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Is sea level rise accelerating?

What the science says...

Looking at global data (rather than tide gauge records just from the U.S.) show that sea level rise has been increasing since 1880. The recent rate of sea level rise is greater than its average value since 1930. As for future sea level rise, these predictions are based on physics, not statistics.

Climate Myth...

Sea level rise is decelerating

"A former research director with the Army Corps of Engineers and a former civil-engineering professor at the University of Florida decided to put the sea-rise claims to the test. They gathered U.S. tide-gauge readings from 57 stations where water levels had been continuously recorded for as long as 156 years. The result did suggest the sea level was increasing in the western Pacific, but this was offset by a drop in the level near the Alaskan coast. “Our analyses do not indicate acceleration in sea level in U.S. tide gauge records during the 20th century,” the study’s authors concluded. “Instead, for each time period we consider, the records show small decelerations that are consistent with a number of earlier studies of worldwide-gauge records." (Washington Times)

A paper by Houston & Dean studies 57 tide gauge records from the U.S. (including Hawaii and oceanic territories) and concludes that sea level rise has not accelerated. In fact the authors seem to go out of their way to state that the average result shows deceleration at every opportunity. But there are some big questions about their analysis. Why do they use tide gauge records from just U.S. stations? Why not a global sample? Why use individual tide gauge records when we have perfectly good combinations, from much larger samples, which give a global picture of sea level change and show vastly less noise? Why do they restrict their analysis to either the time span of the individual tide gauge records, or to the period from 1930 to 2009? Why do they repeatedly drone on about “deceleration” when the average of the acceleration rates they measure, even for their extremely limited and restricted sample, isn’t statistically significant?

But the biggest question of all is: what’s the big deal?

Here’s some sea level data, in fact two data sets. One is a global combination of tide gauge records by Domingues et al. (2008). Using around 500 tide gauge records globally, it’s the latest version of the “Church & White” dataset. The other is satellite data:

I averaged the two data sources during their period of overlap, and computed a smoothed version:

This is a global data set, and it’s a worldwide average so its shows vastly less noise than individual tide gauge records. We could even use it to look for acceleration or deceleration in sea level rise. But one thing we should not do is restrict consideration to the quadratic term of a quadratic polynomial fit from 1930 onward. That would be pretty ignorant — maybe even misleading.

As so often happens, one thing to be cautious of is that the noise shows autocorrelation. As Houston & Dean point out, the Church & White data since 1930 are approximately linear, so to get a conservative estimate of the autocorrelation I used the residuals from a linear fit to just the post-1930 data and fit an ARMA(1,1) model.

If we compute the linear trend rate for all possible starting years from 1880 to 1990, up to the present, we get this:

According to this, the recent rate of sea level rise is greater than its average value since 1930. Significantly so (in the statistical sense), even using a conservative estimate of autocorrelation. But the increase itself hasn’t been steady, so the sea level curve hasn’t followed a parabola, most of the increase has been since about 1980. How could Houston & Dean have missed this?

Here’s how: first, they determined the presence or absence of acceleration or deceleration based only on the quadratic term of a quadratic fit. That utterly misses the point. Changes in the rate of sea level rise don’t have to follow a parabola, since 1930 or any time point you care to name. In fact, by all observations and predictions, they have not done so and will not do so.

Second, by using individual tide gauge records, the noise level is so high that you can’t really hope to find acceleration or deceleration of any kind, with any consistency. Not using quadratic fits, and certainly the non-parabolic trend which is present can’t be found in such noisy data sets.

Even so, we can also fit a quadratic (as Houston & Dean did), and estimate the acceleration (which is twice the quadratic coefficient):

Well well … it looks like starting at 1930 is the way to get the minimum “acceleration” by this analysis method. Could that be why Houston & Dean chose 1930 as their starting point?

If we restrict to only the data since 1930, as Houston & Dean did, and fit a quadratic trend, we get this:

Can you tell, just by looking, whether it curves upward or downward? Clearly, the parabolic fit doesn’t show much acceleration or deceleration, if any. We can get a better picture by first subtracting a linear fit, then fitting a parabola to the residuals?

That answers the question: the quadratic fit shows acceleration in the Church & White data. But, when autocorrelation is taken into account, the “acceleration” is not statistically signficant.

But — just because the data don’t follow a parabola, doesn’t mean that sea level hasn’t accelerated. Let’s take those residuals from a linear model, and fit a cubic polynomial instead:

Well well … there seems to be change after all, with both acceleration and deceleration but most recently, acceleration. And by the way, this fit is significant.

And now to the really important part, which is not the math but the physics. Whether sea level showed 20th-century acceleration or not, it’s the century coming up which is of concern. And during this century, we expect acceleration of sea level rise because of physics. Not only will there likely be nonlinear response to thermal expansion of the oceans, when the ice sheets become major contributors to sea level rise, they will dominate the equation. Their impact could be tremendous, it could be sudden, and it could be horrible.

The relatively modest acceleration in sea level so far is not a cause for great concern, but neither is it cause for comfort. The fact is that statistics simply doesn’t enable us to foresee the future beyond a very brief window of time. Even given the observed acceleration, the forecasts we should attend to are not from statistics but from physics.

Many thanks to Tamino from Open Mind for allowing us to republish his post So What?

Advanced rebuttal written by Tamino

Update July 2015:

Here is a related lecture-video from Denial101x - Making Sense of Climate Science Denial

This rebuttal was updated by Judith Matz on September 13, 2021 to replace broken links. The updates are a result of our call for help published in May 2021.

Last updated on 8 July 2015 by pattimer. View Archives

Printable Version  |  Offline PDF Version  |  Link to this page

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Comments 26 to 45 out of 45:

  1. From time to time I have e-mailed some of the principle names in Climate Science with a specific question but mostly I don't want to waste their time and I don't expect a dialog with them although it did happen once. Furthermore they don't show up on blogs, if they do it isn't under their own name. I most certainly am not going to e-mail John Church to criticize his paper. I don't consider Tamino a principle or objective.

    [DB] "I don't consider Tamino a principle or objective."

    Well then, let me ask you this: 

    How many legs does a dog have if you call the tail a leg?

    Four; calling a tail a leg doesn't make it a leg. (Abraham Lincoln)

    Discounting Tamino's analysis because you don't like it or don't consider him objective doesn't detract from the fact the Tamino is a professional time-series analyst whose work in climate science not only stands the test of time but is widely considered a de facto standard in climate science.

    Yes, Tamino can be irrascible.  Mostly that stems from those who refuse to learn, have a large vein of Dunning-Kruger running through them and those slander working climate scientists.  We are similar in that regard.  But again, that does not detract from his work.

    If you have issues with the work that forms this post, take it up with him.  If you have questions regarding the work of Church & White, take it up with them (I have yet to find a climate scientist unwilling to help those with genuine questions about their work).

  2. Thanks for fixing the tags.
  3. Steve Case @25: Preliminary points: 1) Records where not eliminated if they where longer than 2 years in length (as you, perhaps mistakenly, indicate), but because they were shorter than two years after 1 or 2 month gaps in the record had been infilled. The obvious reason is that a 2 year record tells you almost nothing about long term trends. 2) The 1063 records eliminated on the basis of redundancy where eliminated because they where duplicate records. 3) The 95 records eliminated because they where outside the Topex coverage where eliminated because the study was an explicit comparison of the tidal gauge and Topex data. Such a comparison can only be sensibly be made over the area in which Topex gathers data. 4) Likewise the data eliminated because it was more than 250 km from one of the Topex grid points was eliminated because it could not be directly compared to Topex data. 5) Contrary to your claim, and as you yourself calculated, there were 713 records eliminated because disagreement among closely located tide gauges, physical location, very noisy data, or very high trends provided reason to believe the tide gauge was measuring unusual local circumstances (subsidences, siltation, etc) rather than global changes in sea level. That the number eliminated for each of these reasons is not recorded separately is irrelevant. 6) No records where eliminated by combination. Combination means that "Where there were multiple tide gauges for a single grid point, the change in height at each time step were averaged to produce a single time series." If we are to call that "elimination" then when you took averages of data for each coast line, you 'eliminated' over 1033 records when you took averages by coastline (see your @7) I need to make these preliminary points to clean up your tendentious and inaccurate description of Church and White's method.
  4. Steve Case @25: @7 you said:
    "I intend to ignore any further critiques you have about the PSMSL data as it's not the issue."
    I responded @8:
    " If you want to introduce your chart as evidence, you need to defend its construction. If you don't want to defend its construction, you ought to withdraw it. As it stands, however, it appears you want to make use of a graph in which artifacts of the data will introduce a very large amount of noise."
    Well, it turns out that you do want to introduce your chart as evidence, and have done so @15, @18, and @25. However, you show no inclination to defend it against previously mounted criticisms which show the chart to be dominated by noise. Rather, you falsely call it a "straight forward analysis", using a label rather than a defense of your methods to suggest the chart is actually worth anything. So let's compare Church and White's analysis with your supposedly straightforward analysis: Quality Control: Church & White - extensive vetting for spurious trends in the data; Case: None. Grouping: Church and White: Data grouped by cell with a maximum 250 km radius from the center point of the cell; Case: Data grouped by arbitrary 'coastlines' with no consistent principle in determining coastlines applied across all data. Specifically, all nations are given a separate coast line no matter how small. Some coast lines ared divided by necessity of contiguous status. Thus Canada has two coast lines, one for the west coast, and one for the east and north coast. In contrast the US has separate coastlines for the contiguous Gulf and East coast coastlines. Australia has just one coastline for the entire continent plus offshore islands, while the US has separate coastlines for not just the Gulf and east coast, but also for the west coast, for Alaska, for Hawaii, and for the Aleutians. Correction poor geographical sampling: Church and White:
    "Our approach relies on resolving large-scale ocean variability by using as many tide gauges as possible to estimate the global distribution of sea level for each month/year between 1950 and 2000. We use sea surface height anomaly satellite altimeter data to estimate the global covariance structure as expressed in empirical orthogonal functions (EOFs). We then estimate the amplitude of these EOFs by using the relatively sparse but longer tide gauge records. The estimated (reconstructed) global distribution of sea level for each month is obtained as the sum of these EOFs.
    Case: None Correction for Glacial Isostatic Adjustment: Church and White: Applied; Case: None. Correction for large scale changes in air pressure: Church and White: Reverse Barometric applied; Case: None. Personally, I do not think geopolitics to be the most straightforward way to group data in determining mean sea level. That is, however, the basis of your method. Beyond that, what distinguishes your method is the assumption that the silting of estuaries, land slumping or subsidence etc are of no relevance in measuring sea levels. So while your method can be called simplistic, it is false to call it straight forward.
  5. Steve Case @25 Final comments: Just to pick up on two minor points: 1) You have the units wrong on the the y axis of your graph. 2) The large gap between your graph and that by Church and White is almost entirely a consequence of a >50 mm fall in sea level in 1883 in your graph. You may want us to believe that was a genuine fall in sea level, rather than an artifact of your shoddy methods, but we are not that easily conned. When that obvious artifact of noise in your chart exists, however, it is disingenuous to call attention to the gap between your chart and Church and White's as if that gap some how called Church and White's analysis into question.
  6. Steve Case @19, below is the HadSST2 measure of global sea surface temperature for the period of January, 1990 to December, 2011. As you can see, the convex shape of the 60 month mean is not a function simply of one or two years at the start, or just 1998 (and is clearly not a function of 2011, which is not included. Your attempt to obviate my criticism @11 clearly ignores the duration of Pinatubo's cooling effect, and the El Nino's of 2003, 2005, and 2007, and the La Nina's of 2008 and 2009. The fact that it is so easy to pick out a physical cause of the slightly decelerating sea level rise of over the period 1992-2011, and that that cause is sea surface temperatures should not be giving you confidence for the future. More importantly for the present discussion, it should reinforce in you the need to only consider the trends which are statistically significant.
  7. Tom, I would agree that the most likely cause for the deceleration of SLR in the past decade is the slight cooling recently in SST.
  8. #28 29 30 31 Tom Curtis The GIA adjustment changes the overall slope of the time line, and gives it a boost of a bit over 0.5 mm/yr. It doesn't change the shape of the curve. That is to say it has nothing to do with acceleration rates of sea level change. The issue isn't the noise and fall at the 1883 mark, the issue is the shape of the two curves over the nearly 130 year time line, and the shape of the curve has everything to do with the question, “Is sea level rise accelerating?” But, many of your points are valid, what I did is usually described as quick and dirty back of the napkin figuring and leaves a lot to be desired and is certainly not the fine tuned product of an academic opus. Which reminds me of an analogy. Two guys buy the exact same type of car both EPA rated to get 30 mpg. One of the guys takes his car to a special mechanic for some fine tuning and now he claims to get 50 mpg. Doesn't add up. No one would believe it. (-Snip-) I’ve made that point several times now. I should give it a rest. We have two separate measuring systems, tide gages and satellites. That they report different numbers ought not be a big surprise. In a machine shop there are many ways to measure dimensions; micrometers, coordinate measuring machines, optical comparators, gage pins, bore gages, calipers, snap gages, rulers, and a host of customized gages. They all give slightly different answers and each has their own uses. Trying to get them to all give the same answers is a fool’s errand. But that's what we seem to be doing by trying to match tide gages with the satellites. And finally there’s an expression about picking the fly specks out of the pepper. Whether the rate of sea level bumps up 0.013 mm per year or not isn’t all that important. After all, if you run the numbers we’re only talking an extra 65 mm in 100 years.

    [DB] Speculations of academic fraud snipped.

    "I’ve made that point several times now. I should give it a rest."

    Yes, you should.  Any more violations of the Comments Policy will result in automatic deletion of your entire comments.

    "After all, if you run the numbers we’re only talking an extra 65 mm in 100 years."

    You make the classic error of presuming SLR will be linear when history gives us ample examples that SLR is highly nonlinear.

    "But that's what we seem to be doing by trying to match tide gages with the satellites."

    That's what real scientists, like Dr's Church and White, do.  Amateurs struggling to replicate their work without a foundation in the science and a thorough understanding of the literature are the ones conducting the "fools errand".

  9. Steve Case @33, that is an interesting analogy. However, it is fairly obvious in that analogy that Church and White are the EPA, while you are the back shed mechanic gaping spark plugs with a ball-pein hammer. I wonder why you do not draw the obvious conclusion. Having said that: 1) The GIA may not effect the shape of the curve, but strong changes in the regional balance of your data will. What is more, failure to correct for barymetric pressure may also effect acceleration. Consider, for example, this chart of sea level rises by oceanic basin from Jevrejeva et al, 2006: The different basins to not rise or sink synchronously. The reason for this is that major weather patterns such as ENSO or the NAO shift pressure patterns over large areas of ocean, with a consequent change in sea level as water is pushed from one part of the ocean to another. If your data set shows a regional bias, and this phenomenon is uncorrected, that will result in a significant distortion of the result, a distortion that change the acceleration pattern. 2) The issue is the noise, in that a large part of your failure to reproduce Church and White consists of the fact that you have not successfully excluded noise, and indeed have decreased the signal to noise ratio with your reconstruction technique. 3) It appears you have never worked in a workshop, for if you had you would recognize that if your means of measurement significantly disagree, you have a major problem. We may not expect the micrometer and the steel rule to give us exactly the same measurement, but if they are not identical plus or minus 0.5 mm, then either at least one is faulty, or your measurement technique is error prone. 4) See you are the one who chose to attack the science on this point, it is hypocritical of you to then accuse us of "picking the fly specks out of the pepper". You add to that hypocrisy an egregious error. The current rate of sea level rise is between 2 and 3.2 mm per year, leading to an expected sea level rise of 200 to 320 mm per century if nothing changes. Even as a simple projection you 65mm is an obvious error. Such simple projections, are, however, significant underestimates both because they do not account for additional increases in temperature, nor for glacial melt water, which between them will push sea levels up by between 0.6 and 2 meters by the end of the century. Not the most serious implication of global warming, but not negligible either.
  10. Eric the Red @35, on the contrary, Jevrejeva et al, 2006 and Church and White 2006 (and 2011) both show that sea level rise as determined by gauges is within the error bars of that determined by satellite altimetry over concurrent periods. What is dissimilar is the current trend and those earlier in the twentieth century, which where lower. You evidently want it to be true that there is a mismatch, but neither you nor Steve Case have given us any reason to believe it.
  11. Over at this site: Is the head line: "NASA Satellites Detect Pothole on Road to Higher Seas" And some text: "... every once in a while, sea level rise hits a speed bump." I thought that rising sea level is a negative aspect of "Climate Change" and that we in fact would like to not go there. So the choice of words, "Pothole on Road to", and hitting a "speed bump" are a bit mysterious. Terms like remission, respite, suspension, reprieve, let up, lull etc. weren't considered. Food for thought as to why that is.

    [DB] There is already a SkS thread on that; please place any comments on that topic there:  NASA Satellites Detect Pothole on Road to Higher Seas

  12. Steve, a path or road is a good metaphor for a trend line. Remission: cancer carries too much other baggage to be a good metaphor, even though mitigation can help reverse the trend. Respite: that would be a good word, but its metaphorical value is not nearly as good as 'pothole'. Suspension: nothing has been suspended. The forces working for sea level rise are still in place; they've simply been temporarily overbalanced by other forces. Reprieve: a reprieve carries with it the sense of finality. Respite is better, but, again, both have little metaphorical sense. Let up: indicates that the force at work has stopped working for a while. Not true. Lull: ugh, not appropriate to a trend line. The idea of a 'pothole' and a road serves the idea of a trend line well, and a road (and the implied driver) is a relevant image where the A in AGW is concerned (we are driving climate change at least partially through our mode of transport). A 'speed bump' further implies an accelerating rate. Potholes make me think of asphalt, too, and asphalt makes me think of oil.
  13. Hello all. I recently stumbled upon a paper which states, in the abstract, that global mean sea level "rises with the rate of 3.2 ± 0.4 mm/yr during 1993–2003 and started decelerating since 2004 to a rate of 1.8 ± 0.9 mm/yr in 2012." This seems to indicate that sea level rise is decelerating globally (not just locally as was the case with Houston and Dean's paper). The paper can be viewed here. I would like to get some feedback on whether or not this does any damage to the apparently "consensus" view that sea level rise is accelerating.

  14. jsmith, take a look at why SLR might seem to be decelerating between 2004 and 2012.  Between 2011 and 2013, SLR was rising at ~7mm per year.  You'd do better to ask what caused that trough.

  15. jsmith - that paper has been doing the rounds on contrarian blogs, so you probably 'stumbled' across a contrarian blog.

    I haven't looked at the research paper in detail, but the general slowing of sea level rise after 2004-2005 fits in with the sharp acceleration of heat uptake into the ocean during 2000-2005, and a slower rate of heat uptake thereafter. This 'slowdown' is perhaps the most striking feature of the Hiroshima widget.

    The recent trend in sea level rise is consistent with ocean heat uptake, so we shouldn't be surprised that the recent trend in sea level rise has slowed somewhat too. A similar pattern seems to have occurred during the 20th century too - short-term accelerations and decelerations against a background of long-term acceleration in sea level rise.

    There are a few other factors to consider too (decadal variations in continental storage of water mass, for example), but land-ice melt is accelerating and thermal expansion is not really going to be a factor throughout 21st Century - the disintegration of the vast ice sheets of Greenland and Antarctica will be.

  16. jsmith - I believe the issue of concern is statistical significance. "Since 2004" is a very short time period, including the 2010 dip in sea level associated with La Nina, or "pot hole". 

    You really need to look at multi-decadal time periods to determine trends, as in Church and White 2011 who found "1900 to 2009 is 1.7 ± 0.2 mm/year and since 1961 is 1.9 ± 0.4 mm/year" and "For 1993–2009 and after correcting for glacial isostatic adjustment, the estimated rate of rise is 3.2 ± 0.4 mm/year from the satellite data and 2.8 ± 0.8 mm/year from the in situ data". They also note that "There is considerable variability in the rate of rise during the twentieth century but there has been a statistically significant acceleration since 1880 and 1900 of 0.009 ± 0.003 mm/year2 and 0.009 ± 0.004 mm/year2, respectively." (Emphasis added)

    Short time periods, such as a single decade, are only going to show noise, not trends. While I don't subscribe to that particular journal and have not read the entire article, I fear that the paper is not properly evaluating the statistical significance of their results. If they can clearly support their hypotheses it will be interesting - but as it stands I see little support for such claims. 

  17. The rising Oceans,Global warming or not.

    Simple experiment:
    Fill a bucket to the top with water, then add a brick.
    What happens the water overflows the weight of the lost water equals the weight of the brick, it's called displacement.
    Add some thing to a body of water what happens?
    Throw a brick in the ocean, no noticeable difference.
    But throw billions of tons of bricks in and float thousands of ships and boats of all sizes on then we have Oceans rising,
    melting ice:
    add a large block of ice in your bucket then fill the bucket to the top, the ice floats above & below the water, as the ice melts will the water overflow? Remembering displacement,
    Check out below for some reasons for the rising of the oceans.
    Listed below is just a small amount of the reasons.

    Apparently in WW1 a total of 375 U boats sank 6596 merchant ships, a total of 12,800,000 tons.

    The Japanese lost 1,178 Merchant Ships sunk for a tonnage total of 5,053,491 tons. The Naval losses were 214 ships and submarines totaling 577,626 tons. A staggering five million, six hundred thirty one thousand, one hundred seventeen tons,
    (5,631,117 tons), 1,392 ships

    It's estimated that 10,000 of these large containers are lost at sea each year, Average tonnage 18 tons
    180,000 tons per annum

    According to an annual analysis from insurer Allianz, 94 ships on average(over 100 gross tonnes) each were completely lost in 2013. There are many reasons for a complete loss. “Foundering” (which means sinking or submerging) caused the vast majority of the big losses

    Over 30,000 large Ships over 500 tons launched since 1975 not to mention the 100 of thousands sail boats small yatch's ferries etc

    Now lets add the land Pushed into the ocean to build Airstrips, Islands & Erosion.
    Where doe's the water go, It just disappears, yeah right. “IT RISES”
    For every action, there is an equal (in size) and opposite (in direction) reaction

  18. Kerry Randell @42, taking your figures on total tonnage, and assuming the average container loss rate extends back to 1945, and that the average ship tonnage loss is 250 with the average loss also extending back to 1945, that yields a total 31,054,617 tonnes lost as a rough estimate.  Given that the density of sea water is 1.025 Tonnes per meter cubed, that leads to an estimated displacement of 30,297,187 m^3 of displacement.  Averaged over the ocean surface of 361, 132,000 km^2 of surface area, that leads to an estimated 0.000084 milimeter rise in sea level based on your assumptions, for the entirety of lost shipping in the 20th century.

    However, that is likely a significant overestimate.  The mass of water displaced only equals the mass of the object if the object is floating.  If it sinks, the water displaced equals the volume of the immersed object, which is necessarilly less than the volume of water equal to the tonnage of the immersed object, for if it were not, the object would float rather than sink.  Ergo, your initial assumption is completely wrong headed.  The mass of water displaced by various vessels sunk at sea is far less than the displacement of the vessels.

  19. Kerry... You're doing a classic "missing denominator" calculation. You've estimated out that the number of ships displacing sea water is a very large number. That's your numerator. Your denominator is the total tonnage of all the earth's oceans, and that would make the result an extremely small number.

  20. Discussing sea level and global warming to appreciate fg. the trends one should study the whole process in historical time line:

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