges dating back to the 19th century were located where sea levels happened to be rising. Data reconstructions based on these tide gauges are therefore likely to over-estimate sea level rise.
We therefore study individual tide gauge data on sea levels from the Permanent Service for Mean Sea Level (PSMSL) during 1807 – 2010 without recourse to data reconstruction. Although mean sea levels are rising by 1mm/year, sea level rise is local rather than global, and is concentrated in the Baltic and Adriatic seas, South East Asia and the Atlantic coast of the United States. In these locations, covering 35 percent of tide gauges, sea levels rose on average by 3.8mm/year. Sea levels were stable in locations covered by 61 percent of tide gauges, and sea levels fell in locations covered by 4 percent of tide gauges. In these locations sea levels fell on average by almost 6mm/year.
https://suyts.wordpress.com/2013/09/20/vindication-for-suyts-new-tidal-gauge-sea-level-paper-out-reports-1mmyr-sea-level-rise/

Greg

Looking at the power spectrum , I think I can see where Jevrejava’s 60 years cycle is coming from (assuming here data is similar to Church and White.
http://climategrog.wordpress.com/?attachment_id=935
cos(2.pi.x/7.5) + cos(2.pi.x/10.2) = cos (2.pi.x/56.67) * cos(2.pi.x/8.64)
It’s the old radio amplitude modulation thing again.
Now I’m not a expert on SSA but it’s a bit like principal component analysis and picks out pairs frequencies. So it seems to be pulling out the 57 year periodicity.
Now a limitation of Periodicity Analysis is that it will only pull out a direct and constant amplitude repetition. Much of climate is about resonances and interference patterns and I fear P.A. may not be the most flexible tool to dig this sort of thing out.
I did also find a strong and highly symmetric AM triplet in the sub-annual frequencies that shows a very similar modulation frquency:
p2=0.96225
pc=0.94693
p1=0.931378
# as A.M. 0.947 * 58.060 ; triplet asymmetry: -0.039 %
Now that’s close enough with the accuracy of extracting the modulator from a triplet that this is very likely the same thing.
Now looking at the SI of the Chambers paper that is the subject here they are fitting 55 years.
[ Willis, look at the SI and you will which records they used. ]

Solid.
I hope people who have issues with what willis
Has done download the data and have a wack
At it. I suspect some will give willis homework. Or at least
Try to give him more work to do.
I have no issues.
Solid

On this matter of sea levels rising there is huge variation amongst scientists, from Al Gore’s figure of 65m per century to NIWA’s 1998 Lyttelton study of 1mm per year (10cm per century); a disparity of 65,000%. That degree of error disqualifies claims of plausibility, even throwing doubt on NIWA’s work.
With that degree of uncertainty, it is difficult to see how anybody can be sure the sea is rising at all. How, it may be asked, can 1mm change in sea level be calculated, averaged over one entire year or a hundred years, when even a flat sea at rest undulates more than that with waves every few seconds, and tide height just in one day varies by some two metres?
To say a tide height is higher we require knowing higher than what? To fairly compare tide heights one needs a past reference height to compare with one in the present. Finding the former is not possible because (at least 10) factors that influence tide height do not together repeat. We are talking of phase of the moon, lunar declination, perigee cycle, high and low pressure zones that can suck heights up or depress them, and winds onshore that can blow water into a harbour or offshore depleting a bay.
Equinox tides are higher than solstice tides. The sea is warmer in summer, therefore higher. Underwater earthquakes, eruptions, and fissures raise local sea-levels, most non-recordable and/or undetectable. Rainfall at sea, river flows and land run-offs contribute to sea-levels. Temperature changes control density and water volumes, ever-shifting in the ocean, and the direction of currents both deep, mid and surface, alter sea height. Cycles of glaciers’ advance and retreat change heights of the ocean.
In short, we haven’t a clue how high sea levels are ever supposed to be in any fixed place, to a tolerance of 1mm per year, when everything connected to the sea is in constant flux. The sea is not a lake or a pond. No computer model can pretend that it is, just for the sake of a neat result. Examinating old photographs, sketches and tide markers reveals high watermarks unchanged on NZ and Australian beaches, apart from erosion due to changing currents.
Disappearing sand is a cycle, a function of lower than normal sea levels because lower water undermines foreshore and top sand collapses. Without higher water to re-deposit sand higher up the shoreline, over a long time period a beach can ebb slowly away. Higher tides deposit more sand because sand is heavier than water – surf brings sand in by momentum of wave action, and leaves it there when water recedes. Erosion cycles are just that, cycles. If this was not cyclic, all sand on all beaches would have gone long before now.
Without monitoring over all oceans we cannot know if sea-levels are rising. We only have measuring devices on 0.4% on the earth’s surface where humans live. Special buoys now report via satellite using Argos transmitters, but we need to wait several centuries to achieve a reliable average to comment on any future century’s departure from average.
Antarctic and Arctic ice are thickening, which means sea levels are dropping. On Tuvalu and other island atolls it is the land that is moving, not the sea. Small atolls like Tuvalu cannot be sliding under the sea whilst beaches in Australia and NZ stay unaffected. How would the sea decide which countries to send beneath the waves?
As we emerge from this interglacial the poles are the smallest they have been in a while and some sea-levels the highest they aspire to. Some countries are still rebounding after the last ice age- Scotland is rising and the south of England is lowering. The west of Australia is rising whilst the east is dropping. There is a similar differential between NZ’s north and south island.
The high watermark on any beach varies up and down the sand by about a metre every 10 minutes. To that add just 1 millimetre per year, the thickness of a grain of sand. If this varies over 60 years it may be 60mm, or about 2.5 inches. If you stood there for 60 years you could miss it if you blinked.

George Turner

[sarcasm]
Tide gauges only measure the height of the tide, not the quality of the tide. Due to global warming we’re getting more and more rotten tides, the kind that dump heroin needles and dead whales (killed by ocean acidification, heat stroke, and depression) on our beaches. It won’t be safe for children to play in the surf no matter what the sea-level is unless we drastically curtail CO2 emissions so that the tides return to a healthy normal.
[/sarcasm]

Greg

Latitude I advise you to read that paper carefully before jumping all over the result because you like it. I’m not impressed for a number of reasons.

Kelly

http://nweb.ngs.noaa.gov/heightmod/NOAANOSNGSTR50.pdf
http://tidesandcurrents.noaa.gov/sltrends/sltrends_station.shtml?stnid=8764311
Mean Sea Level Trends for Stations in Lousiana
Water-level records combine data on ocean fluctuations and vertical motion of the land at the station. The sea-level variations determined by these records include the linear trend, the average seasonal cycle, and the interannual variability at each station. Monthly data through the end of 2006 were used in the calculation, and all stations had data spanning a period of 30 years or more.

riparianinc

Note that if the gauge is in a subsiding location, the sink rate of the gauge must be subtracted from the apparent rise in the ocean. My understanding is that something like 74% of the seeming rise in the Gulf around Louisiana is really the land subsiding. The causes of the land change/land loss are as hotly debated as anything else related to climate but there is general agreement on the subsidence problem even though the causes and thus the corrective action (if any) remain unresolved.
See:
http://nweb.ngs.noaa.gov/heightmod/NOAANOSNGSTR50.pdf
http://tidesandcurrents.noaa.gov/sltrends/sltrends_station.shtml?stnid=8764311
Mean Sea Level Trends for Stations in Lousiana [sic]
Water-level records combine data on ocean fluctuations and vertical motion of the land at the station. The sea-level variations determined by these records include the linear trend, the average seasonal cycle, and the interannual variability at each station. Monthly data through the end of 2006 were used in the calculation, and all stations had data spanning a period of 30 years or more.

David
“Hi Willis
Scafetta is another author showing an ~ 60 year cycle in long sea level data.”
in one station. New York City.
Here is a clue. You have a bunch of stations. if you look at enough of them you will find a cycle.
The bottom line is why would anyone think you could find a cycle.

TRG

Willis, thank you for this, and for all of your excellent work.

bones

Pat Frank says:
April 25, 2014 at 4:03 pm
Willis, is it possible that the tide gauge data need to be corrected for any isostatic movement of the land-base?
———————————————–
Whether isostatic rebound or subsidence, wouldn’t that just be automatically discarded by the linear detrending?

Willis Eschenbach

Greg says:
April 25, 2014 at 4:49 pm

power spectrum of Church and White GMSL
http://climategrog.wordpress.com/?attachment_id=935
This is just a quick rough but seems reminiscent of what I found looking at the Jevrejava data last time this came up.

Thanks, Greg. Here’s the problem I have with claims of 60-year periodicity in Church & White and Jevrejeva data. This figure shows the detrended C&W, old C&W, and Jevrejeva data:

A couple comments. First, the three datasets have roughly the same shape. The simplified (presumably smoothed in some fashion) version of Jevrejeva shows the basic shape. The rate of sea level rise was steady until 1900, slowed up until 1930, sped up until 1960, mostly steady after that.
Now, it’s true that the period 1900 to 1960 looks a lot like half of a 120-year cycle … but the rest of the record dispels that idea. While there is nothing resembling a 60-year cycle anywhere in that data. And since the purported 60-year cycle is the subject of this post, I’m taking that as supporting evidence that such a cycle isn’t there …
Finally, while you are correct that there are some small cycles at 8 years or so, as you can see they don’t do much.
Thanks for the link,
w.

Whether or not you’ll notice the approx. 60-year sea-level oscillation depends on the mix of tide-gauges that you choose to examine.
For instance, the North American Atlantic coast displays a significant oscillation, but there’s an “inflection point” somewhere around Cape Hatteras, NC. North of Cape Hatteras (about 35.3°N latitude) the sea is currently “sloshing up” (but nearing its peak rate of sea-level rise), and south of Cape Hatteras it’s “sloshing down” (but nearing its trough). (Note that this slow “sloshing” is in addition to the linear trends, which also vary by location, due to PGR, land subsidence, etc.)
So along the northeastern U.S. Atlantic coast, between northern NC and Eastport, ME, if you compare the rate of sea-level rise now to 10 to 30 years ago, you’ll see a measurable acceleration (increase in rate). That’s why the NOAA-calculated long-term average rate of sea-level rise at those stations is slightly higher when calculated using measurements through 2011 than when calculated using measurements through 2006.
But along the southeastern U.S. Atlantic coast, between Wilmington, NC and the Florida border, if you compare the rate of sea-level rise now to 10 to 30 years ago you’ll see a measurable deceleration. That’s why the NOAA-calculated long-term average rate of sea-level rise at those stations is slightly lower when calculated using measurements through 2011 than when calculated using measurements through 2006.
Here’s a spreadsheet. You can view it as a web page, or load it into Microsoft Excel or Kingsoft Office:
http://sealevel.info/US_Atlantic_coast_sea-level_trends.html
The column labeled “2006 trend” shows the trend calculated by linear regression of all sea-level measurement data through 2006, and the column labeled “2011 trend” shows the trend calculated using data through 2011. For the northern coast, Virginia-to-Maine, the 2011 trends are slightly higher than the 2006 trends, but for the southern coast, North Carolina-to-Georgia, the 2011 trends are slightly lower than the 2006 trends.
BTW, you might notice that the northeastern U.S. “hot-spot” of apparently accelerated sea-level rise encompasses a stretch of Atlantic coastline that is about twice as long as the southeastern U.S. “cold-spot” of apparently decelerated sea-level rise. But before you make the mistake of concluding that that means the overall trend is acceleration, I should warn you that the entire U.S. Pacific coast is showing deceleration, all the way from Seattle to San Diego:
http://sealevel.info/MSL_global_trendtable4.html
The bottom line is that, due to small but measurable multi-decadal regional oscillations in sea-level, with the most noticeable oscillation period equal to about 60 years, when sea-level trends are calculated over short time spans (meaning less than 50-60 years), some stretches of coastline show apparent acceleration, and other stretches show apparent deceleration, neither of which are real long term trends.
Overall, there’s been little or no change in the rate of sea-level rise in the last 85-90 years, despite the fact that atmospheric CO2 levels increased by about 90-95 ppm (30%). That’s about 4/5-ths of the total anthropogenic CO2 increase since the start of the industrial age. Yet it has caused no detectable acceleration in the rate of sea-level rise. In fact, the best studies show a very slight deceleration.
BTW, who can guess which of those two opposing “trends” (apparent acceleration in some places, apparent deceleration in others) got written up in a high-profile paper in Nature? Now let’s not always see the same hands.

Why does anyone expect to find a 60 year cycle in sea level? I’m personally convinced of 60 year atmospheric cycles, but water is so quickly isotactic that when you make a pile of it (like the enso warm pool), the rest of the ocean drops. Meltwater and steric change are surely insignificant at this timescale.

Very interesting work, Willis, but your analysis is limited to datasets in the PSMSL database. As PSMSL writes; there exist several important long datasets not included in the PSMLS database:
http://www.psmsl.org/data/longrecords/
For example:
Amsterdam from 1700
Stockholm from 1774
Kronstadt from 1773
Liverpool from 1768
Brest from 1711
I would guess that the pay-walled paper is based on some these. They are long enough for at least 3 cycles of a 60 year period.
/Jan

Willis Eschenbach

daveburton says:
April 25, 2014 at 9:34 pm

Whether or not you’ll notice the approx. 60-year sea-level oscillation depends on the mix of tide-gauges that you choose to examine.
For instance, the North American Atlantic coast displays a significant oscillation, but there’s an “inflection point” somewhere around Cape Hatteras, NC.

When you show up with some evidence for that, we’ll talk. But assuming what is to be proven is not going to work.
w.

climatereason

Jan
The longer records are very interesting but as far as I am aware the tide gauges in all of them have been physically moved at least once so they are not necessarily like for like.
Also isostatic change needs to be taken into account which is often greater than sea level rise (or fall)
The rate of sea level change around the UK (up and down) can be seen in this paper-this would cover Liverpool but assumes isostatic change has always been constant.
http://www.geosociety.org/gsatoday/archive/19/9/pdf/i1052-5173-19-9-52.pdf
tonyb

@Willis; I commend your effort to personally examine the data and check the science.
I personally can not see how anything can effect sea levels on so short a time scale. As you know so well the oceans are MASSIVE and leveled by gravity, The land surface/ocean interface is much more likely to move a bit then the amount of volume in the oceans.

Willis Eschenbach

David L. Hagen says:
April 25, 2014 at 4:46 pm

Hi Willis
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, doi:
10.5194/prp-1-37-2013, 2013
“(1) multidecadal natural oscillations (e.g. the quasi 60 yr Multidecadal Atlantic Oscillation (AMO), Norther Atlantic Oscillation (NAO) and Pacific Decadal Oscillation (PDO) need to be taken into account for properly quantifying anomalous background accelerations in tide gauge records such as in New York City;”
See Fig. 2, Fig. 3 analyzing New York’s 1893 to 2011 record.
Look forward to your evaluation or testing of his methods.

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.
w.

Willis Eschenbach

Jan Kjetil Andersen says:
April 25, 2014 at 11:24 pm

Very interesting work, Willis, but your analysis is limited to datasets in the PSMSL database. As PSMSL writes; there exist several important long datasets not included in the PSMLS database:
http://www.psmsl.org/data/longrecords/
For example:
Amsterdam from 1700
Stockholm from 1774
Kronstadt from 1773
Liverpool from 1768
Brest from 1711
I would guess that the pay-walled paper is based on some these. They are long enough for at least 3 cycles of a 60 year period.
/Jan

As usual, Jan, your comments are quite valuable. I just took a look at the Amsterdam data … here’s the periodicity analysis:

There’s a strong cycle around 37 years, and a smaller peak at 53 years, but nothing around 60 years.
I’ll report on the rest as I do them, but I may not show the rest.
w.

“Why does anyone expect to find a 60 year cycle in sea level?”
good question.
why do people want to find the cycle is a better question

charles nelson

Nice to see a clear analysis of some (relatively) concrete and reliable data. Interesting and informative.

Willis Eschenbach

Stockholm long record, no 60-year cycle …
w.

Roy

Shouldn’t there be a hockey stick somewhere among all those graphs?

Oldseadog

Interesting that the records for places close together on the Dutch coast are so dissimilar, for example Amsterdam, Ijmuiden, Hook of Holland, Den Helder, but then you would need to look at the river freshwater height as well. The amount of rain upriver days or weeks before can have a massive influence on the height of tide at any time.
But very worthwhile digging.
It would be interesting to look at somewhere with no land effect – Rockall, St. Helena, somewhere in the Azores?

Greg

“There’s a strong cycle around 37 years, and a smaller peak at 53 years, but nothing around 60 years.”
I found 57/58 years and the paper actuall is fitting 55 years. Don’t know why they report this as “60y”.
http://onlinelibrary.wiley.com/store/10.1029/2012GL052885/asset/supinfo/grl29523-sup-0005-t02.txt?v=1&s=0603509b8451e52b1b7109d1181c2521b37ccae4
” Phase, and Implied Trend for 1993-2011 of a 55-Year Oscillation for Long-Tide Gauge Recordsa”
It seems they decided 55 was about right and fitted it to each one by OLS. I see no indication of a method that in some way regressed all the data collectively. But I have not paid to get the full text.
Steve Mosher says “The bottom line is why would anyone think you could find a cycle.”
Will since there is 60y component is AMO, at least, that should be refelcted in the thermal component of MSL which we are told is a world threatening large problem.

Willis Eschenbach

Greg says:
April 26, 2014 at 1:23 am

“There’s a strong cycle around 37 years, and a smaller peak at 53 years, but nothing around 60 years.”

I found 57/58 years and the paper actuall is fitting 55 years. Don’t know why they report this as “60y”.
http://onlinelibrary.wiley.com/store/10.1029/2012GL052885/asset/supinfo/grl29523-sup-0005-t02.txt?v=1&s=0603509b8451e52b1b7109d1181c2521b37ccae4
” Phase, and Implied Trend for 1993-2011 of a 55-Year Oscillation for Long-Tide Gauge Recordsa”

Not sure why you quoted that. I was looking at the Amsterdam record. They don’t use Amsterdam in what you cited. What am I missing?

Steve Mosher says

“The bottom line is why would anyone think you could find a cycle.”

Will since there is 60y component is AMO, at least, that should be refelcted in the thermal component of MSL which we are told is a world threatening large problem.

Haaiiiieee, please, stop assuming what you are trying to prove. You have definitely NOT established the existence of a 60-year cycle in the AMO, nor (despite lots of handwaving claims) has anyone that I know of.
w.

Greg

Willis Eschenbach says:
April 25, 2014 at 8:31 pm
“While there is nothing resembling a 60-year cycle anywhere in that data. And since the purported 60-year cycle is the subject of this post, I’m taking that as supporting evidence that such a cycle isn’t there …”
As you say C7W and JJ look similar in form. Jevrejava plot has a peak around 1890 and and 1960. That’s a separation of ~70. Now since the early one is on a strong downward slope the peak will be displaced earlier, contrariwise for later one. That does not seem incompatible with a circa 60 y cycle, for a rough eye-balling of the data.
This cooling trend to warming is significant feature of both MSL and surface temperature that does not fit the AGW theme tune. This is why a lot of studies prefer to start in 1900 so they have nice simple storey about monotonic rise.
If you fit an exponential or quadratic rise to support the foregone conclusion about GHG warming it goes badly wrong if your data goes back into 19th c. ( You can get away with 1880 as ‘internal variation’ but beyond that you’re in trouble).

Girma

Willis
Excellent work Willis.
Could you do the same on the HadCRUT4 dataset, PLEASE?

Greg

Looking at your P.A. for Amdterdam you will note as well as 53 there is peak at 64 and a smaller one at 60.
Now if you combine 53 and 64 as cos+cos = cos * cos, as I detailed above for the short cycles that will give the _frequency_ averaged result of 57.9y modulated by 616 years. I think this is what the JJ SSA plot is showing. This is typical of what SSA does it produces pairs of modulated harmonics that result in a long term variation in amplitude. Unfortunately I don’t think JJ reports any figures, so we’re left guessing from the graphics.
recall the triplet I found in the sub-annual peaks
# as A.M. 0.947 * 58.060 ; triplet asymmetry: -0.039 %
Almost identical modulation period.
Now I don’t see why Chambers et al are fitting 55 and report “60” years. But there is definitely some significant energy in that part of the spectrum.
My chirp-z analysis found two separate indications : 56.7 and 58 and your PA show 57.8. From such fundamentally different techniques, I think that can be regarded as corroborative.

Greg

W. “Haaiiiieee, please, stop assuming what you are trying to prove. You have definitely NOT established the existence of a 60-year cycle in the AMO, nor (despite lots of handwaving claims) has anyone that I know of.”
OK care with words . There is a circa 60y periodicity in last 120 y of SST , I am not concluding that this is permanent , fixed amplitude harmonic “cycle”. But if that variability is there is SST it could be expected to be reflected in MSL , which was the sense of my reply to Mosh’.

Greg

W “Not sure why you quoted that. I was looking at the Amsterdam record. They don’t use Amsterdam in what you cited. What am I missing?”
I was pointing out that they were fitting 55 not the reported “60”. Since your PA of Amsterdam has the two main peaks in that region with a mean freq corresponding to 57.9 , you are finding similar periods in one of the records they did not use.
Now if you are going fit a single sine (which is what their model does) it fit to the mean frequency. This is period of combined AM modulated result of the two frequencies your PA found.
The method is crude and their reporting inaccurate of their results but there is basic agreement with the more general frequency techniques that both you and I are applying.

Greg

W: “Finally, while you are correct that there are some small cycles at 8 years or so, as you can see they don’t do much.”
All this global averaging is stirring a lot different colours in the same pot. Hence you get muddy brown water. It takes spectral analysis to work out pigments were there before you stirred it up.
Both C&W and Jevrejava are pots of muddy water. Despite that some peaks are fairly well defined.
Indeed since most oceans communicate it all gets mixed anyway but with the added complication of varying lags. It’s actually surprising that anything survives.
http://climategrog.wordpress.com/?attachment_id=935
The amplitudes very small in the chirp-z plot because it is done at a very high spectral resolution and the frequency intervals a very narrow. However, we see just four peaks on the decadal scale.
Each peak is spread by noise and experimental errors. To get the total power of a peak it needs to be plotted in freq, not period and the area under the peak calculated. In fact the 20 y peak is no broader than the 7.5y one.
We can get a fair idea from the relative heights.