How much have sea levels really risen?

Two recent papers refocus attention on how much we really know about the causes of sea level rise and how accurately we can measure it. The most recent, Twentieth century increase in snowfall in coastal West Antarctica by Thomas et al. reports large increases in the rate of snow accumulation over the last 100 years on the West Antarctic Ice Sheet – which is said to be on the point of collapse – but provides no specifics on ice sheet volumes. But the earlier paper, Mass gains of the Antarctic ice sheet exceed losses by Zwally et al., does. The press release that accompanies it contains the following statement:

The good news is that Antarctica is not currently contributing to sea level rise, but is taking 0.23 millimeters per year away,” Zwally said. “But this is also bad news. If the 0.27 millimeters per year of sea level rise attributed to Antarctica in the IPCC report is not really coming from Antarctica, there must be some other contribution to sea level rise that is not accounted for.”

There must be some other contribution to sea level rise that is not accounted for”. No there doesn’t. It could simply mean that sea level rise has been overestimated.

Estimates of global sea level rise have historically been bedeviled by the “attribution problem”, which Miller & Douglas (2004) summed up thus:

The rate of twentieth-century global sea level rise and its causes are the subjects of intense controversy. Most direct estimates from tide gauges give 1.5–2.0 mm yr-1, whereas indirect estimates based on the two processes responsible for global sea level rise, namely mass and volume change, fall far below this range. Estimates of the volume increase due to ocean warming give a rate of about 0.5 mm yr-1 and the rate due to mass increase, primarily from the melting of continental ice, is thought to be even smaller. Therefore, either the tide gauge estimates are too high, as has been suggested recently, or one (or both) of the mass and volume estimates is too low.

Either the tide gauge estimates are too high … or … the mass and volume estimates (are) too low. Over the last ten years efforts have concentrated almost exclusively on proving that the mass and volume estimates are too low, and until Zwally et al. came along the IPCC had made progress towards closing the gap, as shown in Table 13.1 of the AR5 . The tide gauge estimates, however, have not been seriously questioned.

So here we will question them.

There are two ways of measuring sea level rise. The accepted approach is to measure absolute (or geocentric, or eustatic) sea level rise – essentially how much global sea level has risen relative to the center of the Earth. This approach is adopted because only absolute sea level rise provides the estimates of ocean volume change that are needed for mass balance calculations. The Church & White global sea level series  shown in Figure 1 – one of the series featured in the IPCC AR5 – is typical of the results obtained. It shows a continuous rising trend since 1880 and about 240mm of absolute sea level rise since then:

Figure 1: The Church & White absolute sea level rise time series

Church & White constructed their series from raw tide gauge records selected from the Permanent Service for Mean Sea Level (PSMSL) data base . The records were adjusted for vertical land movements at the tide gauge sites, a requirement if one wishes to measure absolute sea levels, and the results were then combined with recent satellite sea level observations and analyzed using a complicated statistical approach that Church & White summarize as follows:

The other way to estimate sea level rise is the way I did it. I selected 382 raw PSMSL tide gauge records – substantially the same records that Church & White used, incidentally – reduced them to a common baseline, weighted them relative to the length of coastline they covered and averaged them. This approach yields estimates of “relative” global sea level rise, or how much sea level has risen relative to the global coastline. Relative sea level rise estimates can’t reliably be used for mass balance calculations, but they don’t require vertical land movement adjustments or complex statistical manipulation and they also tell us a lot more more about the physical impacts of sea level rise. (Absolute sea level rise is of academic interest in cities like Bangkok and Jakarta, large chunks of which are on the point of disappearing beneath the waves because of subsidence caused by groundwater pumping.)

Figure 2 shows the location of the 382 tide gauge stations. I estimate that they provide coverage over at least half of the global coastline after 1950. However, coverage decreases before 1950 to the point where in 1900 only 30 stations, almost all of them in the North Hemisphere, were operating.

Figure 2: The 382 PSMSL tide gauge stations used in the analysis

I segregated the 382 records into 34 areas with similar trends and Figure 3 shows the raw tide gauge records from ten of them – the good, the bad and the ugly (note the variable scales). Note also the differences in trend and the rapidly dwindling number of records before mid-century, which raises the question of whether we have enough to make good estimates of global sea level much before 1950:

Figure 3: Illustrative plots of tide gauge records

Figure 4 shows my relative global sea level series superimposed on the Church & White absolute global sea level series. The two track each other quite closely between 1910 and 1950 (the mismatch before 1910 is probably caused by a lack of data) but after 1950 the Church & White series continues to climb while mine flattens out. My series in fact shows no sea level rise at all between 1948 and 1970, although it does broadly replicate the sea level rise shown by the Topex-Jason satellite data after 1993:

Figure 4: Church & White’s absolute sea level rise series versus my length-weighted relative sea level rise series

Why does the Church & White series show ~120mm of global sea level rise between 1950 and 2010 while mine shows only about half as much? I filled a spreadsheet with 67 megabytes of data trying to find out, but because Church & White don’t publish their adjusted tide gauge records not a great deal of diagnostic information emerged. I did, however, run two checks that I present here.

Church & White measure absolute sea level rise over all the world’s oceans while I measure relative sea level rise along the world’s coastlines, so to make the comparison more apples-to-apples I first constructed an area-weighted series using a 500km radius of influence around individual tide gauge stations, which heavily de-weighted records in confined seas like the Baltic while greatly increasing the weighting of Pacific Island records. This series showed about 20mm more sea level rise since 1950 than the length-weighted series but still 40mm less than Church & White:

Figure 5: Church & White’s absolute sea level rise series versus my length-weighted and area-weighted relative sea level rise series. All three series are zeroed over 1950-55.

Second I checked Church & White’s vertical land movement corrections, which are potentially suspect because they are mostly derived from crustal deformation models that simulate the impacts of glacial isostatic adjustment (GIA) and don’t allow for any other sources of vertical movement, such as sediment compaction or tectonic uplift. Figure 6 shows what a typical GIA model – in this case the Paulson 2007 model – looks like. The red-shaded areas show where the surface is still rebounding from ice unloaded since the end of the last Ice Age. The blue-shaded areas over the oceans show where the increased mass of meltwater in the oceans is depressing the ocean floor and the pink areas in Australia, Southern Africa and Southern South America show where this is generating mild isostatic uplift in the surrounding landmasses:

Figure 6: The Paulson 2007 glacial isostatic rebound model (image credit Basement Geographer)

I had no data for the Matrovica GIA model that Church & White based their corrections on but I did have data for the comparable Peltier GIA model. I therefore used the Peltier data to “correct” the tide gauge records and reconstructed the area-weighted series with the results shown in Figure 7. Peltier’s GIA adjustments add another ~10mm of sea level rise but I still fall about 20mm short of Church & White:

Figure 7: Church & White’s absolute sea level rise series versus my length-weighted, area-weighted and GIA-corrected area weighted relative sea level rise series

These plots don’t of course prove that Church & White’s ~210mm of sea level rise since 1900 is an overestimate, but neither do they eliminate the possibility that a significant fraction of it could be the product of statistical adjustments similar to those applied to some of the land temperature records. And as noted at the beginning of the post Church & White still have an attribution problem. The IPCC’s AR5 estimates of the combined ice melt, thermal expansion and “land water” contributions to sea level rise since 1900 range from 120 to 140mm depending on how one sums them, less if the Antarctic ice sheet is gaining ice and not losing it as Zwally et al. now claim. My ~100mm of relative sea level rise since 1900 is a good deal closer.

Finally, Figure 8 compares the Church & White series with GISS’s man-made radiative forcing estimates . If GISS and Church & White are correct then global sea levels were rising steadily long before AGW became significant, although I’m not the first to recognize this. (The flattening in the forcing plot after 1990 is GISS’s attempt to explain the “warming pause”, incidentally):

Figure 8: Church & White sea level rise series versus GISS man-made radiative forcings

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43 Responses to How much have sea levels really risen?

  1. Javier says:


    Reconstruction of sea level raise by Jevrejeva et al. 2008
    Shows that the rate of increase appears to follow a ~60 yr cycle for the past 200 years, like many other climate phenomena including temperatures and oceanic multidecadal oscillations. See figure 3 (bottom) in the paper.

    Also Walter Munk has a work at PNAS “Twentieth century sea level: An enigma” in 2002 where he deals at length with the disparity in sea level raise between calculated and observed:
    He concludes:

    This paper does little toward solving the problems of the historical rise in sea level. In looking for causes, I have applied what Edward Bullard (31) has called the “Sherlock Holmes procedure” of eliminating one suspect after another. The procedure has left us without any good suspect…

    Among the many possibilities for resolving the enigma, we suggest the following:

    Traditional estimates of the combined (steric plus eustatic) sea level rise (in the range 1.5–2 mm/y) are much too high [the Cabanes et al. (16) view];

    Levitus estimates of ocean heat storage and the associated steric rise are much too low;

    rotational bounds on the eustatic rise are not valid (see text);

    generous error bars in all these estimates mask the enigma (IPCC);

    all of the above;

    none of the above.

    Sea level is important as a metric for climate change as well as in its own right. We are in the uncomfortable position of extrapolating into the next century without understanding the last.

    So much for settled science.

    • Javier: Thanks for your comment. It was Munk’s article that got me interested in sea level rise to begin with. I don’t think anyone has ever come up with a better summation of the situation than “We are in the uncomfortable position of extrapolating into the next century without understanding the last.” It should be nailed to the podium at the Paris Climate Conference.

      On a couple of the specific point you raise:

      Reconstruction of sea level raise by Jevrejeva et al. 2008 shows that the rate of increase appears to follow a ~60 yr cycle. My series does too. Here’s a detrended version of it with a 60-year sine wave cycle superimposed:

      The procedure has left us without any good suspect. Here’s one worth bringing in for questioning. The graphic below compares my sea level series with the raw ICOADS SST series, which is a proxy for thermal expansion. The correlation (R squared = 0.92) seems a little too close for coincidence:

  2. Dave Rutledge says:

    Hi Roger,

    Thanks for a very interesting post. I had given up on Church and White; too much torturing the data.

    I ask the students in my class to compare the Maassluis tide gauge trend before and after 1955 to get a sense of the fossil-fuel effects. The ground movement there is small and there are no gaps in the data. I appreciate the Dutch steadiness through wars and other distractions.


    • Hi Dave:

      You encouraged me to download he Maassluis tide gauge record:

      And indeed you don’t see any sign of acceleration after 1955. But this is the raw record. Massage it with a few leading EOFs and diagonal eigenvalue matrices and there’s no telling what you might get. 🙂

  3. Sea level is critical for understanding the climate of the past, including the recent past and may indicate future climate states.

    This is illustrated by a paper by Nir Shaviv, Using the Oceans as a Calorimeter to Quantify the Solar Radiative Forcing


    Over the 11-year solar cycle, small changes in the total solar irradiance (TSI) give rise to small variations in the global energy budget. It was suggested, however, that di.erent mechanisms could amplify solar activity variations to give large climatic effects, a possibility which is still a subject of debate. With this in mind, we use the oceans as a calorimeter to measure the radiative forcing variations associated with the solar cycle. This is achieved through the study of three independent records, the net heat flux into the oceans over 5 decades, the sea level change rate based on tide gauge records over the 20th century, and the sea surface temperature variations. Each of the records can be used to consistently derive the same oceanic heat flux. We find that the total radiative forcing associated with solar cycles variations is about 5 to 7 times larger than just those associated with the TSI variations, thus implying the necessary existence of an amplification mechanism, though without pointing to which one.

    As I understand this paper, the estimated variation in ocean temperature within one solar cycle is about 0.1 degree Celsius.

    I have a work in progress to estimate the climatic effect longer solar cycles (Gleissberg, Suess/de Vries). Series of solar cycles can add to and subtract from the amount of solar energy stored in the world ocean to obtain the cumulative effect over long periods, such as 50 to 100 years.

    If I apply the estimate by Nir Shaviv to long series of 11-year solar cycles (using the integral of the cycles), the estimated temperature changes would appear to exceed observed changes.

    One of the possible explanations is that steric sea level change has been overestimated. (I mention several other candidate explanations. This is a work in progress.)

    Definition of steric sea level change:

  4. Tom Bates says:

    I went to NOAA and looked up several tide gauge measurements they show a trend of 3 inches in 100 years. This for example or this Unless those places are sinking like say Galveston even your numbers are way overstated.

    • Euan Mearns says:

      Tom, I think you need to look at a bigger average rather than a couple of selected stations. But I guess my view would be that it doesn’t really matter if its 3 inches or 6 inches per century, since both are pretty well indistinguishable from zero.

      • Tom Bates says:

        Actually you do not have to look at a ton of places, if the place you look at is not moving up or down due to continental deflection or ground subsidence , one point will reveal a long term trend. All you measure with multiple points is an average. If that average was not adjusted for the points moving up and down than the result is garbage in garbage out. If you look at the actual stations a whole lot are on unstable continental edges and are moving up ant down a lot. I have looked at a bunch stations in the NOAA tidal gauge network. One thing I come away with is nobody has ever actually measured ground movement in most stations using for example the GPS network. Galveston has been measured and its ground sunk 2 feet while NOAA gauge shows a rise of 2 ft 1.08 inches, that is a rise of 1.08 inches even less than the 3 inches at pacific stations where the ground does not appear to be moving around a lot.

        • Euan Mearns says:

          Tom, I agree that you only need one station, if you know the station that gives you the correct result. The chart is from the link posted by Halken. I think this is a good way to manage the data. But I’m not sure the management here is entirely objective. I’d have my red box going from 0 to +3 mm / year. Median + 1.5 = 150 mm / century or 5.9 inches per century. But I don’t consider this to be materially different to 3 inches per century since all these numbers are effectively zero. This needs to ratchet up 2 orders of magnitude to cause concern IMO.

        • Land movement at increasing numbers of tide gauge stations is now being measured with GPS and the results obtained so far are a lot more credible than those obtained from GIA models. There are, however, two problems. First, it will take decades to accumulate enough GPS data to make really accurate land movement corrections to tide gauge records. Second is the lack of historical GPS data. Can we assume that land movement at a particular site fifty or a hundred years ago was the same as what we measure now? In some areas it won’t have been.

  5. oldfossil says:

    Roger, I thought I was pretty bright but this formidable analysis made me change my mind. Bravo.

    Have you tried correcting for latitude? I’m no geoscientist but (probably mistaken) commonsense tells me two things. First the higher energy of water at low latitudes will enable it to move to higher latitudes. Second this is counteracted by the same centrifugal effect that makes Earth a geoid not a sphere.

    On BBC I regularly see programs about the Great Lakes with water levels that have changed by up to 30 feet in a couple of centuries. In very active regions like North America, I’m surprised that the ocean tide gauges aren’t also showing huge movements.

  6. Luís says:

    There are various murky points in this post that do not allow for a clear assessment at this stage. I would start with this description:

    “weighted them relative to the length of coastline they covered and averaged them. ”

    For starters, the coastline is a fractal. Secondly, no cartographic projection preserves distances; equidistant projections only preserve distances along certain lines. Therefore, unless you calculated the coastline in the geographic domain as a composition of orthodromes of pre-determined resolution, this length weighting is not reflecting geographic reality.

    The area weighting is even less transparent, the only reference to this method is:

    “I first constructed an area-weighted series using a 500km radius of influence around individual tide gauge stations”

    The first chart presents the stations with the Robinson projection; I hope no area weighing was made with this projection since it is not equivalent. Then it is not clear at all what that radius was translated into. Area weighting presupposes the calculation of an area for each station, something that can not possibly be achieved simply with circles.

    Just an ending side note. I had no idea there was no see level data collected in Antarctica, especially since various meterologic stations exist around the coast. In fact there does not seem to exist data south of 45º S.

    • Roger Andrews says:

      I measured coastline lengths from Google Earth using a 100km minimum segment length, but imperfections in my measurements won’t make much difference. A simple arithmetic average of all the records gives about the same results.

      • Luís says:

        Conceptually, your ideas of weighting each station are not bad, but you are far from realising them in a meaningful way. I would not take any conclusions from the results you presented. Much less in what concerns oceanic volumes.

        This article provides a glimpse on how ocean mass and topography are actually measured:


        • Conceptually, your ideas of weighting each station are not bad, but you are far from realising them in a meaningful way.

          Such “ideas” are common practice in mineral resource/reserve estimation and have been employed in a meaningful way for many years.

          I would not take any conclusions from the results you presented.

          I didn’t take any firm conclusions from them either.

          Much less in what concerns oceanic volumes.

          I didn’t present any data on oceanic volumes.

          This article provides a glimpse on how ocean mass and topography are actually measured

          And tells us nothing about how good the results are, although statements like “satellite altimetry ….. can be used to estimate the rate of global mean sea level rise to an accuracy of 0.3 mm/year after extensive calibration efforts” do not inspire confidence. The article also says nothing about how ocean mass is measured prior to 1993 when there were no satellites.

        • Elvis says:

          It might be more meaningful with the graphs plotted using the most recent decades (for which the data is probably most reliable) as the baseline.

  7. Stuart says:


    Rises in mean sea level are entirely without context unless you also measure the delta volume of the ocean by mapping the ocean floor topography and the changes of the ocean floor due to plate tectonics.

    It is pointless to measure the depth of the water in your bucket if the size and shape of your bucket is constantly changing.

    For example as the Indian subcontinent rises up out of the Indian Ocean, it will leave the Mean Sea Level lower.

    Every single square mile of the surface of the earth is moving up or down and sliding at some heading and rotating. Yes it is slow but the entire surface is moving along some vector. What is the net effect of all this on the volume bounded by ocean topography and mean sea level?

    The mean depth of the world’s oceans is 3,688,000 mm IPCC are saying that it is increasing by 1.5mm/yr? That doesn’t seem like so much really.

    The Himalayas are rising at 10mm/yr I’m not sure how climate change can explain that?

    • It is pointless to measure the depth of the water in your bucket if the size and shape of your bucket is constantly changing.

      That’s what makes absolute sea level so difficult to measure.

      And don’t forget that the water in the bucket is expanding as the bucket warms up.

      • Tom Bates says:

        Actually Roger over a short time period say our lifetime, it is easy to determine a trend assuming the melt rate trend is some linear number Since a lot of things are not linear, the sine wave you found for example, take the linear with a grain of salt. Pick one point not moving up or down. That is zero. measure the rise or fall. assume the volume is some fixed amount,it does not matter how much. That gives the absolute rise. Figuring out how much is temperature/salinity is the part where you get into guess and guess again which is not actually necessary as the absolute rise already incorporates the temperature/salinity change of the period measured if one assumes the volume before is much greater than the volume plus the melt a rather simple calculus problem. You do not need to know the volume, the shape of the bucket or any other thing you will have an absolute rise trend. Trying to pretend that is the future is where the garbage in garbage out comes in. When I look at rises of 3 inches or so when the IPCC claims feet you can understand why I think it is garbage in garbage out as they simply have not done the homework to know what the actual movement up and down of the stations is. Pretending some model will tell them that is a failure of science as the only thing to verify the model is data and that is lacking.

  8. Euan Mearns says:

    My main thoughts as a geologist:

    1) Sea level rise of the order 120 to 150 mm / century (4.7 to 5.9 inches) is pretty well indistinguishable from zero. This must be one of the most stable periods for sea level for millions of years.

    2) The fact that the trend (assuming it can be measured) rises more or less continuously from 1880 virtually proves that this has nothing to do with Man or GHG. On going rebound from The Little Ice Age is the only rational explanation. Roger’s Figure 8 illustrates this perfectly.

    How are the measurements made? With solar and lunar tides and air pressure all having major effect in addition to isostasy, how on Earth do they manage to measure water level with confidence with a precision of 1 mm / year? I’m also more than a little intrigued by this chart posted by Roger in comments.

    • Roberto says:

      ‘, how on Earth do they manage to measure water level with confidence with a precision of 1 mm / year?’

      Differential gps using different satellites… that’s not a big deal, actually.

      • Euan Mearns says:

        Hmm!!! The record begins in 1880 and it is said that tide gauges are used.

        • It’s worse than you think. If I read Church and White correctly they correlated satellite observations with the tide gauges over the period since 1993 and then applied the correlation matrices to dwindling numbers of tide gauge records to define sea levels over the open ocean going all the way back to 1880. But maybe I’ve got it wrong.

  9. Halken says:


    Have you read this by Niel-Axel Marner? It’s not my area, but he has been quite outspoken in the debate surrounding sea levels, and he is under the impression that satellite sea leves are adjusted upwards.

    • Roger Andrews says:

      They certainly have been in the case of the GRACE satellite, which measures sea level rise based on minute gravitational changes:

      • Halken says:

        I know, but it is something the sceptical community has not spent som much time on investigating, so it is hard to judge the validity of NAMs claims.

      • Euan Mearns says:

        NASA and NOAA keep launching these satellites and either ignore the data or change it to fit the models. There’s just gotta be a way to stop this.

  10. A C Osborn says:

    Euan, as you say the current rise in sea levels is almost indistinguishable from Zero, just look at the reconstruction of historic sea level changes for last 20,000 years, which is measured in Metres, not mms.

  11. Elvis says:

    An interesting analysis Roger. And you seem to have confirmed that SLR is accelerating – by eye the rate looks to have doubled in the decade to 2009 from the previous. But what happened in the last 6 years to 2015?

    • According to my results the rate of SLR since 1993 is about the same as it was between ~1930 and ~1950.

      Why should sea level rise suddenly accelerate after 1993?

      • Elvis says:

        Fig 5 and 7 seem to show acceleration much the same as C&W in the last decades. I’d imagine that is because of rising temperatures and loss of ice sheet mass, wouldn’t you. But what about post 2009, what happened there?

      • Elvis says:

        Ah, I think I see, do you use the archive data to 2010? That is a pity.

        Did you also create Fig 7 showing the whole dataset?

  12. tallbloke says:

    Great post Roger, thanks.

  13. Bill Illis says:

    Roger, you could try to match up the sea level time series from the tide gauge database that you have already constructed with the ones that also have GPS stations co-located with them. has been maintaining a database of the co-located GPS stations which have around long enough in order that a definite signal of local land up-lift or subsidence can be arrived at.

    It takes 6 or 7 years to be sure but these values have likely been the same for the past several hundred years at least in each location.

    The V_GPS column here (the local rate of up-lift or subsidence rate in mms/year) can be found on this page for (get this) over 300 tide gauge stations which have co-located GPS stations.

    The average is about 0.3 mms/year of local uplift but it varies widely.

    Then one has to match up the GPS station names from this page with the tide gauge station number from the PMSL database which can be found on this page.

    And then if one has the time series for these tide gauges in a usable database already, one could simply subtract the V_GPS local uplift subsidence rate to arrive at GPS adjusted sea level rise rate for 300 tide gauges. This time series would be able to come to a definite conclusion about what the real rate of sea level rise is and how it has varied over time. I am more interested in the most recent time period from 1993 that covered by the satellites but that is for another day.

    I know this would be a lot of work. [The sea level guys never, ever, ever make it easy for someone to carry out this work. They have left all the databases deliberately complicated so that it is very difficult to do.]

    I have started doing this several times and gave up, but I think you already have a good start at it Roger. i think it is very important work.

    • Bill: Thanks for the links. My 67MB spreadsheet in fact contains several analyses based on this data set, or an earlier version of it. I didn’t include them to keep the post down to a manageable length and because there weren’t enough stations to give diagnostic results. But in a nutshell the GIA numbers show the land rising on average by 0.35mm/year more than the GPS numbers, which if we accept the GPS numbers as correct, and if we assume that they have remained constant over time, means that GIA corrections will tend to overstate sea level rise by 35mm/century. Subtracting 35mm from Church & White would lower their estimate of 20th century SLR from ~150mm to ~115mm assuming that they used the same GIA corrections. A lot of assumptions. 🙁

  14. A C Osborn says:

    One area that has to be carefully considered is which Stations are looked at as it has become apparent that their is “slosh” taking place in both seas and Oceanswhere water is taken from one side and builds up on the other. So when the measurement are taken is also important.
    Changes in prevailing winds, Super Moons etc can all have odd affects. I am sure Clive B did quite a bit of work on Lunar affects.

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