Sea Level Rise: Hockey Stick or Roller Coaster?

by Chris Hall


Peer-reviewed scientific literature is quite likely the most boring form of prose known to man. I have some experience with this, having been an author, reviewer, and editor covering a wide array of fields in the Earth Sciences for the past 45 years. Whenever you try to sneak in a narrative, a joke, or even an active voice, somebody catches you and raps your knuckles. I tell you this to explain why I so much admire the posts on this blog by Willis Eschenbach, and I am so envious that he is allowed to write something that’s both readable and interesting. Now that I’m retired and don’t have to “play the game” any more, I promised myself that I could try to write a paper without the usual constraints, just for fun. Don’t worry. I’ll be as honest as possible (within reason) and give you the story almost as it happened.

My background is in argon geochronology and noble gas isotopic geochemistry. That may sound pretty esoteric, but by their very natures, these fields allow and even require you to collaborate with other researchers in an extremely broad array of fields. I have worked on geomagnetism, lunar geology, mining geology, tectonics, mantle processes, geothermal power, volcanology, petroleum geology, oceanography, the cryosphere, cloud physics, early man evolution, meteor impacts, and paleoclimate. Along the way, you pick up a lot, mostly by osmosis. Sadly, I don’t have any tales of living in the Solomon Islands (I’m very envious). Aside from a very occasional field trip, I’m mostly a lab based experimentalist with expertise in vacuum systems, lasers, mass spectrometry and data reduction. But, enough about me.

One area that I had not studied in detail is sea level rise. I’ve seen the arguments on both sides and although I’ve been skeptical of claims of gloom and doom, I didn’t know enough to make any contribution. I became interested when I heard that there were claims that sea level rise was accelerating. Most of the arguments about sea level rise have centered around trying to estimate the current rate of rise, and there seemed to a lot of methods and shoe-horning of different data sets into a single coherent story. This, of course, required “adjustments” and alarmists could always find things to be alarmed about, while skeptics could wag their fingers and minimize any discovered acceleration.

Here is a brief but not exhaustive list of articles on WUWT that address the issue:

My interest in the field started after I saw the excitement generated by Nerem et al. (2018), herein referred to as PNAS2018, that claimed to find “climate-change-driven” sea level acceleration over the past 25 years using satellite and tidal gauge records. Now, I have no doubt that climate change has driven sea level rise, but the big question is whether climate-change-driven equals anthropogenic. If it is, then acceleration should be low or non-existent until possibly the second half of the 20th century, followed by a sharp rise. Sort of like a hockey stick, or the rocket sled of the spaceship in the great George Pal sci-fi classic When Worlds Collide. If, however, climate-change-driven is natural, we would expect acceleration to be more oscillatory, kind of like a roller coaster. PNAS2018 does not address this directly, but to answer the question, we have to look into the past.

The Raw Material and Basic Assumptions

I found a treasure trove of tidal gauge data from the Permanent Service for Mean Sea Level

(Holgate et al., 2013; PSMSL, 2022). The monthly data from over 1,500 sites came in the form of a zip file ( with all of the data plus a very helpful Matlab script that can extract the data and organize it into a data structure suitable for further analysis. I’ve used Matlab a few times, but much prefer the open source Gnu Octave “work-alike” as it has a nicer interface (at least in Linux) and is not quite so resource hungry. The Matlab script that came with the PMSL data didn’t work “out of the box” in Octave, but a little simplification of some input format definitions sorted that out nicely.

Although the PMSL data are adjusted to give a uniform estimate of sea level, my hope was that there were not any adjustments to the data that would affect estimates of sea level acceleration. For any function, you can add or subtract a constant or linear trend without having an affect on the second derivative of the function, and therefore the amount of sea level acceleration in mm/yr/yr should remain unchanged with those kinds of adjustments. If adjustments were done piecewise, that should show up as discontinuities in the second derivative.

I also assumed that virtually any variation in sea level due to tectonic effects such as river delta compaction or glacial rebound, whether near or far field, should be nearly linear with respect to time over the period of interest, which is about the past century. Therefore, such effects should have no impact on estimated acceleration. Any anthropogenic signals, such as enhanced mining of water from deep aquifers, global warming of the oceans, local subsidence due to groundwater exploitation, should show up as a positive acceleration, and would constitute a true anthropogenic signal.

How I Did It

After perusing the PMSL data, it was clear that most of the sites have only spotty coverage over the past century or so. One is confronted with varying start and stop dates, along with frequent data outages, or missing data, the bane of working with large data sets collected by other people. My first job was to identify a subset of tidal gauge records that had decent coverage over a reasonable amount of time along with getting a standard time span over which I could try to tease out acceleration signals. I wound up picking the time period of 1925 to 2015, or a total of 90 years as my standard time period. Before 1925 and strangely enough after 2015, the coverage tends to drop off. I sorted out the records that had the fewest dreaded “NaNs” (Not A Number) and came up with the top 100 sites on the hit parade. About a quarter of those sites have perfect data coverage, and the worst have about 90%. The top 100 site locations are shown in Fig. 1.

As you can see, there’s very little coverage in the Southern Hemisphere, and the Atlantic Basin has a lot more data than the Pacific or Indian Oceans. Them’s the historical breaks, I’m afraid. I was just having to hope that a global sea level record would be, ummm, global and I just worked with what I could get.

Next came how to combine data sets to cancel out high frequency noise and “see” longer term accelerations? Remembering my geophysics courses from a lifetime ago, I figured that linearly combining, or “stacking”, the time series might help to cancel out some noise and reinforce the underlying global signals. However, mindful of the high density of sites in Europe and Eastern North America, I decided to divide the data sets into a 5×5 degree grid and perform area weighted averages. Within a 5×5 cell, a simple average of sites within the cell would represent the cell’s average value.

Along with figuring out how to get some sort of global average signal, it was important to also determine a reliable and non-subjective method of deriving a sea level acceleration time series. It is at this point where I explored many different avenues, many of which wound up being “dead ends”. This included using one of Willis E’s most favorite tool, the CEEMD or Complete Ensemble Empirical Mode Decomposition in the R library “hht”. This could nicely tease out the high and low frequency components of tidal gauge records, but there was no analytical means I could see to derive second derivatives from the Intrinsic Modal Frequencies, or IMFs (not Impossible Mission Force), so calculating acceleration would have to be done numerically. Another issue was that it was not clear which IMFs should be used, leading to irksome subjectivity issues. Also explored were methods like Fourier analysis and convolving tidal records with Gaussian distributions. These “dead end” methods had the charm of yielding analytical second derivatives, but they, along with CEEMD, all had problems with what to do at the beginning and end of the records. “Edge” effects had a bad habit of introducing spurious “signals” near the beginnings and ends of records.

Figure 1: Red dots indicate the location of the 100 sites with the most complete coverage of data in the time period 1925 to 2015

I wound up using the same technique used in PNAS2018, which was to fit a quadratic polynomial over a time window. I copied their time duration of 25 years, but instead of just fitting a quadratic over the past 25 years, I had a sliding window centered around each monthly record, plus or minus 12.5 years. I cheated a bit by fitting the quadratic polynomial to 301 monthly data points (25 years + 1 month), so that the acceleration value derived could be properly centered about a monthly data point and not some midpoint between monthly tide estimates. To avoid spurious artifacts at the beginning and end of the records, I only calculated accelerations from 1937.5 to 2002.5, with 12.5 years chopped off the ends of the standard data time window. So acceleration records are only 65 years long and not the 90 years in the standard time window mentioned above.

To check that a data combination record worked properly, I created a second dataset with a synthetic “anthropogenic” signal added. Starting in 1970, an artificial acceleration of 0.084 mm/yr2 was added to the raw dataset. That value is the amount of “climate-change-driven” acceleration detected in the modern satellite record in PNAS2018. If a method of combining tidal records worked to derive acceleration with a high degree of fidelity, the difference between the acceleration record from the raw+synthetic and just raw data should equal the artificially inserted acceleration. Fig. 2 shows the results from a variety of methods that were tried out.

The faint black line is the actual acceleration “step function” added, but the smoother curve shown as the thick black line is the best estimate that you can achieve by using a moving 25 year quadratic polynomial fit. That’s because the fitting procedure effectively performs a moving average of the data. The orange line shows the result from first performing an area weighted average of all 100 sites and then fitting quadratic functions to the weighted average. It works well, but there is a slight deviation in the beginning of the record, and it’s my belief that this is an artifact of the existence of a larger proportion of the dreaded NaNs in that time period. For fun, I tried out this approach for the top 500 tide gauge sites (show as the blue line), and the NaNs made the whole exercise pointless.

I tried to eliminate the NaN problem by “filling in” missing data using the very clever algorithm in the missMDA library in R, which first does a Principal Component Analysis (PCA) on the complete dataset, picks out the top components, then uses them to eliminate any NaNs that might be lurking in the data. The results of that effort are shown in the green line. This improved the situation in the early part of the record, but introduced an artifact near the end. Sigh. Filling in missing data created artificial information, it seemed. Interestingly, only 5 components were needed to fill in the missing data, which given the fact that we are working with 100 records, it indicates a significant amount of correlation between individual tidal records.

Finally, like Swamp Castle, I found a method that stood up. By first fitting quadratic polynomials to the raw data, then doing an area weighted average of the individual acceleration records, it was possible to get a perfect recreation of the synthetic acceleration added to the original data. This record is shown in red. I believe that this worked only because the 301 data point window used for the fitting easily spanned all of the NaNs in the individual records, where no contiguous series of over about 100 or so NaNs occurs.

Figure 2: Comparison of the different methods explored to combine tide gauge data to measure sea level acceleration. An acceleration of 0.084 mm/yr2 was added to the raw data in 1970. This figure shows the difference between raw+synthetic minus the raw data. The thin dashed line shows the synthetic signal. the thick black dashed line shows the best achievable result from fitting quadratic function to a 25 yr span ot data. The best results were achieved by fitting quadratics before doing an area weighted average. See text for a description of the different methods.

OK, so how did we do? The main question I needed answered at this point was:

  • Can we replicate the positive acceleration seen in PNAS?

Fig. 3 shows a blow-up of the averaged acceleration data near the end of the record, as it approaches the value estimated in PNAS2018. My record ends before their’s but as you can see, it is certainly approaching the value they got. So, yes, I’d say that around the year 2000, acceleration was positive and somewhat increasing. My acceleration record did not have any of the corrections used in PNAS2018, such as an ENSO correction and an estimate of interannual precipitation estimates, but my record is pointed in the right direction. I might have tried some corrections, but I was stymied by what I consider a poor “feature” of PNAS2018: a lack of online data and computer code. I’m guessing that if I spent a year or so digging around in various references, it might be possible to figure it out as someone not in the club, but my enthusiasm for that waned very quickly. I fault PNAS for this as many journals now, including the one where I was an associate editor, now require this. Bad show.

Fig. 3 also shows something interesting as there is a distinct annual signal (blue line), possibly due to varying Northern Hemisphere Terrestrial Water Storage (TWS) on land. The red line shows the lower frequency part of the acceleration record by removing the first 2 IMFs from the CEEMD decomposition of the acceleration average.

Figure 3: Close up of the results of performing an area weighted average of the top 100 sites by pre-fitting a moving quadratic funtion over a 25 yr span. The average acceleration is increasing and is headed toward the estimate in PNAS2018. The red line is the weighted average minus the two highest frequency IMFs derived from a CEEMD decomposition of the signal. This removes the annual variations seen in the data.
Figure 4: Full results of the area weighted average model. The dark blue line indicates the full model from all 100 sites. The light blue background is from a sensitivity test where 100 separate models were created from randomly selected subsets of 50 sites. This gives an indication of how sensitive the results are to the selection of sites. For comparison, the acceleration of the HasCRUT4 sea surface temperature record is shown in red.

The next question is:

  • Is there a distinct anthropogenic signal in the area weighted average acceleration record?

The answer to this is shown in Fig. 4, and I suspect that it is definitely “no”. The blue line shows the apparent sea level acceleration over the entire 65 year time span. As you can clearly see, acceleration seems to have varied significantly during the 20th century, with both positive and negative values, whose absolute values far exceed the “climate-change-driven” values in PNAS2018. The 1940s seemed to be a time of reducing acceleration, with the 1950s having sea level deceleration. Acceleration resumed in the 1960s, followed by 1970s deceleration and smaller amplitude variations since then. I tried to do a sensitivity test by running 100 combinations of randomly selected groups of 50 sites (light blue shading in Fig. 4). This gives one a feel for how sensitive the final average is to any particular group of datasets. For fun, I also plotted the “acceleration” of the HadCRUT4 sea surface temperature record (SST) in red, which has some features suspiciously similar to the average sea level acceleration.

I noticed something rather strange when I looked at the results of the sensitivity analysis. The results did not show a Gaussian style grouping around the global average. Instead, there is a gap, where some groupings depart in an oscillatory fashion both above and below the average. This is particularly apparent in the 1950s dip, the 1960s peak and the 1970s valley. Looking into this further, it seems that the presence or absence of the small subset of Southern Hemisphere sites within a group was having a disproportionate effect on the results.

So I decided to calculate a purely Southern Hemisphere acceleration record and it has a maximal correlation with SST acceleration of 0.668, where sea level lags SST by 7 years. This is illustrated in Fig. 5, where SST acceleration is shifted to the right by 7 years. The time series were detrended with mean of zero and scaled to have a variance of one. My Mark I eyeball test suggests that these two time series just might be slightly related. It also suggests that although sea level was apparently decelerating in the Southern Hemisphere in the early 2000s, it is probably accelerating now, but things might be topping out as we speak. Also, the idea of a 7 year lag between SST acceleration and a response in the massive Southern Hemisphere ocean basin does not send my BS meter into sounding any alarms.

However, before we get too excited, it’s important to note that we are dealing with highly autocorrelated time series, and correlations could easily be spurious. I used the auto.arima function in the “forecast” R library to characterise the autocorrelation parameters for the average acceleration record. Then I made 200 randomly generated records having the same autocorrelation parameters using the sarina.sim function in the R “astsa” library. The average correlation coefficient with SST acceleration was 0.479, which is pretty high, so the correlation between the Southern Hemisphere and SST accelerations could definitely be spurious. I constrained the search for maxima to the region where sea level lags temperature, as I didn’t want to find out that the sun comes up because the rooster crows. But Fig. 5 is pretty, no?

So what can we conclude? It seems to me that the tidal gauge dataset suggests that over the last two thirds of the 20th century, apparent sea level acceleration may have oscillated about a mean of zero and an amplitude of roughly 0.4 mm/yr/yr. There’s a hint that sea level acceleration may be related to SST acceleraton, where SST leads sea level by about 7 years. This could clearly be called “climate-change-driven”, but there does not appear to me to be evidence for it to be anthropogenic, if that means that it is driven by the release of CO2. It’s even possible that the sharp peaks and valleys in Figs. 4 and 5 are due to “helpful” corrections to sea level rise data, the discontinuities hinted at earlier. I don’t know.

I welcome reasonable and constructive suggestions and criticisms. Please treat me as courteously as you treat Willis Eschenbach and follow his standard rules.

Figure 5: Comparison of the area weighted model from just the Southern Hemisphere sites and the SST acceleration record. Both records have been normalized to have zero means and unit variance. The SST record is shifted to the right by 7 yr. It is possible that seal level acceleration responds to accelerations in SST with about a 7 yr lag and this is most clearly seen in the Southern Hemisphere sites.


Nerem, R.S., Beckley, B.D., Fasullo, J.T., Hamlington, B.D., Masters, D. and Mitchum, G.T., 2018. Climate-change–driven accelerated sea-level rise detected in the altimeter era. Proceedings of the national academy of sciences, 115(9), pp.2022-2025.

Permanent Service for Mean Sea Level (PSMSL), 2022, “Tide Gauge Data”, Retrieved 09 May 2022 from

Simon J. Holgate, Andrew Matthews, Philip L. Woodworth, Lesley J. Rickards, Mark E. Tamisiea, Elizabeth Bradshaw, Peter R. Foden, Kathleen M. Gordon, Svetlana Jevrejeva, and Jeff Pugh (2013) New Data Systems and Products at the Permanent Service for Mean Sea Level. Journal of Coastal Research: Volume 29, Issue 3: pp. 493 – 504.  doi:10.2112/JCOASTRES-D-12-00175.1.

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January 31, 2023 10:29 am

Thanks, I consider sea level rise to be the primary sum of all climate change, an important measure of climate change, due to the difficulties in measuring temperatures.

michael hart
Reply to  Michael
January 31, 2023 11:05 am

One of the problems is that x amount of heat will equal y amount of sea level rise is a false assumption.

The coefficient of expansion of (sea) water is temperature dependent. Thus, if Trenberth’s “missing heat” went into the surface levels then you would see a much greater sea level rise than if it went into the much colder waters at the bottom or descending waters in polar regions.

It’s a conundrum that allows everybody to be right, or wrong, without knowing the facts.

Last edited 1 month ago by michael hart
Rod Evans
Reply to  michael hart
February 1, 2023 12:18 am

“It’s a conundrum that allows everybody to be right, or wrong, without knowing the facts”.
Not sure if you have given the perfect definition of religion or politics there, Michael?
Either way, I like it. Possibly a perfect summary of religious politicians…..?

Reply to  Michael
February 1, 2023 7:27 am

Not necessarily as sea level rise is biased to arctic and antarctic temperature changes (rise other than thermal expansion/contraction).

John Hultquist
January 31, 2023 11:06 am

 A very interesting analysis. Thanks.
I’m not familiar with all you have done, but wondered about this . . .

only 5 (PCA) components were needed

Studies I’ve seen suggest 5 PCs to be many, that is, the first two do most of the “explaining”. This is a minor point in your work, so I’m just expressing a curiosity thing.

It seems to me that your findings fit well with the reports by folks that actually go and walk on beaches and wave-cut platforms, such as Jennifer Marohasy:

Chris Hall
Reply to  John Hultquist
January 31, 2023 11:44 am

As I recall, the first 2 PCs did explain ~70% or more of the variance for the top 100 detrended tide gauge records. I used the estim_ncpPCA function of missMDA to automatically pick the number of PCs needed to “impute” missing data, and it came up with 5 pretty regularly. I suspect some extras were needed to fill in some very high frequency noise in the raw detrended data.

Last edited 1 month ago by Chris Hall
John Hultquist
Reply to  Chris Hall
January 31, 2023 12:48 pm

Thanks Chris.

January 31, 2023 11:08 am

James Hansen has probably been the most alarmist scientist of note concerning sea level rise caused by man. Do his warnings of possible 3 feet of rise by the end of the century still carry any weight? I, myself, think he is in over his head on the topic.

Reply to  daveandrews723
January 31, 2023 11:26 am

If 3 feet is over James Hansen’s head, then he’s very short.


Reply to  Bob Tisdale
January 31, 2023 1:03 pm

I wish my jokes were half as funny as yours was.

We watched this expert comic improviser on YouTube yesterday:

Jonathan Winters Is in a League of His Own | Carson Tonight Show – YouTube

Listen to at least half of the video

Last edited 1 month ago by Richard Greene
Reply to  Richard Greene
January 31, 2023 9:15 pm

Jonathon Winters and Robin Williams are Tonight show guests. Winters wound up Williams until Robin was getting frenetic; cuts, parries and amusement for all.

Look for the Johnny Carson episode where Winters and Matthew Broderick are guests.
Winters arrives in a Union Cavalry officer uniform, playing as a serious officer.
Matthew Broderick jumped right in and began taking orders, saluting, “yes sir” responses, role playing.

Reply to  daveandrews723
January 31, 2023 12:59 pm

Al Gore is selling one percent shares in his Manhattan Gondola Line to take Wall Street executives to work when Manhattan streets are flooded by sea level rise. I bought a 1% share to diversify my Get Rich Quick Portfolio, which also includes a 25% share of the Brooklyn Bridge. My net worth is going up, up, up — now at $129. Al Gore has 1,953 more one percent shares for sale.
Richard Greene
Graduate, Academy of Lame Humor.
And future Manhattan gondolier

Reply to  Richard Greene
January 31, 2023 1:30 pm

1,953 more one percent shares” Yes you are not (completely) yelling into vacuum. Be careful not to post an identical response to every article though. A lot of “regularity” arrives at this depth of scrolling down.

Bill Powers
January 31, 2023 11:09 am

It matters not what they proclaim because whatever the climate is doing i.e. warming cooling or staying the same, when “Weather” is bad (something that use to be not conflatable with climate) the propagandists position it as proof positive that it is the fault of human actions and the only way to stop bad things from happening is to give over control of all human activity to a central authoritarian government in order to save human kind.

January 31, 2023 11:41 am

Timescales matter.

comment image

Modern sea level rise is a rounding error for the Holocene history.

Ron Long
Reply to  Giving_Cat
January 31, 2023 12:41 pm

Thanks, Giving_Cat, you have cut right to the heart of the issue. The analysis of Chris Hall is interesting, and an honest attempt at resolving an issue, but the give-away is when he says “…time over the period of interest, which is about the last century.” If the non-anthropogenic sea level change, over millions of years, is around 40 meters higher and 140 meters lower than current, then chasing a century of change, measured in a few centimeters, is unable to show any useable signal against the noisy background. What was the century-scale variance in the 180 meters of natural sea level change? Giving_CAt money quote: Modern sea level rise is a rounding error for the Holocene history.

Reply to  Giving_Cat
January 31, 2023 1:04 pm

Great use of charts

Rod Evans
Reply to  Giving_Cat
February 1, 2023 1:14 am

Can you image what the poor souls living around 8,000 years ago had to put up with.
Their version of How Dare You, would have been on a roll blaming the increasing tide on those new fangled farmers cutting down the bush.

Last edited 1 month ago by Rod Evans
January 31, 2023 11:50 am

Let’s get real:
1). Satellite location is measured from ground stations and their orbits. Many calcs involved.
2). Ground stations rise and fall 8 to12 inches a day based on ground “tides” caused by the gravitational pull of the Moon and Sun. Many calcs involved.
3). There is also a correction required for refraction of the radar waves as they enter and leave the atmosphere. Including the amount of water vapor in the radar path. Many calcs involved.
4). Practically, if you’ve done your calcs correctly, you should really just end up determining ocean level as compared to the ground stations, NOT really the distance from the satellites. Since this is not how the numbers are presented, one can only assume that too much faith is placed by scientists on their calculations.
And it is a pretty safe assumption that the “drift” they show as sea level different from tide gauges is actually a measure of error or other bias in their calculations.
Unfortunately if they tell their funding source the truth, they would be out of a job…..

January 31, 2023 11:55 am

Peer-reviewed scientific literature is quite likely the most boring form of prose known to man.

hold my beer

My background is in argon geochronology and noble gas isotopic geochemistry. 

Reply to  Steven Mosher
January 31, 2023 1:07 pm

I thought you were a marketing wallah.

Reply to  Steven Mosher
January 31, 2023 7:19 pm

You contribute nothing to this site, Kindly take a hike.

Reply to  Graemethecat
February 1, 2023 7:07 am

It’s sarcasm and bombast in genius proportions….

Captain Climate
Reply to  Steven Mosher
February 1, 2023 4:58 am

Versus an obese, aged PR hack.

January 31, 2023 12:00 pm

To avoid spurious artifacts at the beginning and end of the records, I only calculated accelerations from 1937.5 to 2002.5, with 12.5 years chopped off the ends of the standard data time window.

To avoid spurious artifacts at the beginning and end of the records, I chopped off the ends of the standard data time window. without testing whether this approach of throwing out data creates its own artifacts.

Chris Hall
Reply to  Steven Mosher
January 31, 2023 12:28 pm

Just let me spit out the words that wound up in my mouth. I did not “throw out” any data. If I had attributed accelerations beyond the point where the center of the fit was closer than 12.5 yr to the end of the record, it would have required me to “invent” data, or assume that acceleration did not change over 12.5 years. I know what artifacts this would have created. It’s very simple. You have 3 choices: a) use the full 301 data points closest to your specific month; or b) shorten the number of months over which you fit the quadratic polynomial; or c) stop trying to fit quadratic polynomials once the 301 month window bumps into the end of the dataset. For a), all “acceleration” values are constant for 12.5 years, for b) you get an increasing amount of high frequency components. I chose c) because I wanted to derive an acceleration record whose statistical properties did not significantly change near the beginning or end of the record.

Captain Climate
Reply to  Steven Mosher
February 1, 2023 5:01 am

Don’t bother with Mosher. He thinks taking an anomaly of data makes its uncertainty disappear. But then, he’s not a scientist or even particularly bright.

Javier Vinós
January 31, 2023 12:12 pm

Congrats on the analysis. It seems to me the conclusion is quite logical and what one would expect naively. Sea level rise is driven by the temperature increase (steric rise) and the cryosphere melting. CO2 has no way of acting on sea level. CO2 has no way of acting on cryosphere melting. Anthropogenic factors must act through two mechanisms. Through human-caused temperature increase (whether significant or not), and through enhanced cryosphere melting from anthropogenic soot (likely to be significant).

Peta of Newark
January 31, 2023 12:27 pm

Sea level rise is an Urban Island Phenomenon
just like temperature

Because: Most tide gauges will be the nautical equivalent of thermometers at airports.
They will thus be at large ports, usually ‘attached’ to large cities which in turn will be on the banks of a large river.
Instead of raking over over coals that myriad other folks have raked over, using the exact same tools, do it the other way round.

First, bin all notion of man made climate change and CO2
Start from absolute scratch.

How to do it: Instead of lamenting long & short records, missing data, invented data and how to create a pretty picture of blah blah blah average -look at each tide gauge individually in extreme detail.

Initially not at its output, don’t pre-bias yourself

For each gauge- look at its geography. Look at how the nearby city has grown and by how much since the gauge became operative
We’re thinking run-off from house roofs, factories, streets, roads, paved areas etc

Look also at the watershed feeding the river that the city is situate on.
How has the watershed changed over that time
Was there extensive forest. Or were wetlands drained so as to plant forest?
Did the farming revolve around perennial crops (grass for livestock) or annual crops (sugar for people),
How did it change – how did the tillage evolve and the easiest way to do that is find some record of how much nitrogen fertiliser has been used over the time period and how that changed. Nitrogen fert is your proxy.
(Many folks will know by now what I’m after)

My assertion is that city building and soil erosion has altered how the landscape handles rainwater.
That cities and eroded soils effectively produce Flash Floods – that river off the watershed, through the city and out into the estuary/delta is either = All or Nothing
(We know that although no-one will accept it, It is that, unless A Really Major ‘something’ has happened, flood waters in rivers should NOT be brown in colour)

And the tide gauge is there waiting and watching.

It is bound to happen that A Flash Flood (almost every rain event will be one on eroded landscapes and large cities) will arrive in the estuary at the same time as a tide is reaching its peak
When it does, the flood will have nothing else to do but plant itself atop the tide and wait awhile till it turns.

Is it true, I can’t see otherwise, that the rising sea is recorded by the height of The High Tide?
Thus the tide gauge will see the flood sitting atop the tide and conclude ‘Aha, the sea has risen’
Of course, placement of the gauge relative to ‘wide open sea’ will be an effect as well.
Sheltered or ‘natural harbours’ will be expect to show a greater effect

So there you have it.
The new hypothesis: Sea level rise is an artefact of urban and land use change

Thus is why some gauges are going up, others down and others nowhere at all

So instead of homogating, inventing and averaging, pick each record apart individually and look for an explanation other than:
CO2 and Everybody Else Is To Blame Now Compensate Me

Just like Surface Stations Project does for thermometers

Last edited 1 month ago by Peta of Newark
John Hultquist
Reply to  Peta of Newark
January 31, 2023 1:00 pm

Put the budget request on the end and send it to the National Science Foundation.

Reply to  Peta of Newark
January 31, 2023 1:21 pm

Sounds good. Have you done it?

DD More
Reply to  Peta of Newark
January 31, 2023 1:27 pm

Peta – “look at each tide gauge individually in extreme detail.”

Some Dutch guys did that with 6 gauges. Seems having half your country below sea level makes it a little more relevant. Broken down enough that they found to have a proper record, you must include a correction for the 18.6-yearly Luna Nodal cycle?

Local Relative Sea Level
 To determine the relevance of the nodal cycle at the Dutch coast, a spectral analysis was carried out on the yearly means of six main tidal gauges for the period 1890–2008. The data were corrected for atmospheric pressure variation using an inverse barometer correction. The spectral density shows a clear peak at the 18.6 -year period (Figure 1). The multiple linear regression yields a sea-level rise (b1) of 0.19 +/- 0.015 cm y-1 (95%), an amplitude (A) of 1.2 +/- 0.92 cm, and a phase (w) of -1.16 (with 1970 as 0), resulting in a peak in February 2005 (Figure 2). No significant acceleration (inclusion of b2) was found. 

 Coastal management requires estimates of the rate of sea level rise. The trends found locally for the Dutch coast are the same as have been found in the past 50 years (Deltacommissie, 1960; Dillingh et al., 1993). Even though including the nodal cycle made it more likely that the high-level scenarios would become apparent in the observations, no acceleration in the rate of sea-level rise was found. The higher, recent rise (van den Hurk et al., 2007) coincides with the up phase of the nodal cycle. For the period 2005 through 2011, the Dutch mean sea-level is expected to drop because the lunar cycle is in the down phase. This shows the importance of including the 18.6-year cycle in regional sea-level estimates. Not doing so on a regional or local scale for decadal length projections leads to inaccuracies. 

Dave Andrews
Reply to  Peta of Newark
February 1, 2023 7:45 am

You’re on to something here Peta. In many cities front gardens are being paved over to create parking spaces for cars. This trend will be accelerated by people wishing to have bespoke charging places for their EVs. This will create greater run off of water leading to local flooding and eventual sea level rise. EVs cause sea level to rise! Brilliant!

Last edited 1 month ago by Dave Andrews
abolition man
January 31, 2023 12:28 pm

Bravo! Encore, please, Chris!
The evidence continues to accumulate that CAGW is poorly crafted hoax, swallowed mostly by the foolish, the ignorant and the immature. Without all the money being thrown at it, it would have died an ignoble death years ago, and been buried in the pauper’s grave it deserves!
I have no nits to pick, but I was wondering about the “How I Did It” section. Were you following a hunch, or was there something Abby Normal that piqued your interest?

Last edited 1 month ago by abolition man
Chris Hanley
January 31, 2023 12:32 pm

The top 100 site locations are shown in Fig. 1.

I hesitate to mention that there appears to be a dense cluster of sites around the Baltic Sea, Finland Sweden and Norway where the sea levels are falling due to post-glacial (isostatic) rebound (see Climate4you — Oceans), sites that are not representative of global trends.

Chris Hall
Reply to  Chris Hanley
January 31, 2023 4:51 pm

Glacial rebound on this time scale should be linear with respect to time, so this should not affect acceleration calculations. This was addressed in the article.

January 31, 2023 12:50 pm

“Peer-reviewed scientific literature is quite likely the most boring form of prose known to man.”

And this article comes pretty close. I set a personal record as a blog editor by reading 48 generally short articles this morning, that I recommended on my climate science and energy blog: Honest Climate Science and Energy

This was article #49 for me, and I sure wished I’d stopped reading after 48.
I read the whole article because that is required before making these comments:

Sea level rise is caused primarily by two factors related to global warming: the added water from melting ice sheets and glaciers, and the expansion of seawater as it warms.

There was (inconvenient) global cooling from 1940 to 1975, as reported in 1975, that was later “revised away,” but it did happen. There was global warming from 1975 to 2015. I imagine that warming could have affected absolute sea level somewhat. Then a flat temperature trend from 2015 to 2023.

I will worry about sea level rise when rich folks stop buying oceanside mansions and start selling the ones they own.

The tide gauges measure relative sea level, with decent accuracy.
The satellites measure absolute sea level with low accuracy — measuring millimeters while they can drift up to 10 feet in orbit.

Where are some randomly selected NOAA tide gauge charts, of several long-term tide gauge records, in the article? A glance at a half dozen of them chosen at random would answer the sea level accelerating question.

How about anecdotes from people who live on oceanfront properties … like the Obamas, and their two oceanside mansions? Someone who has lived in an oceanside home for a long time would have real first hand experience with relative sea level rise.

We have 8 billon first-hand witnesses to climate change, for every year of their lives, and no one ever asks them about it. Why is it that only scientists are qualified to pontificate on climate change?

Some writing tips for future articles:
I wrote a monthly finance and economics newsletter for 43 years.

I have to recommend some simple writing tips for future articles

The title should summarize the article.

The first paragraph should be a summary of the article

Some people will not read further — at least they got your message anyway

The rest of the article should support the first paragraph

Charts should be easy to read.

The writing is good if you can read it aloud and it sounds like you are talking to an audience

If you are going to mention other articles, have a hot link that takes the reader there. You mentioned other articles, but there were no links when I clicked on the titles.

If this list is annoying, just read a few Willie E. articles here. He’s a good writer and presents easy to read charts. Science does not have to be complicated or long winded.

I’m building an ark in Michigan, just in case sea level rise accelerates.

Okay. it’s time to downvote my comment, and my lame joke.
I can take it.

Last edited 1 month ago by Richard Greene
Reply to  Richard Greene
January 31, 2023 1:15 pm

I will worry about sea level rise when rich folks stop buying oceanside mansions and start selling the ones they own.
By definition both actions must happen simultaneously.

Scarecrow Repair
Reply to  Richard Greene
January 31, 2023 4:01 pm

Strange that you responded with such a long boring screed to what you consider a long and boring article. Slow day, eh?

Reply to  Scarecrow Repair
February 1, 2023 12:20 am

You added nothing of value to the conversation, except an insult. If my comment was long and boring to you, then why not just skip it? That’s easy to do.

I use my real name and do not hide behind a silly moniker like you do.

If I disagree with another comment, I try to explain why, usually in detail.

Your method is a childish character attack. Your Mother would be proud of you?

Last edited 1 month ago by Richard Greene
Chris Hall
Reply to  Richard Greene
January 31, 2023 4:52 pm

I see you have not read many peer reviewed articles.

Reply to  Chris Hall
February 1, 2023 12:30 am

I have read hundreds of peer reviewed articles. At least one CO2 – plant enrichment study a month from 1997 through 2022. That subject interested me. I decided to stop reading plant studies at the end of last year because almost all had the same conclusion — C3 plants love more CO2.

That’s about 300 studies that I have read in 25 years. They are tedious reading even if the subject interests you.

I found this article was also tedious reading compared with others at this website. So your charge is completely wrong.

Reply to  Richard Greene
January 31, 2023 6:10 pm

How about anecdotes from people who live on oceanfront properties … like the Obamas, and their two oceanside mansions? Someone who has lived in an oceanside home for a long time would have real first hand experience with relative sea level rise.

I once watched a video clip from a fire and brimstone Al Gore Sunday night meeting in the Carolinas. He made some ridiculous statements about sea level sweeping away human kind or some such and an old fisherman asked a question.

This guy said his family has owned an small island in the bay for a couple generations or so. He has been setting lobster traps (or some kind of sea life traps) at certain favored points around the island and along the island’s boat jetty for more than 50 years. He has never seen any changes in water level. How does this square with Gore’s claims?

Al Gore raised his eyes to the heavens, took a deep breath, and remarked that he has been pondering on how to explain this to a non-scientist for many years. Then he went on with his preaching.

Reply to  AndyHce
January 31, 2023 7:25 pm

Al Gore was awarded a Nobel Prize! How dare you impugn his scientific credentials?

Reply to  Graemethecat
February 1, 2023 12:38 am

Barack Obama won a Nobel Peace Prize
Yet he (the US) was at war for every single day of his eight years in office. War with Iraq (3 years), Afghanistan (8 years), Syria and there may have been others.

Reply to  Richard Greene
February 1, 2023 1:44 am

You’re mistaken. Its an excellent piece. Its not the piece you would have written, but so what? This site should definitely publish some pieces like this. It shouldn’t publish only such things, but some definitely have a place here.

I’m not competent to criticize the math methods used, but taking them on trust, the analysis appears sound and rigorous. The overall method of the test for an anthropogenic signal seems very reasonable.

My view after reading it was, interesting and original method, serious level of analysis, case made, thanks to the writer and to the site.

The Real Engineer
Reply to  michel
February 1, 2023 3:14 am

I found the best thing, which is that Chris tested his method with test data to see that it worked, using a simulated data set with an acceleration added. Many, many papers never test the null hypothesis, particularly medical ones, which is next to lying!

The Real Engineer
Reply to  Richard Greene
February 1, 2023 3:04 am

People are not sensitive to sea level acceleration, unless it is extreme. The article is all about acceleration (or not). the answer is not! Some of your comments suggest you did not understand the article, or perhaps you didn’t read it?

Gunga Din
January 31, 2023 1:06 pm

Sea level rise submerging things and places is an old scare.
Some ancient Romans sites are underwater now, but what’s now underwater that wasn’t underwater 30 or more years ago?

Last edited 1 month ago by Gunga Din
Reply to  Gunga Din
January 31, 2023 1:29 pm

There are also some former Roman docks in England that are a mile inland now–there have been articles about them on WUWT. Sea level was higher during the Roman Warm Period than now?

Pat from Kerbob
Reply to  SteveZ56
January 31, 2023 8:06 pm

Every previous warm period was warmer than this one

Reply to  Pat from Kerbob
February 1, 2023 12:41 am

Not true in the past 5000 years
That is speculation.
Accurate data do not exist to make that claim.

The Holocene Climate Optimum from 5000 to 9000 years ago was probably warmer than the past ten years. But an average of local climate reconstructions is not an accurate global average temperature for that period. So we can’t be sure.

don k
Reply to  SteveZ56
February 2, 2023 2:28 am

Gunga and SteveZ56: What you folks are probably looking at is long term land subsidence and elevation. Those phenomena can have magnitudes comparable to sea level changes and often over VERY long time spans — tens, hundreds of thousands, millions of years. They are how marine fossils end up on top of mountains and how terrestrial fossils end up buried under thousands of meters of younger sediments — by moving up (or down) a small amount every year for a lot of years.

January 31, 2023 1:11 pm

The key takeaway for me is that tool capabilities strongly influence data analysis. ie There will be a way to “check the work”, as done in the well written post, so long as the data processing tool development efforts remain in the hands of finicky nerdy math types. A clue that tools get coopted will be when the user interfaces branch between “climate mode” and “business mode” based on user-controlled input(s). ie A signal/flag/button could be used to get the desired result that data might not support without special handling.

Reply to  KevinM
January 31, 2023 6:17 pm

What I read is that there are now a goodly number of computerized analysis tools, some relatively inexpensive, like Excel, some very expensive, and others at various points in between. What they have in common is the ability of anyone to do all sorts of things with data without having any idea what the tools really do or what they require in order for the results to be meaningful.

The Real Engineer
Reply to  AndyHce
February 1, 2023 2:59 am

Are you suggesting that Chris didn’t know what he was doing, because I disagree strongly. Tools used incorrectly produce results which are meaningless, for example the hockey stick temperatures. We know that it was bad maths, undisclosed, and probably data “adjustment” as well. Chris’s method used on temperature data would be very interesting, it should reveal any data tweeking etc.

Chris Hall
Reply to  AndyHce
February 1, 2023 7:46 am

The tools used in this analysis were all open source programs, consisting of either programming languages or programs that employ standard statistical techniques that are referenced in their documentation. Most analytical programs have lurking “under the hood” lots of old, well-debugged code, often in FORTRAN. The programs I used include:

Gnu Octave, LibreOffice Calc, Free Pascal, R, RStudio, GLE, all run using the Ubuntu 22.04 operating system. The article was written using LibreOffice Writer.

Most of the work was done on an ancient laptop that originally came with Windows Vista, but which stubbornly refused to upgrade past Win7 to Win10. So Win11 is definitely off the table. Wiped the drive partition and installed Ubuntu. Big improvement.

Reply to  Chris Hall
February 3, 2023 3:21 pm

I meant to imply no misuse – merely acknowledging that specialization has produced tools that hopefully become standardized by profit-seeking entities so that errors cost somebody something. As a corollary, old institutions use old tools because they learned how to use them – learning new tools is an investment. A statistical charting tool that printed warnings on the chart about “not enough data” or “not the right data” for predictions would make that tool unloved.

January 31, 2023 1:55 pm

In Figure 4, the graph for SST (Sea Surface Temperature?) acceleration in C/yr^2 is always negative between 1938 and 2002, with the least negative acceleration in 1970.

Does this mean that sea surface temperature was decreasing prior to 2002, or only rising at a slower rate in 2002 than in 1938? Do you have a graph of the actual SST vs. time, or its “velocity” in C/yr vs. time?

As Michael Hart below points out, the coefficient of expansion of water depends strongly on temperature. For fresh water, the average expansion over temperature ranges is as follows:

40 – 50 F 4.4 – 10.0 C 2.5(10^-4)
50 – 60 F 10.0 – 15.6 C 6.2(10^-4)
60 – 70 F 15.6 – 21.1 C 1.06(10^-3)
70 – 80 F 21.1 – 26.7 C 1.37(10^-3)
80 – 90 F 26.7 – 32.2 C 1.68(10^-3)

Sea level would rise much more if any additional heat went into warming the surface layer than if it was conducted into the deep abyss, where any expansion is negligible.

However, sea level rise would depend not only on thermal expansion, but also on any net ice loss from the Antarctic and Greenland ice caps, and (to a lesser extent) mountain glaciers.

Since the Southern Hemisphere sea level seems to closely follow the sea surface temperature, this would imply that Antarctica isn’t losing much ice,

Chris Hall
Reply to  SteveZ56
January 31, 2023 4:56 pm

The SST graph is the acceleration of SST, not the rate of rise. So when you see a large negative acceleration, it usually means that this occurs when the rate of rise is a maximum. Remember that the second derivative of the sine function is proportional to the negative of the sine function.

January 31, 2023 2:03 pm

So I decided to calculate a purely Southern Hemisphere acceleration record and it has a maximal correlation with SST acceleration of 0.668, where sea level lags SST by 7 years.

There are some serious misunderstandings about ocean surface temperature and ocean heat retention.

Globally, the oceans absorb most heat in December an January. All it does is accelerate the water cycle to transfer heat coming into the SH to land in both SH and NH – the so named “wet” season in the tropics. The atmospheric water is at minimum when the heat input and evaporation is greatest. It just means more rain and snow over land driven by temperature difference between ocean and land.

The global ocean surface temperature reaches its maximum in June and July. But that is when atmospheric water reaches its maximum due to heat advection from ocean to land slowing down. The warming NH land during the boreal summer reduces heat advection. The oceans and land temperature reach the same maximum.

Deep ocean heat content is a function of the water cycle. When it slows down, more heat is retained in the ocean. That is what is happening, on average, globally.

So if you want to correlate ocean expansion with ocean temperature, you should be looking at ARGO data at least down to 2000m. Net evaporation is the only factor that can alter deep ocean heat in a matter of decades. Heat transport from surface to below 200m is a slow process. Think in the order of kindreds to 2000 years. This is a good paper on abyssal heat transport and the periods involved:

It is impossible to heat water from the surface when it has an unlimited supply of icy water at depth. The formation of sea ice is the most significant driver of deep ocean heat. That is actually reducing in the NH. There is a very interesting change occurring in the deep water to the south and east of Greenland.

All that aside, it is good work and could be improved by looking at river runoff to assess net evaporation, which is inversely correlated to deep ocean temperature, and ARGO data for actual deep ocean temperature.

One certainty is that any current rise in ocean level is not too far off reversing. Greenland and Iceland already have increasing ice coverage and Greenland is gaining elevation at 17mm/year. So the concern over sea level rise will rightly shift to sea level fall because that will occur with a vengeance; 40m lower within the next 10,000 years. Nothing has changed apart from climate bothers think that CO2 can cause it.

Steve Case
January 31, 2023 2:43 pm

These 65 tide gauges from the Permanent Service for Sea Level (PSMSL):

 SanFrancisco, Fernandia, Honolulu, New York, Key West, Fremantle, Sydney, Brest, Seattle, Helsinki, Baltimore, Balboa, Boston, Philadelphia, Los Angeles, Pensacola, Sewells Pt, Galveston, Stockholm, Portland ME, Marseille, Oslo, San Diego, Ketchikan, Victoria, Trieste, Charelston I, Astoria, Newlyn, Trois-Rivieres, Poti, Slipshavn, Frederikshavn, Hirtshals, Aarhus, Travemunde, Turku/abo, Korsor, Pietarsaari/Jakobstad, Kobenhavn, Mantyluoto, Hornbaek, Gedser, Frederica, Esbjerg, W Terschelling, Tuapse, Furuogrund, Visby, Ratan, Warnemunde 2, Wismar 2, Cuxhaven 2, Smogen, Kungsholmsfort, Olands Norra Udde, Ijmuiden, Harlingen, Delfzijl, Den Helder, Hoek Van Holland, Vlissingen, Maassluis, Galveston an La Jolla, 

when analysed for acceleration in mm/yr², a very tight distribution centered between 0.0 and 0.1 mm/yr² is produced as follows;

-.07> 1
-.01> 2
0.02> 5
0.03> 1

Any rational person would say that’s no acceleration.

The -.07 mm/yr² outlier is Trois-Rivieres on the St Lawrence in Canada.

Chris Hall
Reply to  Steve Case
January 31, 2023 4:57 pm

Over what time period did you do these calculations?

Steve Case
Reply to  Chris Hall
January 31, 2023 5:31 pm

Over the length of their individual records. The Brest France record goes back to 1807 nearly all of the 65 records had nearly 100 year’s worth of data. Thirty years which is what Colorado University has just isn’t
enough, the noise overwhelms the signal.

Chris Hall
Reply to  Steve Case
February 1, 2023 12:29 am

Ah. Then you are trying to measure the average acceleration over a very protracted period of time, which in the case of Brest, is over 200 years. For Brest, your acceleration value is only correct for the time near the beginning of the 20th century. PNAS2018 was trying to estimate acceleration near the beginning of the 21st century, using a 25 year window. I used the same width of window, but allowed the window to shift earlier in time, with the earliest time for the middle of the window being the middle of 1937. My results do show an overall mean acceleration near zero over the 90 year period I was examining. So we’re not really disagreeing. However, if you want to “see” an anthropogenic signal, you have to use a shorter window, otherwise you are averaging in far too many records that exist before a CO2-induced sea level rise signal could even start. For an effect really kicking in at around 1970, the longest period of acceleration fitting you could possibly use is about 40 years, and that would have rather poor temporal resolution.

Steve Case
Reply to  Chris Hall
February 1, 2023 2:38 am

For an effect really kicking in at around 1970, the longest period of acceleration fitting you could possibly use is about 40 years, and that would have rather poor temporal resolution.

Quick and dirty for two successive 40 periods from those 65 tide gauges comes up with:

1940-1980 0.125 mm/yr²

1980-2020 0.5 mm/yr²

There’s just too much noise to make much sense out of short periods. And remember that Dr. R. Steve Nerem’s Sea Level Research Group tells us that it’s 0.084 mm/yr² for a 30 year period.

Here’s a quick graph to illustrate the point:

65 TideGauges 40 yr running rate.png
Last edited 1 month ago by Steve Case
January 31, 2023 3:10 pm

No Tide Gauge Sea Level calculation is valid in any sense without correcting individual tide stations for local vertical land movement. Failing to use station data corrected by long-term continuously operating GPS stations results in incorrect (read false) results. There are stations available and sea level researchers know this — but few use it.

Tide Gauge Records ONLY record local Relative Sea Level and cannot be combined to determine regional or global SLR.

Chris Hall
Reply to  Kip Hansen
January 31, 2023 4:59 pm

If local vertical movement is linear with time over the past century, this will not affect the acceleration calculation. This is addressed in the article.

Steve Case
Reply to  Chris Hall
January 31, 2023 5:27 pm

Pretty much what anyone can figure out on their own.

Reply to  Chris Hall
February 1, 2023 7:43 am

Chris ==> IF VLM was perfectly linear, which it is not, then it would not affect trend.

However, many many studies of VLM at tide gauges show that VLM is NOT linear — it is the results of many causes: settling of fill under the structure to which the tide gauge is attached (pier, dock, etc), GIA (which is somewhat linear), fresh water extraction (which increases steadily with population), on and on.

Doers it matter? Of course it does! SLR at most locations is in the single millimeters per year range. A pier piling is known to shrink (get shorter) by a mm or so per year — adding to RSLR if the tide gauge is attached to the pier.

I have covered this issue here at WUWT many times.

Using the fantasy that all confounders can be 1) ignored 2) average out or 3) can be statistically controlled for just doesn’t cut it in real science.

Of course, I agree that the “sea level rise is accelerating!” meme is meaningless…but not based on such simplistic (even if complicated) calculations of bad data.

Chris Hall
Reply to  Kip Hansen
February 1, 2023 1:43 pm

You seem to have missed a major point of my article. The various factors that you talk about could indeed cause local sea level rise to change in a non-linear way, especially factors such as local extraction of groundwater, loading of the ground near the gauge from construction, etc. However, those are anthropogenic signals and would be expected to show up by increasing acceleration by the end of the 20th century. If effects show up in only a small subset of sites, the signal would be diluted by data from other sites, but the signal would still contribute to an overall increase in acceleration. However, the big non-anthropogenic factors such as widespread sediment compaction at river deltas and glacial rebound effects can almost certainly be assumed to be linear with respect to time at the decade to century timescale I’m looking at. So one should not expect to see a hockey stick acceleration graph from natural local factors, only from local anthropogenic factors. In addition, anthropogenic signals would not be expected to produce an overall oscillatory response, which is what I apparently found. A response suspiciously reminiscent to the acceleration trends of sea surface temperature, by the way, but I hesitate to push that causality button.

don k
Reply to  Chris Hall
February 2, 2023 3:17 am

Chris: Kip is correct. And sadly, the vertical movement may not be linear if human activity — e.g. pumping fluids — is responsible. If they’re pumping water, they’ll likely stop if/when it turns salty. If oil, they’ll stop when they run out of recoverable oil or when the associated infrastructure damage gets to be a problem and they stabilize things by replacing the oil with water as they pump. How big can the problem be? Pretty big. cm or tens of cm a year. But only locally. I’m not sure it even affects any of your tide gauges. I don’t know what you’re supposed to do about that situation. Treating it as noise may be the only realistic option.

spangled drongo
January 31, 2023 6:19 pm

This agrees with this paper paper that shows for a large part of the world’s oceans, when corrected for vertical movement, tide gauges show virtually no SLR:

Relative sea-level rise and land subsidence in Oceania from tide gauge and satellite GPS (

And the latest mean sea level for arguably the best gauge is still a couple of inches lower than the first MSL in 1914:

January 31, 2023 8:02 pm

1: Acceleration is not the yearly increase, or even the total increase over a longer record.
What are Newton’s Laws of Motion?

  1. The acceleration of an object depends on the mass of the object and the amount of force applied”

An example of acceleration is the effect from dropping an object in a vacuum under Earth’s ground level gravity; e.g., Distance falling multiplied by time, i.e. 32 feet per second squared.

Marking a number on a chart, then an another number for the next time period, and yet another number for the next number is not graphing acceleration. That method simply charts incremental change over a period of time.

Yes, you can calculate the averaged tidal increase/decrease over a time period, but that ignores the +- averaging over distant locations and that the only rational observation is that the heavily adjusted tidal numbers still only incrementally change annually in both plus and minus directions.

The Real Engineer
Reply to  ATheoK
February 1, 2023 2:50 am

That is why he is extracting the second derivative! This method is probably as good as is possible with the data available.

Reply to  The Real Engineer
February 1, 2023 5:32 am

He still doesn’t measure “acceleration”!

What is measured are incremental changes, on adjusted data (The NOAA way).

Using alleged tidal measurements that are impossible to accurately measure as NOAA claims by satellite.
Satellites measurements have an error range in multiple centimeters. Identifying changes less than satellite measurement error are absurdity.

February 1, 2023 12:11 am

Chris Hall,

Thank you for your article and mathematical analysis.
My choice in writing something similar would be to leave out the satellte-based measurements. They cannot be properly linked to international, fundamental standards.
Re your list of earlier WUWT articles on sea level change,
can I please promote one of my own?
I wrote this in 2013 in the hope that it would influence National Geographic to be more critical of veracity with their published assertions from a decade before.
Tempis fugit. Soon it will be 20 years after National Geographic wrote that issue of alarmist drivel, so should we WUWT readers promote a new approach to Nat Geo for the 20–year celebration?
Reader comments welcomed. Geoff S

Alastair Brickell
February 1, 2023 2:22 am

Many thanks for taking the time to prepare this information for us all. Very interesting and useful.

The Real Engineer
February 1, 2023 2:47 am

Chris, you have achieved the goal you wanted to reach! This is the most clearly explained and logical complex scientific paper I have read for YEARS. Such is the academic publishing world that actually telling a story which can be followed is not allowed, presumably because it might help someone else! Very well done.
David CEng etc.

Chris Hall
Reply to  The Real Engineer
February 1, 2023 7:28 am

Golly gee.

Joseph Zorzin
February 1, 2023 3:31 am

Tony Heller has dozens if not hundreds of videos on the topic of sea level rise.

don k
February 2, 2023 2:45 am

Chris: Nice article and good comments. I’m normally dubious about using polynomials to get acceleration. Right units. But polynomials describe conic sections or worse and that’s not how non-astronomical things behave. At least not very often. Exponential or cyclic behavior seem more common for geophysical things. On the other hand, you seem conscious of common problems with data fitting, so what you’ve done may well be OK. I’ll need to reread the article a few times over a period of weeks/months to come to a conclusion.

Anyway, thanks for posting it. A lot of work there. Appreciated.

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