An Investigation using Tidal Gauge Data Part 1 – Preliminary Analysis
by Dr. Alan Welch FBIS FRAS — 2 December 2025
Note: This paper will be published in two mutually-dependent parts, this part and the second to follow in day or two, depending on the publishing schedule here.
Introduction
The question “Why does the Global Sea Level Rise have a sinusoidal variation with a period of about 26 years?” was asked in the comments to one of my papers in 2023. My reply pointed out that the satellite coverage was only 95% and so what was happening in the other 5% may be relevant. In my follow up paper “Measuring and Analysing Sea Levels using Satellites during 2023 – Part 2” . I analysed the Tidal Gauge results of 9 ports in the northern regions of the Atlantic Ocean and above up to the Arctic Ocean. The analysis was very simplistic but showed promise so now a more detailed analysis will be carried out using procedures and methods developed more recently.
Before proceeding another question could be “so what?”. The graph is basically almost linear (R2 = 0.99) with fits using quadratic or sinusoidal adding very little on this. But in 2018 Nerem et al produced their paper concentrating on a quadratic curve, using the small quadratic coefficient to be representative of an acceleration. If they had contained this to the confines of the data all would have been acceptable, but they proceeded to extrapolate for over 80 years and release their paper. The paper as still being used as a reference in many papers each month. Over the 8 years it has been used to create dramatic scenarios of flooded cities and frighten all the children. The investigation of a sinusoidal curve has tried to balance the picture. A point overlooked in using the quadratic curve is that if the calculations had been started in 2008, they would now show a deceleration. What paper would Nerem et al then write?
The paper is in two parts.
Part 1 contains preliminary analyses in which each Tidal Gauge is processed up to the Spectral Analysis stage.
Part 2 carries out Curve Fitting in which residual values (Actual values minus values on a best fit curve) are judged against a curve that is the combination of 2 or 3 sinusoidal curves using peak periods derived from the spectral analyes.
Preliminary Analysis
This study makes more use of Tidal Gauge data than NOAA data but uses Spectral Analysis.
The 9 locations are Reykjavik – Iceland Torshavn – Faroe Islands
Aberdeen – Scotland Lerwick – Scotland Bergen – Norway Barentsberg – Svalbard Narvik – Norway Murmansk – Russia Tiksi – Russia
Only Aberdeen and Bergen have datasets spanning more than 100 years, with Torshavn covering only about 50 years.
Before analysing these 9 ports the results for Brest will be studied as this covers over 210 years although there are a couple of sizeable breaks in data. This work was carried out earlier, but some aspects will be of interest. The data are shown in Figure 1.
Figure 1
The usual curve fitting is carried out as shown in Figure 2. Again, possibly excessive precision has been used to be on the safe side. This is not in order to indicate accurate fitting but with possible high values on the “x” axis power terms might need this extra precision.
Figure 2
A Spectral Analysis was carried out on the data and Figures 3 and 4 show the outcome for long and short periods.
Figure 3
Figure 4
Figure 3 indicates a peak (barely a peak) at a period of 1429 years. Most other Tidal Gauges show much higher periods, but it would be interesting to see how sinusoidal curves with periods in the region of 1000 years would compare with the quadratic fit.
Curve fitting was carried out for curves with periods of 1000, 1100 and 1200 years. The equations are shown in Excel Format.
= CONST + AMP * SIN(((SHIFT + 2 * A1)/PERIOD) * PI()) (Equation 1)
| CONST | AMP | SHIFT | PERIOD |
| mm | mm | years | years |
| 7341.5 | 406.5 | 1409.0 | 1000 |
| 7371.2 | 437.5 | 1575.4 | 1100 |
| 7430.1 | 496.9 | 1731.4 | 1200 |
Figures 5,6 and 7 compare the quadratic curve with the 3 sinusoidal curves, together with comparisons of slope and acceleration.
Figure 5
Figure 6
Figure 7
The next part may be good lateral thinking or a bit more La La Land!!
Using the 1200 year curve and extrapolating from 500 BC to 2500 AD results in the following.
Figure 8
The indicated periods may be arguable. It surprised me that the last Thames Ice Fair occurred as late as 1814. A more worrying interpretation of this graph, if it is remotely indicative, would be that the sea levels (and associated Temperatures) do not peak until about 2450. Could events be as bad as that? How hot were the Roman and Medieval Warm Periods?
Finally with respect to Brest Figure 9 shows the residuals, that is the actual values minus the values on the quadratic curve and Figure 10 the spectral analysis of these residuals.
Figure 9
Figure 10
The periods of the peaks vary from those on the full data spectral analysis, and it is not very easily seen on figure 9 that there may be a decadal oscillation of about 93 years. This was
investigated by creating data files of random values, one set as straightforward random values and one set as random numbers with a standard variation. Many cases were run and figures 11 and 12 show one case from each series.
Figure 11
Figure 12
First impressions are a bit worrying as they indicate curves with periods in the range 10 to100 years but closer inspection shows these all have small amplitude (labelled theta on these plots) of about 2 whereas in the actual tidal gauge plots these are between 10 and 30 for the residuals. These Theta values are relative values and do not indicate actual physical values.
(I may not have described the process clearly, and may not have described it correctly, so if anyone out there can help I would be very grateful)
Turning now to the 9 Tidal Gauge datasets they will be considered starting with the longest period of measurement and then in roughly an order of reducing period. But before proceeding the following 9 small figures (in Figure 13) show the outcome of the earlier curve fitting exercise of a 26-year period curve to plots of the residual values, that is the actual values minus the value on the quadratic fit. Whilst a roughly 26-year period curve fits in many positions there is evidence of other, usually, longer period components as can be seen in the Aberdeen plot where a larger 85ish year variation is obvious. The larger spectral analysis peaks will refer to primary modes, but shorter ones may be other primary modes or secondary modes. One problem with these 9 analyses was that the data plotted is a moving average based on 101 data points. With no breaks in data this equates to just over 8 years but as there are several gaps in the data this may distort matters. Averaging removes most of the short-term frequencies and makes it easier to perceive the general form.
Aberdeen .. Bergen .. Narvik
Reykjavik .. Murmansk .. Barentsburg
Lerwick .. Tiksi .. Torshavn
Figure 13
Each of the 9 Tidal Gauges will now be looked at showing the initial data from NOAA Web Site, processed data showing best fit quadratic curve, residuals (actual value minus value on best fit curve), spectral analysis plots and tables of results. The tables are basically values from the software’s original use, which was variable star analysis. The first column is Frequency
(1/Period) in cycles per year. Time is the Period at which this Frequency occurs in Years. Theta has been referenced in this paper as Amplitude.
At this stage no curve fitting was carried out as in most cases there are 2 or more peaks. The Amplitudes used on the Spectral Analysis (amp) and the Amplitudes of the Sinusoidal Curves (AMP) have been studied for known multi sinusoidal curves and it has been found that the Amplitudes for a pair of curves, 1 and 2, are related by the equation
AMP2 = AMP1 * SQRT(amp2/ amp1) (Equation 2)
Using this it can be estimated the relative dominance of each curve shown on the Spectral Analysis graphs.
Bergen
Narvik
Narvik (reduced data set)
The data before 1947 has been discarded due to the large gap in readings and the suspicious initial data values close to the beginning of the data.
Reykjavik
Murmansk
Barentsburg
Lerwick
Tiksi
Torshavn
Coming Soon:
Having applied spectral analysis to a number of Tidal Gauges, Part 2 will use the findings to derive sinusoidal curves.
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per Figure 4, You have a 100-year frequency chart based on 100-year time chart. When you go t-to-f you lose half the years unless you undersample, In order to undersample you have to _assume_ a periodic time waveform. The writing obviously contains thorough work but I now have to read it looking for bad math.
“Figure 3 indicates a peak (barely a peak) at a period of 1429 years.”
Not ready for prime time.
Link in the INTRO didn’t work but I found:
https://wattsupwiththat.com/?s=Measuring+and+Analysing+Sea+Levels+using+Satellites+during+2023+%E2%80%93+Part+2
My comment is not really related to this article. However, I’ve noticed other places that some folks equate “rise” with “acceleration.” Also, while searching using DuckDuckGo, its Search Assist provided this: “… leading to a rise in sea levels that has continued to accelerate due to ongoing climate change.”
Short answer – no. The gullible and ignorant may believe otherwise.
For those who understand my answer, no explanation is necessary. For those who don’t, no explanation is possible.
This is entirely consistent with what the late, great John Daly was stating in his website “Still Waiting for Greenhouse” two decades ago. He was perhaps the first to point out the worthlessness of IPCC AR statements on increasing sea levels. He pointed out the failure of claims about rising seas to be reflected in actual tide gauge measurements.
What is interesting is that wikipedia still contains a number of outright lies about him and his work.
Story tip (sorta)
A Singapore company built a wind turbine installation vessel for Maersk, which Maersk canceled, and they want justice. $475 million seems high for a ship, but it’s not clear what special functionality it has or how much of the contract’s payments were canceled, since it is 98.9% complete and three months from delivery.
What it really shows is the collapsing wind turbine market.
https://gcaptain.com/seatrium-launches-arbitration-against-maersk-affiliate-over-terminated-475-million-wind-vessel-contract/
Related by means of the ocean, this time gCaptain swallows the decarbonization party line inconsistently.
https://gcaptain.com/methanol-gains-momentum-as-marine-fuel-but-cost-and-supply-challenges-persist/
A few days ago a query to Google’s AI came up with this:
According to the PSMSL tide gauges,
what is the acceleration in the rate
of sea level rise since 1992?
According to analysis of global tide
gauge data from the Permanent Service
for Mean Sea Level (PSMSL), the acceleration
in the rate of global mean sea level
(GMSL) rise since the early 1990s has
been estimated to be approximately
0.013 mm/yr² to 0.0128 mm/yr².
DateStmp
YYYYMMDD
20251129
That is at odds with Dr. R. Steve Nerem’s claim of 0.071 ± 0.025mm/y² here
It’s puzzling why Dr. Welch cited Dr. Nerem’s work since his Sea Level Research Group changed the historical data over the entire life of their satellite record. The chart below only goes to 2016 as all the changes they made starting with their 2018 release was just too difficult to depict on a similar chart. The 2018 release changed values on the X and Y axis resulting in the acceleration that Dr. Nerem obviously wanted to find: HERE
Oops I see I did try to depict the post 2018 data hence the chart’s title “Overlay …” Here’s the original:
What I found useful was the graph of “acceleration” predicted against time which shows that that 80 or more years are required to show an acceptable value. Up to then the graph behaves like a slightly under-damped vibration.
I have been working with the NASA data since 2018 and it does change a lot but hopefully time will tell.
The following three titles by Dr. R. Steve Nerem tells a story:
Why has an acceleration of sea level rise not been observed during the altimeter era? LINK
Is the detection of accelerated sea level rise imminent? LINK
Climate-change–driven accelerated sea-level rise detected in the altimeter era LINK
I asked Google what the difference between 0.013 mm and 0.0128 mm in microns was. It gave the answer as 0.2 microns.
Also from Google “The thickness of thick human hair ranges from approximately 80 to 90 microns or more, . . .”.
Somebody complained about my mental arithmetic before, so I asked Google to divide 80 by 0.2 – it told me the answer was 400.
Well, it is only an estimate, I suppose – to a variation of one 400th of the thickness of a human hair per year. Not only that, it’s “the rate of change . . . ” of the rise. Only a truly deranged ignorant and gullible “climate science” believer could possibly accept such ridiculous nonsense without batting an eyelid!
Moreover, i really do not understand the explicit ways how satellites can measure EXACT sea levels. We are talking really small differences. I just look at long tide gauges. But maybe somebody can point out to me why satellites are important on this issue.
I could not fathom the big differences between satellite and tidal gage measurement, especially since both set of numbers are touted by NOAA.
In Dave Burton’s website he points to a presentation by Dr. Willie Soon, starting at minute 17. He states inexplicable corrections of raw satellite data and the drift calibration problems, as well as the coarseness of data. Very revealing. Personally I stick with tidal gage data.
[youtube https://www.youtube.com/watch?v=1gmW9GEUYvA?version=3&rel=1&showsearch=0&showinfo=1&iv_load_policy=1&fs=1&hl=en-US&autohide=2&wmode=transparent%5D
The problem with comparing Tidal Gauges and Satellites is that at no stage can we compare like with like. Also, what are we comparing. The Tidal gauges are spot readings spread, not uniformly, across the globe. The satellites after processing give “global “ values and a range of sub areas. The “global” value is not exactly that due to it not being a total coverage.
When it comes to the dreaded “acceleration” (wish we had a better name) it is very dependent on total period the readings cover. Tidal Gauges can be anything up to 200ish years and the shorter the period the higher any “acceleration” or even” deceleration” can be but with very long periods the “acceleration” generally converges on values in the region of 0.01mm/year2. With the satellites it is also dependent on the starting time of any readings in that a few years difference can change an “acceleration” into a “deceleration”.
Slopes can also be compared but these are not total average slopes but in the case of Tidal Gauges the current slope. Satellites are showing about 3 mm/year and a quick look at some Tidal Gauges shows values above and below this, but the checks are not comprehensive.
In the video with Dr. Soon’s arguments (see above) he shows time separated fudging of whole data sets with satellite readings.
Further, I sought some input from ChatGPT. He/she/it states
a) satellites measure relative to the earth center as opposed to tidal gages, which reference adjacent terra firma. I suggest the end result should be the same, when averaged globally.
b) satellite data apparently receive glacial isostatic adjustments (GIAs), since the ocean basins are still getting larger as the earth rebounds from weight compression during the last ice age’s weight-down. It is said to be 0.3mm/yr (or 1.2 inch/century). Since the ice age roughly 100 centuries passed, while assuming a linear change, the localized GIA rise calculates to 120 inches. That looks like a huge ‘fudger’, when added to sea level, not knowing water influx nor temperature changes during this long time frame. The earth does not act like compressible foam, but ultimately the local compression will be equal in uplifting elsewhere, again on a large scale.
As to Sparta Nova’s comment below, yes, large waves deflect an incoming radar wave front, according to the relative surface angle on the water wave, not bouncing the signal back to the origin. Though, this radar scheme might work on a still morning in the doldrums. And yes, the needed fractional mm resolution is not possible with a 25 mm radar wavelength. More fudging.
Finally, if, how and when are the satellites calibrated, including for drift?
They could target land data, like a dry salt lake, but then the earth center must be referenced by gravity ‘fixing’, since that is the satellite data focus. Another source of systemic error.
“a) satellites measure relative to the earth center as opposed to tidal gages, which reference adjacent terra firma. I suggest the end result should be the same, when averaged globally.”
Tide gage error cancellation could be true if the same number of gages are on upward-moving land and downward-moving land. West coast gage count does not equal East coast gage count.
You need a time machine and a printed slide deck to allow global seafaring data to come from more places than the Northern Hemisphere Atlantic.
Someone please correct this.
As I recall, satellite measurements of this type fall in the range of centimeters.
I am also unclear how one can measure the sea level with surface waves.
“…maybe somebody can point out to me
why satellites are important on this issue.”
____________________________________________________________________
If you control the means of measurement and you control the analysis and nobody can check your work then you can make your data find whatever you want it to find.
Hence Nerem around 2011 LINK wanted to find acceleration and was able to finally do it in 2018 after adjusting the 1992 – 1998 data which produced a quadratic curve with a belly instead of a hump as shown in the 2016 and 2018 comparison in the chart below:
Similar things happen in large companies with data access permissions.
Only hope is that the original data was not deleted and replaced with edited versions.
———————————————–
rise since the early 1990s has
been estimated to be approximately
0.013 mm/yr² to 0.0128 mm/yr².
DateStmp
YYYYMMDD
20251129
That is at odds with Dr. R. Steve Nerem’s claim of 0.071 ± 0.025mm/y²
———————————————-
I should point out tht 0.013mm/yr^2 and 0.0128 mm/yr^2 are both inside Dr. Nerem’s measurement uncertianty of +/- 0.025mm/y^2.
If Dr. Nerem’s estimate of uncertainty is correct, then neither 0.013 or 0.128 can actually be known to be accurate. The uncertainty interval subsumes the stated values.
Subsumes, a new word for me to remember. (-:
That aside, I’m wondering if Google’s AI didn’t understand that the question was asking for the time series from 1992 to current not the series:
1807-1992; 1807-1993; 1807-1994; 1807-1995 and so on up to 1807-2024
Because it sure agrees with an analysis of acceleration back to the beginning of the tide gauge records See the chart below:.
https://klimaatgek.nl/wordpress/2025/08/29/baanbrekend-onderzoek-zeespiegel/
It’s in Dutch but Google translate does a reasonable job. Part of the discussion about sealevel measures from tidal gauges in the North Sea concerns the presence of the 18.6 year Lunar nodal cycle.
The Lunar Cycle shows up in part 2 in both the Tidal and Satellite data.
The problem in Holland is how to assess the difference between land falling and sea rises. In fact, given its history that has been a major concern.
I know because i was born in the thick of it, in Haarlem so i am very aware of the history. Fascinating stuff btw..
Thanks for the link to the article..i read it in Dutch (of course).
Given yr name you probably did as wel, toch?
Yep. Haarlem noord, Schoterbos, 1950.
Nou, kijk es aan. Ik zat vroeger op HFC Haarlem.Vlakbij dus. Ik kom uit het Ramplaankwartier, bouwjaar 1964. Mijn oudere broer Dick komt uit 1950. Zijn vroegste herinnering was de watersnoodramp v 1953.
Mijn oom en tante woonden in de Meester Jan Gerritslaan.
Groetjes.
From the Nerem paper
Its really sad that this fit is seen to have any predictive power at all by people who ought to know better.
Is Nerem also expecting the radiative imbalance to more than triple over that time to supply the energy needed to warm the oceans and melt the ice? I dont think anyone is predicting that so on the face of it, the Nerem paper doesn’t pass the sniff test.
Agreed. As an Engineer we always treated extrapolation with caution, Quadratic fitting could be useful, at times, within the bounds of the data.
I had hoped that the following would be added at the start of the paper as well as the sentence from Kip.
“The author of these two papers is aware that some methodology and processes used may be subject to doubt and criticism which he has voiced within the papers. Nevertheless, much of the content may be of interest and useful in that a cluster of Tidal Gauges surrounding the upper Atlantic and Arctic Oceans are systematically studied.”
sinusoidal variation with a period of about 26 years?
The Dutch found it to be an 18.6 year cycle. https://www.researchgate.net/publication/236019217_The_Effect_of_the_186-Year_Lunar_Nodal_Cycle_on_Regional_Sea-Level_Rise_Estimates
It is the Lunar cycle infulance.
Dr. Nils-Axel Mörner – “So sea level cannot be rising. That is a physical law. in figure-skating: when they rotate very fast, the arms are close and then when they put out their arms, they stop by themselves.” Faster day, lower sea level.
So it has been slowly dropping overal since the 1970’s.
Also noticed all 9 of your stations are Artic areas. How are you adjusting for Glacial Rebound?
The 26 year (29 year) cycles are when judging the residual data to the straight line as part of undermining the Nerem Quadratic curve fitting with its resulting “acceleration” hysteria and how we must judge that “acceleration” in the long term for a few more decades. In Part 2 I show how the period of about 19 years is common to Satellite and Tidal Gauge data.
No adjustments incorporated – tried, rightly or wrongly, to keep it simple.