Sea Level Acceleration

A regular big lie from climate deniers, in fact a huge lie from climate deniers, is when they deny that there’s been acceleration of sea level rise. Sea level acceleration is a fact.

Let’s start with what happened during the 20th century (before the year 2000). The most respected reconstruction of global sea level during that time based on the global network of tide gauges is from Church & White:


According to these data, the average rate of sea level rise from 1900 to 2000 is about 1.6 mm/yr. There are other reconstructions of course, and they lead to the same conclusion: that the average rate during the 20th century is less than 2 mm/yr.

Now let’s look at how sea level has changed since 1993, using altimetry from the satellites which give us global coverage (monthly averages with the seasonal cycle removed):


The average rate over the last 24 years is about 3.4 mm/yr. That’s about twice the average rate since 1880. It’s certainly over 3 mm/yr.

20th-century average rate: less than 2 mm/yr. 21st-century average rate: more than 3 mm/yr. Three is larger than two. Conclusion: the rate of sea level rise went up. That’s acceleration.

Some have urged caution estimating the trend of sea level rise using satellite data because the record only covers 24 years. They express concern about the lunar nodal cycle, an 18.61-year oscillation of the moon’s orbit, which causes a small change in mean sea level. Some, in particular those who want to help prepare for the risks, have issued this caution because they’re genuinely concerned with the uncertainty of rate estimates. Others, particularly “free-market think tanks” (translation: corporate profit over public good) do so for no other reason than to discredit the trend from satellite data.

But the argument is specious. The lunar nodal cycle causes an oscillation of mean sea level at a particular location, one which depends on latitude. Its global pattern generally follows the low-order spherical harmonics, so when sea level is raised at the equator it’s depressed at the poles and vice versa. The global effect is just about zero, because it doesn’t affect the total volume of water in the ocean, and that’s what global sea level is really about. You can find some of the details here.

We can detect acceleration in the Church & White sea level data itself. The average rate of 1.6 mm/yr is based on fitting a straight line to the data after 1900 and before 2000, but there’s pre-1900 and post-2000 data, and it turns out sea level isn’t actually following a straight line. We can fit a smooth curve instead, which allows for non-linear changes, and I’ll use a modified lowess smooth:


An extremely useful aspect of smoothing is that it enables us to estimate the rate of change through time, as well as the actual value. This particular smooth gives this estimate of the rate at which sea level has been rising:


The red line shows the sea level rate through time; the blue line shows the average level for comparison. The acceleration is obvious.

There was, however, a time span (from about 1940 to 1980) when sea level did not accelerate; if anything, the rate decreased slightly so sea level rise decelerated. I have often pointed out that one of the most interesting facts about sea level rise during the 20th and 21st centuries is that it shows both acceleration and deceleration. There’s no “inconsistency” to explain from this; models — both process models (which simulate the physics) and semi-empirical models (which are mathematical rather than “computer models”) reproduce this behavior. All this is utterly ignored by climate deniers, who simply argue that there’s no acceleration in a vain attempt to promote a “don’t do anything” agenda.

According to these data, the latest bout of acceleration covers about the last 50 years. So, I decided to look for it in individual tide gauge records by isolating the data since 1965 and fitting a quadratic function of time; the quadratic coefficient gives an estimate of the acceleration. I insisted that any record included have data in least 40 of the years since 1965.

Tide gauge data tend to be quite noisy, so for many of them a 50-year span is insufficient to detect acceleration even if present. Nonethess, we can use the ensemble of estimated quadratic coefficients to get at least some insight into which are showing acceleration (positive coefficients) or deceleration (negative coefficients). The results won’t be perfect of course, but perhaps they’ll give us some perspective.

Here’s a map showing gray cirlces for each tide gauge station with sufficient data, larger circles for larger coefficients (either positive or negative), with red circles indicating statistically significant acceleration, blue circles significant deceleration (autocorrelation correction was included in the significance test):


Stations with significant acceleration outnumber those with significant decleration, 74-to-11.

Here’s the same map, but will all stations coded red for acceleration (positive) and blue for deceleration (negative) whether statistically significant or not:


What’s most interesting is where the stations showing possible deceleration are located. They’re concentrated at high latitudes, in particular at parts of northern Europe and North America at which the melting of glaciers has been pronounced enough to cause local deceleration because of the reduced gravity from smaller modern glaciers. It’s truly fascinating that even these locations showing decelerating sea level rise are most likely because of global warming: melting glaciers, less gravity, lower local sea level.

It’s also quite interesting that so many more stations show signs of acceleration than deceleration, especially when one requires statistical significance. The evidence is strong: sea level rise is truly accelerating, as evident in global reconstructions from tide gauges, in the analysis of recent data from individual tide gauges, and in the satellite data.

As if its present rate and acceleration weren’t bad enough, the best science indicates more sea level acceleration to come. Both physical and mathematical models suggest a range of from 2 to 6 feet by the year 2100. Unfortunately the latest IPCC report isn’t up-to-date with the latest science; one hopes the next will reflect the overall opinion of the community of genuine sea level experts, that the problem has gone beyond “worrisome” and become critical. Coastal regions everywhere should be preparing for what’s to come, and the uncertainties in how much and how fast those changes will happen is not a valid reason to minimize preparation; a wise society realizes that uncertainty is not your friend.

But of course “free-market think tanks” (translation: corporate profit over public good) will continue to dispute this, will continue to discredit any data which shows how bad the problem is while touting any data which they can present in some way to make their “don’t worry be happy” case. Personally, I’d rather be prepared for what’s really ahead. Living in a fantasy world where sea level rise will only be an annoyance, is fine for the super-rich. For the rest of humanity, believing such fantasy will only make the inevitable worse.

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35 responses to “Sea Level Acceleration

  1. A small favour: looking at the satellite data with my Mk 1 eyeball, it looks as though there may be an acceleration in the last 7 years. Starting with a sharp dip (related to ENSO causing large amounts of rain to fall on land, IIRC), the “recovery” to the trend looks much steeper than pre 2010. So what is the rate of increase over the last 7 years?

  2. Is the detection of accelerated sea level rise imminent? – Fasullo, Nerem, and Hamlington

    Among the major unanswered questions is why GMSL acceleration has not yet been detected in the altimeter record, given the increasing rates at which glacial and ice sheet melt are estimated to have occurred6,7 and as greenhouse gas concentrations have risen8.

    And this in their supplementary information:

    As a result, this paper does not present a definitive assessment of the acceleration of sea level rise during the altimeter era, but rather suggests a mechanism for the masking acceleration by non-anthropogenic sources, a mechanism that is relevant for the interpretation of the altimeter era irrespective of the optimal calibration of TOPEX. …

    As I have mentioned, the current 10-year rate of SLR is 4.11 mm/yr; the current 5-year rate of SLR is 4.97 mm/yr.

    4th quarter OHC resumed its upward trend. How far away can “imminent” be?

  3. It is somewhat hard to see the acceleration of sea level rise because it is already rising at the beginning of the observational record. If you take a longer perspective and look at the last 2000 years, the acceleration is very very clear. Maybe nothing for this blog: No need to fancy stats whatsoever.

    That sea level was already rising in 1880 is a hint that we may have underestimated the warming in that period.

  4. “The most respected reconstruction of global sea level during that time based on the global network of tide gauges is from Church & White”: I actually think that the Hay et al. study is superior to Church & White ( I’m guessing you would find even greater acceleration using the Hay et al. reconstruction.

    [Response: I suspect you may be right. Do you know how to acquire their data?]

    • If you click on Figure 2 in the paper, there is a link at the bottom for “download Excel source data” which provides annual sea level estimates for their Kalman Smoother approach and decadal estimates for the Gaussian Process Regression approach, along with standard deviations.

      • Doing a very crude analysis (e.g., first difference of sea level to get sea level rise, first difference of SLR to get acceleration, and then averaging over a given time period) I get an average SLR over the entire period of 1.49 mm/yr with an acceleration of 0.03 mm/yr/yr. Looking only at the period 1964-2010 (based on eyeballing a break point), I get an average SLR of 1.8 mm/yr, with an acceleration of 0.09 mm/yr/yr.

        If I naively extrapolate from 2010, using a starting SLR of 3 mm/yr and an acceleration of 0.09 mm/yr/yr, by 2100 SLR would be 11 mm/yr and total SLR from 2011-2100 would have been 64 cm.

  5. In addition to sea levels falling near melting glaciers, in many Northern Areas have significant Post-Glacial rebound which can be as much as 1 cm/year. The high latitude stations reported as sea level lowering may just have land rising and lifting the gauge.

    In any case, you present a very strong case for accelerating sea level rise.

    [Response: As far as I know, post-glacial rebound is occurring at reasonably constant rates, hence doesn’t interfere with estimates of acceleration.]

    • All sea level is local. Besides the ongoing isostatic rebound (crustal rebound from “rapid” glacier mass loss since the Ice Age) that you mentioned, variables include:
      – collapsing of Gulf Stream raises levels along the US Eastern Seaboard.
      – ENSO variations change the relative sea levels of the eastern and western sides of the equatorial Pacific Ocean
      – ice cap mass loss decreases sea level in the immediate vicinity of the ice cap and raises sea level at the ice caps antipode
      – natural subsidence is accelerated when dams prevent sediment from reaching river mouths (e.g., Texas coast, Mississippi delta, Nile delta)
      – geologically fast crustal movement from magma chambers (e.g. Marsili off Italy’s coast) increase or decrease local shoreline sea level
      – extraction of oil, gas and groundwater near shore accelerates subsidence (e.g., Houston, southern Louisiana)

  6. Yet if you look at the tide gage data:
    almost all show rate of increase less than 3 mm/yr. I think this may be because thermal expansion of the water, about half of the increase, does not occur along the shore because the depth of water approaches zero. Although i have never seen it explained this way.

    [Response: I suspect it’s because the NOAA trends are for the entire time span, hence include much data from earlier days when sea level wasn’t rising as fast.]

    • B Buckner:
      So, the shallow water can’t expand much when it’s heated, because there isn’t much of it. Is there some particular aspect of physics that prevents increased sea level in thicker parts of the ocean from draining over to these shallow areas? Or do we just end up with a permanent bulge over the deeper ocean?

    • “Although i have never seen it explained this way.”

      That’s because your explanation is totally wrong. Temperature changes the volume of the water. It doesn’t depend on the local depth.

      I doubt this will make sense to you, though.

      • Thanks for the gratuitous insult. Ocean surface elevations are not flat but vary about 7 inches plus and minus due in part to water temperature.
        Considering other factors such as air temperature changes, surface and upwelling flow, thermal gradients and wind, a “bulge” of 1″ in the central pacific provides a flow gradient to the shore of 1″ over 1500 miles, or 0.00000001 ft/ft. Insignificant, and will not result in a “level” ocean.

      • “Thanks for the gratuitous insult.”

        It was more a of a lamentation for being unable to make a compelling enough argument to convince you.

    • <a href=""PSMSL derived trends

      Below the map there is a place to type in start year and end year. The default is 1900 to 2014, so you’ll only see tide gauges with a record that long. Type in 1985.

    • Sorry about the bad link. This one checks out:

      psmsl trends</a

    • Gauge 111, Fremantle; 1985 to 2014 trend: 5.82 mm/yr.

      Tamino has posted about this gauge in the past. A large number of Australian gauges are plus 4 mm/yr.

  7. I doubt that there is a “shore effect” at least not the one you suggest. If the open ocean rises by a cm then the ocean near the shore needs to rise by the same amount or water would flow from the open ocean towards the shore.

  8. Instead of ‘deniers’, perhaps the word ‘deceivers’ more accurately describes them.

  9. Methane madness

    Isostatic rebound has been demonstrated to be responsive, by some Italians in Greenland, the faster the collapse the faster the bounce. I remember this because I asked James Hansen about it and he said the rate would be constant, then the Italians demonstrated otherwise.

    I, personally am looking forward to the Isostatic rebound associated with the rapid release of Antarctica, a kilometer of rebound, that’s really going to rub things up the wrong way. I predict a super Volcano along the Trans Antarctic mountain range, something along the lines of the Siberian traps.

    • For Tamino’s argument that a constant rate is not seen in the plots showing acceleration, the rate of isostatic rebound only needs to be approximately constant in time, variations in space would be irrelevant.

    • “Isostatic rebound has been demonstrated to be responsive, by some Italians in Greenland, the faster the collapse the faster the bounce.”
      Cumulatively the drought, the mining of aquifers, the draw-downs of reservoirs and the near continuous “export” of water via crops have removed enough mass that the crust is exhibiting isostatic rebound.

      It makes a girl think, y’know?

  10. Methane madness

    ps maybe even the collapse and inversion of the entire Lithosphere.

    • Ummm.. dosen’t happen when we have a glacial-interglacial transition.

      Removing the Antarctic ice sheet may change the pattern of existing volcanic activity for a bit (a few 10k years) and result in some magnitude-7+ earthquakes as the crust re-adjusts, but not much more. A super volcano requires the melting of thousands of cubic kilometers of rock; where would the energy come from?

      • Methane madness

        Yeah ..doesn’t happen interglacially because of slowness.

        All it needs is for the Ross and Rhonne (used to be) permanent ice shelves (900 000 square kilometers, collectively) to snap off and float away from either side of the WAIS and then the WAIS rapidly falls off the land sans buttressing.
        As the West Antarctic land mass rapidly rises up a kilometer, the East Antarctic land mass is held in place by the EAIS. West Antarctica is suddenly a kilometer higher than East Antarctica.
        The energy to fuel a super Volcano comes from the continent ripping in half,

  11. “Both physical and mathematical models suggest a range of from 2 to 6 feet by the year 2100.”

    NOAA Technical Report NOS CO-OPS 083, “Global and regional sea level rise scenarios for the United States,” has an extreme case sea level rise of 2.5 meters (over 8 feet). See Fig. 8 on page 22 of the report (

    This report is discussed briefly John Englander at the blog post

  12. Coincidentally, I’ve just included a reference in my blog to Brunnabend, (2017) which addresses SLR scenarios using high resolution modelling for the North Atlantic. It’s an interesting read:

  13. Michael Hillinger

    Thanks for your analysis, Tamino.

  14. Very nicely done. I especially like the estimate of rates from the smoothed Church & White, and the spatial plots showing sea level accelerations.

  15. For some of the northern N-Atlantic stations, particularly in Scandinavia, land uplift caused by glacial isostatic adjustment needs to be taken into account (e.g. Fig. 3 in, with updated time series here: When land uplift rates are included in the computation, the (open ocean) sea level rises off the Scandinavian coast as well. Detection of long-term acceleration is tricky regionally and can – as Tamino correctly points out – be influenced by changes in near-by land ice, as well as longer-term meteorological fluctuations). But even then, at least for many of the Norwegian stations, long term changes are about to emerge.

  16. Methane madness

    Kenneth Haapala of the Heartland Institute to choose top administrators at NOAA.. in other news actual fox put in charge of hen house.