An answer to: Is the rise in sea levels accelerating?

Guest essay by: Jan Kjetil Andersen

There is a well-established consensus concluding that the global sea level has risen over the last century, and that the level continues to rise. However, the question about whether the rate is accelerating or not, is more inconclusive.

To cast some light on this, I have analyzed the latest scientific papers on this topic. Thereafter I made my own time series analyzes based on tide gauges in the GLOSS network.

All data and software used in the analysis are available for download. See links in the end of the article.

I invite the readers to a discussion about the conclusions.

Firstly the findings from the academic papers:

I start by the IPPC AR5.

Chapter 3 is about Ocean observations, and here is exactly what I am looking for:


Figure 1 (IPCC AR 5 page 287 their figure 3.13)

(a) Shows the global mean sea level anomalies (in mm) from the different measuring systems as they have evolved in time, plotted relative to 5-year mean values that start at 1900. We see that the sea level has risen with 20-25 cm in the last 130 years, which gives an average rate of 1.5 to 1.9 mm/year.

(b) Shows the gauges observations from Church & White compared with satellite altimeter. In this close-up, we see a rise of 5 cm in 19 years, which gives an annual rate of 2.6 mm/year.

This shows that the rate has been higher in the last two decades than in the last century, but the next figure in AR 5 shows that this rate is not unprecedented in the record.


Figure 2: (IPCC AR5 page 289 their Figure 3.14)

Quote from IPCC text: “18-year trends of GMSL rise estimated at 1-year intervals. The time is the start date of the 18-year period, and the shading represents the 90% confidence.

The estimate from satellite altimetry is also given, with the 90% confidence given as

an error bar.”

The figure need some extra explanation to be understood outside the context of the AR5 report. According to the figure, there has been no accelerating since 1920. We see that both Church & White and Ray & Douglas observe approximately the same annual rise of around 2.5 mm/year between 1920 and 1940, and then there is a fall 1 mm/year before the rate rebounds to 2.5 mm in the late 1980-ies.

The Jevrejeva et. Al observes a maximum rate of 4 mm/year in the 1940-es but the series stop before the increase in recent decades. Satellite altimeters shows a steady rise with a relative small variation between 2.9 and 3.9 mm/year.

The satellite measurements has a very short series in the figure because the series only goes from 1992 to 2012. That means that only two years can be calculated with an 18-years trend.

I think a very important piece of information comes out of this figure. We see here that in reality IPCC find no evidence for accelerating sea level rise after 1920. The rise before 1920 was real, but can hardly have been caused by the small amounts of greenhouse gases emitted at that time. The CO2 level in 1920 was according to Nasa 303 ppm, or just 10% above the pre-industrial level and the warming that could have caused the sea level rise has to come before that. (

So why are we then hearing about the accelerating sea level rise in the media? Well, I think there are at least two reasons for that; firstly even though the figure does not show any acceleration, they does not draw that conclusion from it. What they say is this (AR5 Page 290): ”while there is more disagreement on the value of a 20th century acceleration in GMSL when accounting for multi-decadal fluc­tuations, two out of three records still indicate a significant positive value. The trend in GMSL observed since 1993, however, is not signif­icantly larger than the estimate of 18-year trends in previous decades”.

This is rather inconclusive.

Secondly, other academic papers show an acceleration, I examine one of those below.

First, I want to update the IPCC analysis with the latest data.

The results presented in this section of AR5 are quite old. The newest of the three papers presented in the figure is Church & White, which was published in 2011, and this paper use data up to December 2009 only.

However, the authors keep extending the raw data used in their paper and the data series now includes December 2013. The reason for not having newer data is that quite many stations around the globe report late and a large bias would be introduced if the last years were based on the early reporters only.

I have run the extended series through my own statistical analysis created in php, Javascript and Google Graph, which gives the results below.


Figure 3: Blue line show Church & White 2011, with data up to Decemebr 2009. Yellow line is the authors later added data. Red line is satellite altimeter data used in AR5. Green line is altimeter until February 2016.

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Figure 4: My Results from running an18-year trends of GMSL rise estimated at 1-year intervals. The time is the start date of the 18-year period. This should be similar to IPCC figure for Church & White and Altimeter, except that I have not included any confidence interval, but I think the uncertainty is equally well visualized by plotting each monthly data point. I think the match is close, although not perfect, but it should be close enough to confirm that the same data sources are used.

Then I have extended with latest Church & White data, and latest altimeter data.


Figure 5. The data in this plot goes to December 2014 for Church & White and, February 2016 for Satellite altimeter.

We see that the last added gauge data (in orange color) lift the last part of the plot to unprecedented high rate, but the period is far too short to make any conclusions from that.

This is what we get out of the AR5 with updated data.

I then go to another recently published paper on the topic.

A resent paper is the Temperature driven global sea level variability in the Common Era by Kopp et al. of Rutgers University, published in PNAS January 4th 2016. This paper provides an estimate of the global sea level changes over the last 3000 years.

They claim:

Historic GSL rise began in the 19th century, and it is very likely (P≥0.93 P≥0.93) that GSL has risen over every 40-y interval since 1860 CE. The average rate of GSL rise was 0.4±0.5 0.4±0.5 mm/y from 1860 CE to 1900 CE and 1.4±0.2 1.4±0.2 mm/y over the 20th century. It is extremely likely (P≥0.95 P≥0.95) that 20th century GSL rise was faster than during any preceding century since at least −800 CE. “

That may be right, but it does not answer whether we experience an accelerating rate or not. The figure below is from this paper.


Figure 6 (From Kopp et al; PNAS2016 their figure 1d)

What I read from figure 6 is that the sea level started to rise in the 19th century, well before climate change could have any effect and has continued on a quite stable rate since then, but the authors project that an acceleration may occur soon.

Rather than to continue searching more academic papers, I decided it was time to make my own research, so I went to the sources.

Analysis of gauge data from the GLOSS network

Global Sea Level Observing System (Gloss) is a network of 281 globally distributed coastal tide gauge stations. The Core Network is designed to provide an approximately evenly-distributed sampling of global coastal sea level variations.

One of the challenges in making use of statistics from gauge stations is the importance of using a so-called common vertical datum i.e. a reference point. The stations in the GLOSS network has such reference called Revised Local Reference (RLR). Each station use a calibrated local datum for all the data series, but there are no common global vertical datum for all stations. This means that we get an error if we try to mend together different short series to make one large average.

However, if we limit the series and analysis to a timespan where all the selected series goes continuously from start to end, we do not need any common datum to make a correct average.

I have selected three set of series, which I call very long series, long series and medium long series.

Very long series are 1900 through 2013; long series 1925 through 2014 and medium long are 1950 through 2014.

In addition, all selected series have at least 80% complete monthly readings.

Of the 281 stations in the Gloss network only 6 fulfils the criteria for very long series, 9 for long series and 22 for medium long series. The list of these stations is given in the end of the article.

Two averages are made for each set of series; one simple average, and one global gridded average. The latter one was computed by dividing the globe in a 6×12 grid consisting of 72 cells measuring 30 degrees latitude times 30 degrees longitude. First, an average of all stations within each grid cell are computed. The global average is then an average of the all grid cells with a weighting of each grid cells according to its area. Because degrees longitude are shorter closer to the poles, the grid cells are also smaller. The relative length of one degree longitude, is cosinus of the degree latitude at the same spot. The weight of each grid cell is therefore the absolute value of cosinus of the degree latitude in the middle of the cell.

The benefit with this method is that we get less bias toward the areas with most stations. The gridded average is therefore the most important of the two.

The plots of absolute rise and 18-year trend are shown below.

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a)Very long series(1900 through 2013):Simple average in blue, gridded in red. The plot shows 36 months floating average and linear trendline of mean sea level above local reference point. b)18-year trend for very long series. Both start and end years for the 18-year period are shown. No discernible acceleration is evident from the moving average plot, but the linear trend line reveals a very small acceleration. However, all of this small acceleration is due to the small spikes in each end of the series.
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c)Long series (1924 through 2014): The gridded average show smaller growths d)18-year trend for long series. We see that the largest rise occurred in the period starting around 1965. No discernible acceleration can be seen after the 1965 – 1973 period
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e)Medium long series(1950 through 2014), simple average in blue, gridded in red f)18-year trend for medium long series. We see an acceleration for the simple average, but any acceleration for the gridded set is more dubious. Except for a very short spike in the end, the rise in recent decades are no higher than 1960-ies. All the trend in the gridded series is due to the spike since 2011. To visualize this I have included a trend line of a series that stops in 2011 (green color).

Figure 7 a)-f). Absolute rise and 18-year trend for three different time intervals.

The plots in figure 7 suggest that there has been a small spike in the rise the last few years. This spike is also consistent with altimeter readings

However, this spike may be contributed to natural variability. All the studies presented in AR5 above indicate 18-year trends that were significantly higher than the 20th century average at certain times and lower at other periods. This is likely related to multi-decadal variability like the Atlan­tic Multi-decadal Oscillation and/or Pacific Decadal Oscillation. The last spike may also have been caused by such a natural occurring variation.

So what to make of all this?

I have not made any regression analysis to show whether the small increase is statistically significant or not. I welcome anyone to do that. However, I think the graphs gives a quite clear message even without further analysis; if there is any acceleration, it is infinitesimal.




1. IPCC AR5 Chapter 3:

2. The Global Sea Level Observing System (GLOSS):

3. Church, J. A., and N. J. White, 2011: Sea-level rise from the late 19th to the early 21st century. Surv. Geophys., 32, 585–602.

Both the paper and sources are freely accessible

4. Kopp & al. Temperature-driven global sea-level variability in the Common Era. PNAS 2016

Full text:

5. Nasa GHG gases: (

6. Satellite altimeter at Boulder university:

7. Data and software used to make this analysis:

List of GLOSS stations used:

Very long series (6 stations):

Station Country code Station ID
Fremantle AUS 111
Stockholm SWE 78
Trieste ITA 154
Brest FRA 1
Marseille FRA 61
San Francisco USA 10

Long series (9 stations):

Tuapse RUS 215
Pensacol USA 246
Newlyn GBR 202
Atlantic City USA 180
Galveston II USA 161
Key West USA 188
Balboa PAN 163
La Jolla USA 256
Honolulu USA 155

Medium long series (22 stations):

Kushiro JPN 518
Mera JPN 359
Manila PHL 145
Legaspi Albay PHL 522
Ko Lak THA 174
Tregde NOR 302
Adak Sweeper Cove USA 487
Newport 351 USA
Fort Pulaski USA 395
Hilo Hawaii USA 300
Ceuta ESP 498
La Couna ESP 484
Barentsburg SJM 541
Antofagasta 2 CHL 510
Tofino CAN 165
Prince Rupert CAN 167
Sitka USA 426
Apra Harbur Guam GUM 540
Pago Pago ASM 539
Kwajalein MHL 513
Midway Island UMI 523
Wellington Harbour NZL 221

99 thoughts on “An answer to: Is the rise in sea levels accelerating?

  1. To get to a two meter rise by 2100 would require an acceleration of 3.7%. Which means it would have to rise some 8cm IN THE LAST YEAR! This is physically impossible. Having any acceleration is meaningless, it mathematically it has to be 3.7% to make the 2 meters.

    • To get to a two meter rise by 2100 would require an acceleration of 3.7%.

      There’s other ways to get 2m sea level rise than by constant acceleration.
      Also 3.7% isn’t an acceleration. Accelerations are in distance/(time)^2 like x mm per year per year.

      • “There’s other ways to get 2m sea level rise than by constant acceleration.”
        Nope. Mathematically it is the only way. Try it on a spread sheet. Unless you mean at a constant rate, which means sea level would instantaneously have to jump to 20mm per year from the current 1.74mm per year. Nature doesnt work that way, there is always an acceleration to change rates.

      • Yes, but a constant acceleration requires the smallest constant
        rises. Any other model requires that if it doesn’t go up much now
        it has to accelerate even more in the future.

    • You need a time in there to make it an acceleration. 3.7% for how long? For example, per year^2.
      Also, a percentage increase per year^2 isn’t a constant acceleration. A constant acceleration would be the same amount increase per year^2. A constant percentage per year^2 means a larger acceleration when the value is larger.

  2. “However, I think the graphs gives a quite clear message even without further analysis; if there is any acceleration, it is infinitesimal.”
    Great article, and great conclusion. I, obviously, concur 100 percent. Sometimes just looking at a graph tells us all we need to know.

    • Yep! If I’ve learned anything from W Briggs it’s that when investigating a time series, all you have to do sometimes is to look at it!

  3. Good post, and I think graphs are a reasonable way to deal with noisy data. A shift from 2.5 to 4mm a year to 40+mm a year looks patently unreasonable.

    • Javier says:
      ….sea level started to increase around 1700. Every century afterwards appears to have seen an increase in sea level rise…
      …IPCC projection appears reasonable if global warming continues.
      UN/IPCC is politics. Period, full stop. Disregard them
      If sea level rise began to increase in the 1700’a, there is no way that human emissions were the cause.

      • Clearly not the cause of the rise since 1700. According to that last graph is steeper recently, so that does not preclude a human contribution. Since that data is showing increasing variability over the whole period that recent increase is not necessarily AGW either.

      • dbstealy says:
        If sea level rise began to increase in the 1700’a, there is no way that human emissions were the cause.
        Which begs the question: what is the cause? The CAGW hypothesis is inadequate as the rise predates any application of the hypothesis. Nothing in the prevailing scientific earth science paradigm provides an explanation for an increasing rate of rise over three centuries.
        Time to review the paradigm by questioning all assumed knowledge and where possible adopting alternative explanations from the perspective of alternate paradigms.

      • Bob,
        I didn’t see anything that needed a sarc tag…only the null hypothesis expressed with maybe a little dig at the warmists.

      • Bob Shapiro says:
        ‘Oh, look. There’s the Medieval Warm Period and the Little Ice Age. Gee, maybe it is all/mostly Natural Variation!’
        The MWP & LIA represent Natural Variation to the extent that the hypothesis is accepted that thermal expansion is the primary driver of sea level rise, ie that the heat is hiding in the oceans. However on longer time scales indications are that sea level rise has been near relentless.
        The Cobb et al 2016 paper referenced in this text above figure 6 found only one period of sea level decline over 27 centuries of sea level rise.
        If this is correct then there are other factors driving sea level rise. I think that restricting the cause of sea level rise to thermal expansion is reducing a complex problem to a neat solution, but it does not really provide a persuasive argument for me.

  4. ..Slight correction …” they does not draw that conclusion from it. ”
    ……….. Does should be do ?

  5. Sorry, could I ask for help? I need a link to any good critique of Parrenin, et al’s paper in which he insists that the rise of CO2 and temperature are historically synchronous. I keep searching for “wuwt Parrenin” or any other likely terms, but no matter what search engine I use I get that malfunction that I don’t have a name for: The search results all show Parrenin & a complimentary phrase, but when you click on it, the site has nil about Parrenin or his paper. I’m sure I explained that badly. If you try it yourself you’ll see what I mean.

    • Hello Penelope,
      I see what you mean. I tried:
      parrenin global warming
      and got a huge number of hits on a music group.
      parrenin+global warming+wuwt
      got all global warming (and a huge chunk of the entire internet)
      parrenin + global warming + wuwt
      got good results. I used Duck Duck Go, not G**gle. No idea why it is so fussy about spaces surrounding the ‘+’.
      Here is a paper at NoTricksZone:
      They do not think too much of the paper.

      • Thanks, Tony, that was the only one I had already found. I was hoping for something more substantial than just calling it a gag. I, of course, know of a couple studies that contradict Parrenin’s conclusions. But I had it thrown up to me & would like to be able to actually comment on it.
        Maybe someone else has actually seen something on it I can’t imagine how they get the search engines to malfunction like this. Really annoying.

  6. Even if it WAS accelerating, what the hell does anybody think they could do about it? Invest in mountainside chalets?

      • Nice point. In a 1905 paper, Akitsune Imamura predicted the big one would hit Tokyo and cause 100,000 deaths due to the subsequent fires. He recommended beefing up fire fighting capability. He was ridiculed for spreading ‘groundless rumor that deludes the society.’ Of course the big one did hit in 1923, killing 100,000 in a fire storm.
        Wonder how much California is investing in earthquake response compared to ‘green’ energy. Instead of shutting down functioning energy producers, how about demolishing a few thousand unsound (death trap) apartment buildings?

  7. cm, mm, inches, feet, furlongs, km, miles — make up your mind! Pick one unit and use it on all the graphs. That way moving from one to another won’t give the false impression of some great slope or change.

  8. So…with supposedly massive amounts of CO2 being spewed into the air by humanity, even since 1950, there has been absolutely NO CHANGE at all, that could be considered an “acceleration” in the NATURAL sea level rise trend, on this planet, at all.
    Well THAT has to suck for a theory that depends on stuff like that happening…

  9. In my opinion the measurements of sea level are nearly worthless.
    Statistical analysis can not make the data accurate.
    Statistics applied to inaccurate data is just mathematical m asturbation.
    I doubt if sea level can be determined to the nearest +/- two inches
    What kind of accuracy can you get with only 281 stations in the Gloss network?
    A quick analysis in my head says each station must cover 500,000 square miles of ocean !!!
    281 measurements for 70% of our planet’s surface are a wild guess, not accurate data.
    When the data are no good, alternate indicators are needed:
    (1) Are rich people around the world still building huge homes on the ocean?
    Answer” Yes.
    Do they know something about sea level we don’t know?
    (2) Are the Republic of Maldives atolls getting huge new resorts, and they already have a big airport?
    Answer: Yes.
    Do they know something about sea level we don’t know?
    Do all these rich people and corporations want to throw their money away building something that will be threatened by accelerating sea level rise?
    Of course not.
    My conclusion is sea level rise is not accelerating, unless there good data to prove it is.
    Good data do not exist.
    Alternate data suggest some very smart and rich people do not see any sea level risk.

      • Bongo.

        A quick analysis in my head says each station must cover 500,000 square miles of ocean !!!

        Tide gauges cover the local where they are sited. The fact that water is a liquid means that you do not need to measure every square mile of open ocean.

    • Richard Greene,
      There is some good data. Not much, but what there is indicates thar sea level rise is pretty close to zero.
      There are photographs taken a century ago that show no sea level rise. And the late, great John Daly wrote about a high tide MSL mark cut into stone that shows current sea levels are not much more than when the mark was cut in the early 1800’s.

      • Don’t forget that local tectonics are similar to or even exceed sea level rise. Globally, the sea level is rising, but numerous areas are stagnant or rising out of the ocean due to various reasons.

    • “(1) Are rich people around the world still building huge homes on the ocean?
      Answer” Yes.
      Do they know something about sea level we don’t know?”
      They probably know that they can buy a huge home on the ocean today and move to another huge home on the ocean in 10 years. (for some rich people, it’s way less than 10 years) When you have huge amount of money, and still earn more than what you can use in the same time, you need to spend it, otherwise it’s worthless.
      For the hotels in the Maldives, you have to ask them in how many years they expect to break even. If their business plan tell them that it’s 10 years, they don’t really care about sea level in 20 years.

    • Thank you Richard, but I if we could use rich people’s behavior as a proxy to understand sea level change that would mean that the rich people knew something we other do not know.
      And I don’t think they do, at least not about the rate of sea level change.

  10. What is the latest numbers by year from the tide gauges.
    When I worked with Church and White’s database, I always wondered why they selected a certain subset of the all the tide gauges available. The number was very high, but they left out a large number that just looked like data selection to me.
    Of course, the PMSL database is so, so hard to work with and I wonder how you did it. I think nobody has been able to say that the average tide gauge rose by 1.5 mms/year in 2013 for example versus 1.4 mms/year in 2012.
    The issue is, we have to be able to say that there is no acceleration starting in 1992 and ending in 2014 from the tide gauges because this is when the satellite algorithms say there has been an acceleration. But no one can really work out by year what the tide gauges are really saying.

  11. Figure 1(b) shows a distinct spike of about 5 mm above the long-term trend at 1997-98 in both tide gauge and satellite data followed by a lapse back to their long-term trends. I am trying to get my head around how an El Niño event could cause a short-term sea level rise. Any ideas on this would be welcome, from those who know about oceans and weather and such.
    Other than that, I would say that the satellite altimeter measurements in figure 1(b) show – if they show anything – a slight deceleration starting about 2007. Certainly no acceleration.
    Glad to see I’m not the only one who thinks eyes are a very good tool for picking trends out of graphically presented data series.

  12. groundwater abstraction for irrigation is apparently resposible for something like 0.8mm/ year, and only started after WWII. Tends to squash any arguments over unprecedented rise as without it the rise would have been lower in recent decades than previous

  13. I live in the later stages of an interglacial, during yet another warmish phase, one which is not likely to last. Like the viagra-popping grandpa, I’m grateful for whatever slight rise I can still get.

  14. If the solid surface of the earth was smooth, it would be entirely covered in water with a bit of ice, some floating, some not. The solid surface is not smooth but is seen as a bucket. We can’t measure the water level very well. We can measure the changes in the volume of the bucket even less well. The margins of error seem a bit pointless.

  15. Jan, you have done a lot of work to get your conclusions. I think you are working too hard. Let me show you a shortcut you would benefit from. First, I ignore all the accelerator guys and go back to basics. I like what Chao, Yu and Li did (Science April 11th 2008). They corrected all available sea level data since 1900 for any water held back in artificial reservoirs. This gave them a straight line water level curve for the last 80 years. Anything that has been linear that long is not about to change anytime soon. The slope of their straight line section was 2.46 millimeters per year. That works out to just under 10 inches per century. Al Gore at the same time was touting 20 foot dea risf per century. According to him that was enough to inundate Florida so he shows a map of Florida under water in his book. And gets a Nobel Prize for that trash. I don’t doubt that there can be some deviations from the prediction based on Chao Yu & Li paper but I expect it to hold in the long run and will not be surprised if a hundred years of melting will give us a sea level rise of just10 inches. As to all these half meter or two meter sea level changes, these are just fantasies of novices you can safely ignore.

    • Arno, I see they estimate that about 30 mm of sea-level equivalent is now stored in man-made dams and the surrounding soils, and I see that they then get a straight line in their estimates.
      However, there are several studies of sea level rise with diverging results and this 30 mm is not enough to explain the difference.
      Church and White use the results from Chao Lu and Li, and argues that about a third of this effect are offset by groundwater depletion which contribute to ocean rising.
      One very interesting information concerning reservoirs is that globally, the rate of dam entrapment has slowed significantly in the last decade or two. This should contribute to some acceleration in the sea level rise.

  16. A better question and which cannot be answered because we don’t know enough about sea level change is “is sea level change unexpected?” At this question, which btw ignores the direction of change, we can examine our expectations and try to understand why our expectations lead us where uncertainty suggests we have no business going. Based on what we know we lack the moral authority to conclude anything about sea level change.

  17. From 1960-2016 there has been no measurable increase in sea level, at Hobart Tasmania and at Albany Western Australia. From 1915-2016 at Fort Denison, Sydney New South Wales, there has been a 5 cm rise in sea level. At Port Pirie in South Australia, there has been a 10cm fall from 1945 to 2016. I cannot see any acceleration or even net rise coming out of these figures. The variation in level between consecutive years is often far greater than the variation over the century.
    I think that this question remains in play because the Warmistas and CAGW fanatics want it so desperately to be true, even if the figures do not support them.

    • Interesting plot. However, you need to consider that MEI ( is that what you are plotting ) is partially a temperature index. You have detrended SSL It is to be expected that temperature changes will be visible in SSL due to thermal expansion, so noting that temperature causes thermal expansion is not a shock result.

      • To be clear was neither my plot nor my idea to compare the two.
        As we currently understand it, the atmospheric and oceanic components of ENSO do not create cold or warm water. They just spread the water across the ocean surface in different ways. This is what makes the relationship surprising.

  18. Jan, A semantics nit-pick. You write, “…well before climate change could have any effect …”
    In fact, only climate change could be the cause. There would have been little or no effect from human sources though. Climate change is constantly present. The argument is about human effects if any. In fact, depending upon the geologist, the mid-19th century may be marked as the end of the Little Ice Age, which would quite naturally be accompanied by sea level rise. Some geologists like Mary Hill place the end later, in the earliest 20th century. Otherwise thank you putting your work out for us to read and consider.

    • Sorry but it does not depend “only on Climate change”, it also depends on what the tectonic plates are doing and what the sea and ocean bottoms are doing as well.
      Earthquakes can seriously change tide level gauge reading as can isostatic rebound.

  19. Firstly, thanks for a well written article. (Bigger graphs would be nice, some of the text is illegible.)
    The main problem I have with all this is adoption of the idea of sliding trends. What is this supposed to show? If you are trying to remove some of the higher frequencies to “smooth” the data use a proper low-pass filter. A sliding trend is yet another of the crap “filters” used in climatology.
    It has a very lumpy frequency response and lets through quite a lot you hoped to filter out, but far more importantly it has negative lobes which invert some of the variability
    This explains the problem ( a sliding trend is like a running mean on the rate of change : same problem).

    • Here is the freq response of sliding trend “filter”. This is unsigned *magnitude*, so I have coloured the inverting lobes to make it clear. ( Fourrier transforms produce a complex number, so it is conventional to visualise this by looking at the size or magnitude of that complex number. This is by definition a positive quantity ).
      If you want to improve your analysis by using a proper filter you can find some code you should be able to adapt for you php page here:
      Rather than doing sliding trends, I would suggest you analyse rate of change of sea level ( by taking the first difference of your data points ) then apply a suitable filter. You will find that a much shorter filter will “smooth” the data well enough if you chose a well behaved filter.

      • BTW , if ( Prof. Marotzke ) you don’t believe the negative lobes make yourself some test data with a period of 10 years and compare with the 18y sliding trend ( ensuring that you log the trend at the central date of the window, not the end date )

      • Prof. Marotzke replied to my criticism of his paper which used slinding trends to mangle the data by saying there were no inverting lobes in a Welch filter ( which was not even the filter he was using). re Marotzke & Forster 2015.
        Here is the kind of thing you get ( this is for a Welch fitler, another one with inverting lobes. At least this one attenuates enough so that they are not too big. )

  20. Greg said:
    “It has a very lumpy frequency response and lets through quite a lot you hoped to filter out, but far more importantly it has negative lobes which invert some of the variability
    This explains the problem ( a sliding trend is like a running mean on the rate of change : same problem).”
    Only if you choose a bad period for the running mean – as you did in your badly argued example. The data you plotted has a clear 4-5 year periodicity, so that the 60-month running mean you used produces a very bad result. You compared a simple 60-month running mean with a triple one based on 30 months – apples and oranges. A simple 30-month running mean gives quite a good result:
    You make an elementary error by using an even-period running mean – to be properly centred, and be statistically robust, it must actually have a centre, as with 61 months or 31 months.

    • The whole point is that no one is doing a frequency spectrum on the data before choosing which window length to use for their runny average, so there is no way to choose a “good” or “bad” length. If you use a well behaved filter you don’t need to worry about whether it is “good” or “bad” length for the content of the data, you chose the filter with respect of the frequencies you want to remove. That’s the purpose of filters.
      The point of the comparison is that if you want a “smoother” you actually get a smoother result with much shorter filter if it is does not leak and distort the data. One of the most common ( post criticism ) justifications for using runny averages is that they are “compact”. The 30mo triple running mean is no longer than the 60 mo RM but does not invert the peaks in the data.
      Your WTF plot makes that point rather well, despite your assertion that it “gives quite a good result”. Just notice how the two main peaks in the data get truncated into slight dips; the circa 1982 dip gets inverted. There is also a lot of high frequency wiggles that should not even be there after a 30mo filter operation. That is what you consider “quite good”? How “statistically robust” do you think that is? LOL.
      You also make the elementary error of assuming that an even number of elements can not be correctly centred. Probably because you are limited to clicking around on on rubbish like and are not capable of designing or writing a filter yourself.
      You should be wary of accusing others of making errors without checking.

    • From the link you provided about hazards of “smoothing”:

      In general, if the original data contain asymmetric peaks, smoothing can seriously and persistently shift the peak locations;

      This is NOT a result of “smoothing” in general, a well-behaved filter will not produce such artefacts. It IS the hallmark of runny averages, and for that matter, sliding trends.

  21. I wrote in October 2015 an article for the skeptical italian blog about the sea level acceleration in
    Norway-Russia(37) and Italian (42+3) stations. Also I used the data from
    Houston & Dean, 2011 for the acceleration of USA stations.
    My article is in italian but the so-called
    contains plots and tables in english.
    The final conclusions I drew were not so different from the one presented
    USA: (-0.001+-0.015)mm/yr2 (1.96 sigma or 95% confidence) from Huston and Dean,2011
    NORWAY-RUSSIA: 0.078+-0.039)mm/yr2 (1 sigma). Noting sistematic differences
    between Norvegian and Russian stations:
    NORWAY:(0.029+-0.041)mm/yr2 (1 sigma)
    RUSSIA:(0.11+-0.13)mm/yr2 (1 sigma)
    ITALY:(-0.004+-0.095)mm/yr2 (1 sigma)
    Maps and values in the support site.
    So, the most probable situation seems to be no acceleration and I
    agree with the author’s conclusion.

    • RUSSIA:(0.11+-0.13)mm/yr2
      That’s a huge acceleration. That means that over 100y the annual rate of sea rise increases by 11mm/y.
      …. with an even bigger uncertainty.

    • NORWAY:(0.029+-0.041)mm/yr2
      That is also pretty significant amount of rise but again with an even bugger uncertainty. What these results show is that there may be a problematic acceleration but the data is too poor to detect whether it is real or not.
      Concluding that there is no acceleration is not the correct way to interpret that.

  22. One thing that is interesting is how much difference the gridding makes to the early part of the very long series though with only 6 series there won’t be much gridding going on, it does reflect the geographical weighting function. Presumably this is giving much more weight to one or two low latitude sites and down playing higher latitude sites.
    It looks questionable whether this gridding is appropriate and whether some of these longer series can be trusted.

    • Greg, much of the difference in the very long series is because one of the six is Stockholm. The land area around Stockholm has a sinking sea level because the area experience a post-glacial rebound.
      Stockholm may come in the same grid cell as some of the other European stations, and will then carry less weight when gridded
      However, the big difference is only for the rise, not for the acceleration as is seen in the right plot

    • The satellite data has been thoroughly turned upside down and inside out to match up different satellite soundings. You now get “inverse barometer” adjustments, whether you like it or not so no means to see what effect it has ( why would you even want IB on a global figure !? ). You get speculative GAIA “corrections” whether you want it or not. The stated reason for this is that U.C. Bolder want GMSL to be a AGW metric instead of being SEA LEVEL metric. Strange.
      In short is has been rigged for politically motived reasons and no longer of any scientific value. Since it is based on the idea of measuring mean sea level by looking at the reflections of the BOTTOM of the swell and guestimating the height of the swell, I doubt it has much objective use anyway.
      Maybe some information about local/regional changes but for long term MSL change it’s a joke.

      • And starting with this year’s release they’ve dropped the “GIA Corrected” and “Inverse barometer Applied” notes. They want their graph to represent Ocean Volume, but you have to read the find print to find that out. I’m waiting for them to drop that too.

      • Thanks for the update Steve, I have not been back to Colorado site in few years, since they started rigging the data and GMSL started floating, ghost-like, above the waves.
        In 2011 , I found an interesting correlation between GMSL and UAH TLT. When I went back a year later to see how it had evolved, I found the whole thing was completely different. WTF?
        At that point I realised it meant nothing objectively and was just yet another dataset that was no longer any use for climate study, run by zealots with an agenda, not scientists.

    • Thank you for the comment Bob
      There are many long records available, but I chose to rely on the GLOSS stations only. There are about 2000 stations in PNAS, but only a small subset of them are in the GLOSS network.
      I chose the GLOSS because what they write (Quote): “GLOSS aims at the establishment of high quality global and regional sea level networks for application to climate, oceanographic and coastal sea level research. The programme became known as GLOSS as it provides data for deriving the ‘Global Level of the Sea Surface’.
      The Core Network is designed to provide an approximately evenly-distributed sampling of global coastal sea level variations. Another component is the GLOSS Long Term Trends (LTT) set of gauge sites (some, but not all, of which are in the GCN) for monitoring long term trends and accelerations in global sea level.”
      (Quote end)
      From this I take that the GLOSS subset of stations are regarded as the best ones for measuring long-term trends.

      • Think Helmut says
        if there’s any accounting sea level rise
        then it has an impact on earth’s rotatation curve
        ( I’d rather say: then it has an impact on earth’s rotation time )
        Regards – Hans

  23. But what roles are played by gradual geologic subsidence in tandem with sudden uplift? As an example, in 1855 in Wellington, New Zealand, a big earthquake uplifted the land such that we now have roads all around hilly coastlands because those shorelands were lifted out of the water by the quake. Since then, the land has slowly subsided — until the next uplifting earthquake which is feared. That slow subsidence is entangled with the so-called gradual sea-level rise because you can’t separate them instrumentally. This same scenario is playing out all over. Maybe “sea level rise” is mostly just normal geological subsidence.

    • It was really interesting to hear about the uplift and subsidence you experience in Wellington.
      However, Although New Zealand is not the only place that experience tectonic movements, most of the stations are placed on more stable geological ground. The GLOSS project has high focus on establishing good reference points so we are certain that the global sea level rise is real, although land movements may cause some noise in the series.

    • NZ Willy,
      Your point is well worth making, perhaps not very relevant to this study, but over longer time scales it’s a factor that should have more consideration. There are few places on this planet that are truely geologically stable over the longer term. Thus the problem in finding sites for long term nuclear waste storage.
      The earth is a dynamic place with uplift and subsidence being continuing ongoing processes. Not enough solid earth geological processes are considered in the long term sea level rise issue.

  24. How do we measure from the center of the Earth’s core to the reference point of the tide gages to 0.1mm? Where is the graph of this reference point over the life of the tide gage to 0.1mm?
    The gage measurement is ONLY as good as its reference point’s accuracy and STABILITY on the constantly shifting surface plate…..not to mention, of course, the effects of the constantly changing currents piling water up and sucking it out of the estuaries and harbors the gages are all mounted in.
    How absurd it is to just ignore the MOVING REFERENCES.

    • Thank you for the comment Larry,
      f we could measure all reference points to 0.1 mm accuracy, and could also nullify the effect of ocean currents, we would need only one tide gauge on the globe. If tide gauge at that that super reference point, which also was unaffected by changes in the Ocean surface, was rising by one millimeter we could be certain that the Ocean was indeed rising
      But we cannot do that, and that is why we need many measurement points. When we have many independent sampling points it is possible to narrow the total uncertainty even if each measurement has a larger uncertainty.
      This effect is well explained on page 6 (Statistical Analysis of Large Data Sets) from Penn university here:

  25. For the folks who feel that graphs “say it all”, be sure to eyeball a graph of sea level over the past 10,000+ years. Sea level has risen 400+ feet, and several thousand years ago the incline hit an inflection point, where rate of sea level increase began dropping. We are enjoying a brief warming period between ice ages. In the past 1.3 m years, there have been 13 ice ages, average duration 90,000 years, each followed by a warmer period, average duration 10,000 years. It’s obvious that year to year, even decade to decade, sea level fluctuations create little more than miniscule bumps on that graph. One glance shows that sea level is topping out and this trend has very likely been repeated during past interglacial periods.
    Our current warming (such as it is) began NOT in the mid 1800s, (“cherry-picked”) when co2 level began rising and our industrial revolution began. Our current warming began, by definition, at the bottom of the LIA, in the mid 1600s, two centuries before co2 began rising. Also, it would have taken another century before co2 level could have (assuming it can!) had any impact on the global temperature. That brings us to about 1950, so 300 years of natural warming. But wait! … from the 40s to the 70s was a period of mild cooling.
    So the alarmists have hung their hats on a 2 decade warming period which stretches from about the mid 70s to 1998. (Both weather satellites show no additional increase in temperature from then, at least until after our current El Nino which cranked up about mid 2015. ) The atmospheric warming of the ocean contributed by human activity had to follow the 1970s. How much impact do you suppose that small temperature increase would have on the ocean given the enormous (by comparison) ocean heat capacity?

    • yep, then they fit an exponential growth that tiny segment and extrapolate it 100y beyond the data.
      The craziest part is that they’ve been doing this shit for 30y and are still getting away with calling it “the science”.

  26. iso quality material pro or con info re: Pacific Ocean rising along China and Russia,
    not rising along N America West Coast.

  27. It seems to me that when anyone starts claiming accelerating sea level rise there is a question that has to be answered before it’s cause can be attributed. ‘Where did the water come from?’

  28. When I click on one of these graphs I should get an enlarged version of the graph, so that I can at least read the years on the horizontal axis.

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