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Climate Hustle

Misinterpreting a retraction of rising sea level predictions

Posted on 25 February 2010 by John Cook

A new skeptic argument has emerged that upon close inspection, is a polar opposite to the scientific reality. This week, scientists who published a 2009 paper on sea level rise retracted their prediction due to errors in their methodology. This has led some to claim sea levels are no longer predicted to rise. This interpretation was helped no doubt by the unfortunate Guardian headline "Climate scientists withdraw journal claims of rising sea levels". However, when you read the article and peruse the peer-reviewed science on future sea level, you learn that the opposite is the case.

The IPCC 4th Assessment Report predicted sea level will rise between 18 to 59 cm by the year 2100. Many consider this a conservative estimate as observed sea level rise is tracking at the top range of IPCC estimates (Rahmstorf 2007, Allison 2009). However, a study led by Mark Siddall examined how sea levels have changed over the past 22,000 years in response to temperature change (Siddall 2009). This enabled them to predict how sea level would respond to future warming, estimating sea level rise between 7 to 82 cm by the year 2100. Siddall's paper concluded that this increased confidence in the IPCC projections.

However, a later study using similar methods to Siddall 2009 came to dramatically different results, estimating sea level rise of 75 to 190 cm by 2100 (Vermeer & Rahmstorf 2009). Why the discrepancy? Judging by the acknowledgement in Siddall's retraction, one speculates that Vermeer and Rahmstorf discovered flaws in Siddall's methodology and notified the authors. Siddall saw that the errors undermined their results and retracted their paper. So we have two papers using similar methods - one predicting low sea level rise, the other predicting high sea level rise. The low sea level rise is found to be in error. While some are spinning this result to imply no sea level rise, in actuality it increases our confidence in high sea level rise.

Vermeer's results are confirmed by another study that approach the sea level question from a different angle, examining the dynamics of calving glaciers (Pfeffer 2008). The conclusion was a predicted sea level rise of 80 cm to 2 metres by 2100. Further evidence of the ice sheets' high sensitivity to warmer temperature comes from paleoclimate studies of the last interglacial period 125,000 years ago. At that time, global temperatures were around 2 degrees warmer than now. This is the amount of warming expected for some of the lower emission scenarios. At that time of the last interglacial, sea levels were at least 6 metres higher than present levels. So while we expect sea levels to rise up to 2 metres by 2100, they will continue to rise afterwards to at least 6 metres.

Future sea level rise will be one of the most serious impacts of global warming on humanity, with much of the world's population clustered around coastlines. That my daughter will see sea level rise of 1 to 2 metres in her lifetime is for me, an unhappy prospect. This scientific reality is a stark contrast to the 'Now You Can Forget About Those Rising Seas' attitude. Despite the serious picture painted by the peer-reviewed science, these kinds of misinterpretations turn the climate debate in an almost farcical direction. One could blame the Guardian for a carelessly worded headline. More blame should be apportioned to those who pontificate from their soapboxes without bothering to acquaint themselves with the science. That skeptics allow themselves to be tossed and turned by media headlines is the very antithesis of genuine skepticism.

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Comments 51 to 100 out of 107:

  1. Berényi Péter @14 "I care neither for reviewers nor the scientific community, but I do care for logic & truth."

    That statement is not consistent with you posting here in a science forum. Also, there is not a diconnect between science and "logic and truth" as you suggest.

    Whether you like it or not, the research in question has been undertaken and reviewed by scientists who are experts in the field. You should care what they have to say b/c they have invested infinitely more thought and effort on this problem than anyone us here.

    "Appealing to authority is NOT the way science is done. Not even scientific authority is competent in this respect. As long as you are able to understand stuff, you are self sufficient."

    I'm not appealing to authority, and I am very familiar with how science is done. There is nothing wrong with acceptingand acknowledging that soneone is an expert whether they be a cosmologist, oncologist or climate scientist. I do not know to which "scientific authority" you are referring. As for understanding stuff, dhogaza and others have explained to you why you do not understand as much about this complex problem as you might think. And that is not a slight, we here are all in pretty much the same position in terms of level of understanding and, for reasons stated earlier in this post, we should be very cautious about being cavalier or simply dismissing the science.

    Science is, whether you like it or not, remarkably good at self correcting. It also advances if someone, like you who is critical of the methods and analysis, is willing to invest the time and effort to improve upon previous work and address the perceived weaknesses, rather than simply poking holes in someone elses work. I, for one, don't care what your credentials are, so long as you can undertake solid research which survives the rigour of peer-review and subsequent critique by the collective expertise in the field, then you have advanced the science.

    Like it or not, the science is converging towards the higher end of the expected range of increase in SLR. A recent study by SCAR projected that sea level will increase by as much as 1.4 m by 2100-- and SLR will not magically stop rising in 2100.

    Just as an oncologist is not paid to ignore unfortunate diagnosis and plausible outcomes/prospects for recovery (or not), nor are scientists paid to avoid telling us about the threat of potentially serious scenarios. That is not being "alarmist" is is being prudent and responsible.
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  2. Berényi Péter, please see :

    "In the United States:

    Sea level has been rising 0.08-0.12 inches per year (2.0-3.0 mm per year) along most of the U.S. Atlantic and Gulf coasts.

    The rate of sea level rise varies from about 0.36 inches per year (10 mm per year) along the Louisiana Coast (due to land sinking), to a drop of a few inches per decade in parts of Alaska (because land is rising)."

    Also :

    "Depending on the rates of vertical land motion relative to changes in sea level, observed local sea level trends may differ greatly from the average rate of global sea level rise, and vary widely from one location to the next."
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  3. John Russell:

    Was it Ghandi who said, "first you'll be ignored; then you'll be laughed at; then they'll fight you; and finally you'll win"?

    Gather strength everyone; it's always darkest just before the dawn.

    I don't know what Ghandi actually said. However, he was a politician with an idealistic vision, not a scientist.

    I live near Port Jackson (aka Sydney Harbour) - one of the most beautiful harbours in the world. It's also a flooded river valley carved out aeons ago before a massive sea level rise.

    One river valley lost - one beautiful harbour gained. Climate change brings winners and losers like any process in nature. It's helpful to discern likely outcomes - we can try to modify them or adapt to them. However, we have to learn to accept the uncertainties inherent in scientific discourse about highly complex systems and perhaps our own limitations in the face of processes incorporating variables as yet unknown to us.

    This requires humility - a quality sadly lacking in many advocates on both sides of the climate change divide.
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  4. #21 Jeff Freymueller at 10:48 AM on 25 February, 2010:
    "Whether or not you can detect an acceleration in a single tide gauge record is really beside the point"

    No acceleration upward at Stockholm, Sweden either. I could download the entire PSMSL dataset and compute acceleration for each tide gauge, but I can't believe it is not done already. Any pointer?

    However, acceleration of even a single tide gauge (or the lack thereof) is remarkable, provided the record is reliable and there is no vigorous tectonic activity in the region.

    As satellite measured recent sea level rise is faster than estimated 20th century average, it is often cited as proof of acceleration. However, satellites need calibration, must be faulty if no acceleration is detected at ground level.
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  5. "It's also a flooded river valley carved out aeons ago before a massive sea level rise. One river valley lost - one beautiful harbour gained." just a tiny missed point here Chris. The period from the river valley to the flooded harbour was long, and the people being affected by it had a highly mobile small population, no permanent infrastructure, and a hunter-gatherer economy that was just as happy fishing in a harbour as hunting in a valley. None of that applies to 21st century Australia or indeed any other modern country.

    And by way of warning - the last time Australia's climate switched from cool and wet to hot and dry (essentially the modern climate although a bit drier), dozens of large animal species went extinct, unable to deal with vegetation zones shifting outwards over a period of a few thousand years. If this scenario is repeated over a time span of a hundred years or less there are going to be massive extinctions of flora and fauna, and the agricultural communities of regional areas. The only "winners" at the end of the Pleistocene were a few desert species like red kangaroos. Hard to see any winners this time around. Certainly no human winners.
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  6. #24 Albatross at 10:58 AM on 25 February, 2010
    "there is not a diconnect between science and "logic and truth" as you suggest"

    Right. This is the way it is supposed to be. Unfortunately ideals are not always met.

    #25 JMurphy at 10:59 AM on 25 February, 2010
    "observed local sea level trends may differ greatly from the average rate of global sea level rise, and vary widely from one location to the next"

    Of course. But right now we are not talking about speed of rise/sinking but acceleration.
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  7. Based on some back/forth I'm seeing in these posts, I see a fallacy that the so-called "skeptics" use. They mis-apply the "appeal to authority" fallacy - which in itself is a fallacy.

    First, any reasonable person knows no one person can possibly know the minutiae of every detail about climate change. Like any scientific discipline, it's a collective (peer-reviewed) process.

    Second, because of the first point, we MUST, at some point, defer to other experts. The so-called "skeptics" then claim this is the "appeal to the authority" fallacy. Not. So. Fast.

    If that were true, we'd all be guilty of that, each time we visit the family Dr. After all, we don't know all there is to know about medicine, but we do "appeal to the authority" when it comes to medical advice.

    Here's a link that explains that at times it is reasonable to appeal to the RIGHT authority.

    So for me, I am perfectly happy deferring to the collective knowledge of the climate scientist, as much as I am happy to take the advice of my family Dr. :-)

    As I said in my earlier post - being a bit off on the predictions about the timing of the effects of climate change, does not change the fact that ACC is indeed happening. There are, and will be, consequences.
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  8. Berényi Péter (22) wrote:
    "Fitted least squares parabola to data (960121.rlrdata), coefficient of x^2 negative. "

    That's quite odd, because when I do that I get a positive coefficient for x^2. 0.0023, if I use the interval from 1883 - 2008 (skipping the 1878 - 1893 gap) or 0.0036 over the entire 1856 - 2008 period.

    But the acceleration becomes even more obvious when you plot a series of 30-year linear trend lines.
    1900 - 1929 slope = 1.6723
    1940 - 1969 slope = 2.8465
    1976 - 2008 slope = 3.983
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  9. David:

    'Hard to see any winners this time around.'

    As a highly technological society, we are vastly more adaptable then hunter-gatherer societies. Moreover, extinctions are neither good nor bad - were there no extinctions, there would be no evolution.

    Extinctions (like the poor) will always be with us. So too with change. Not that we want to accelerate extinctions (or increasse poverty) if that can be avoided.

    The real issue relates to the priorities we set for our resources. If we try to do this as rationally as our limited knowledge permits and avoid emotive value judgments, we are likely to emerge with better outcomes.
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  10. Berényi Péter, your chance of regaining credibility here would probably go up a bit if you acknowledged your interpretation of Siddal's comment about "overestimating the sea level response" was incorrect.

    I didn't go to all the trouble of making that post just to see you ignore it.
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  11. I'm not sure that the blog you linked to is really arguing that sea levels won't rise. The title and first line maybe a little tongue in cheek but generally they are reporting the facts of the situation.

    Similarly a more (dis)respected skeptic blog WUWT reported this mentioning the Vermeer and Rahmstorf estimates as you do.

    Seems like you are setting up a paper house to knock down.
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    Response: Some will report it accurately, others lead with headlines like 'Now You Can Forget About Those Rising Seas'. I'm in the unfortunate position of having to respond to the lowest common denominator.
  12. Uh, HumanityRules, the lawyer in question got corrected in the comments. That's not quite the same as suggesting that his blog post isn't arguing that sea levels won't rise.

    His only post in the comments section suggests he didn't quite understand the implication the first time his error was pointed out (he suggests it means that the *lowest* estimate can't be established, and says nothing about the upper). And least he did try to understand the correction.

    I'll give him points for:

    1. Letting posts through showing his interpretation was wrong.

    2. Not showing the kind of stubborn attachment to a misinterpretation that a Certain Someone on this blog is showing.

    3. Being such an unknown blog that the corrections weren't immediately screamed down by a horde of the typical denialist trash.

    We'll see whether he'll state something showing he actually understands the full depth of his misunderstanding .
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  13. Response to #34 and #35

    I'm not even sure that is a climate skeptic blog it looks like a rightwinger mainly concerned with slamming Obama from the list of entry titles.

    I just think if you are going to lead with a title that suggests skeptics are using this retraction to say sea-levels aren't rising you shouldn't use an obscure rightwing blog to make your point. After all in the final paragraph you seem to tarnish all skeptics with this one mans opinion. This is not the skeptical concensus from the look of things.
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  14. To be fair to Berényi Péter, the word 'overestimation' also led me to ask upthread if that meant sea-level rise had been overestimated. Only having access to the abstract, I didn't know what 'response' referred to, and I did wonder. Thus I asked a question rather than pretended to an authoritative view, which is hardly warranted if you haven't read the whole paper.

    My query was satisfied by following the trail pointed out by others here.

    No acceleration upward at Stockholm, Sweden either. I could download the entire PSMSL dataset and compute acceleration for each tide gauge, but I can't believe it is not done already.

    Sea level change and rate of change is different even within a few hundred kilometers. As far as I'm aware, the tide gauge record from 1870 shows an accelerated increase.
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  15. To be fair to Berényi Péter, the word 'overestimation' also led me to ask upthread if that meant sea-level rise had been overestimated.

    It had me wondering, too. You and I investigated. Berényi Péter said it means there'd be less sea level rise than predicted.

    That's a qualitative difference some folks might learn from ...
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  16. "Skeptic" is the operative label at this website for those that doubt or even question IPCC conclusions. For all my reading here, I am still not sure what the correct term is for non skeptics. Would anyone know the answer to this question?
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  17. Skepticism denotes one main component of epistemic virtue. Everyone is for virtue. So, everyone claims to be advocating true skepticism. I can hardly find a more polite way to refer to people who expresses a level of doubt that seems to me unwarranted than to call them skeptics -- in relation with some position that seems well established, such as AGW -- when they usually claim the title for themselves. I'd rather not call someone a denier when I wish to engage in dialogue with him/her.
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  18. Also, as a practical matter, one normally applies the branch of science that best fits the problem to be solved. When dealing with a global problem such as global warming, it would seem that simple thermodynamics could give you most of the answers one needs when it comes to analyzing energy balance.

    After that, the problem is either regarded acute/drastic, or subtle/minor. According to all the predictions, supposedly the situation is fairly acute/drastic. Acute/drastic problems, require acute/drastic solutions, and yet it seems that the very folks that take their work so seriously here are the same that are only able to prescribe whimpy solutions such as curbing CO2 emissions and looking for "alternative" energy sources that in end also have their own thermal footprints.

    If the problem is indeed linked to humans activity, it is not because of what a few people are doing. It is a problem of big numbers. And if there being so many people is creating a problem, the issue is about dimensionality. This then calls on other scientific disciplines that naturally fit the problem, such as behaviorial psychology, sociology, economics, and political science.
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  19. #40
    The answer to my question requires just one word. I dont see your reply as answering my question (at all).

    It is characteristic in circles or prejudice to consider those within the group as "normal", and only have labels for those outside the group.
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  20. RSVP @39/42, I am a reader and do not represent the views of the people that maintain this site, but I don't think it is very meaningful/constructive to divide the people that post here into opposing camps labeled "skeptics" and "others" (your question seems to be "what are the "others" called?)... I think doubt lies at the heart of the scientific method, so in that sense everybody here is a skeptic. It seems to me that the purpose of this site is to shed light on/expose those arguments that either misinterpret, misunderstand or misrepresent the current body of scientific research (ideally the focus should be on the arguments, not the people).

    Returning to the topic, it does seem the Siddall abstract is very easy to misinterpret (unless you are careful to find the definition of sea level response), I am surprised the authors did not see the potential for that misunderstanding (especially as they were withdrawing a paper). Unfortunately, climate scientists are working in a very politically charged field and need to take extra care to be completely clear about their findings, especially in the abstract and conclusion. It is no longer just an academic audience that is reading their papers and in the age of the internet a misunderstanding can spread like wild fire and can be very difficult to reverse (there are lots of examples of that!)
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  21. "It stood 4-6 meters above the present during the last interglacial period, 125,000 years ago, but was 120 m LOWER [...] at the peak of the last ice age, around 20,000 years ago." - "Sea Level Rise, After the Ice Melted and Today" (
    Post-glacial isostatic rebound, and it also should be included ...
    Much better to compare (here) is an early Holocene optimum.
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  22. The mass of ice, the extent of glaciation from the last interglacial period (125.000 years ago), were higher than during the last glaciation.
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  23. RSVP, 'skeptic' is a term that those individuals have chosen for themselves... not a 'prejudicial label' applied to them by others as you suggest. Indeed, I consider it (along with the also self-chosen label of 'realist') a highly inaccurate description for the vast majority of the people who claim it on this issue.

    I'm not aware of any self applied label for the 'other' group... which I suspect is because we see ourselves as individuals separately evaluating the facts, rather than some sort of political/cultural movement.

    As to curbing CO2 emissions being a "whimpy" solution... if it is such a tiny step, why such resistance? Eventually it comes down to the simple fact that the more CO2 we put into the atmosphere the worse the problem will get. If we could somehow replace fossil fuels with clean energy today global warming might even be a net positive... sure, we'd still end up flooding alot of coastal areas over the next few centuries, but a slightly warmer planet would actually be beneficial in many ways. However, the human race obviously isn't going to give up fossil fuel addiction that easily... so it becomes a question of how bad the situation will get. Your suggestion of population control, even if it weren't impossible, wouldn't help at all if we continued fossil fuel use at current levels.
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  24. AndrewY,
    "I am surprised the authors did not see the potential for that misunderstanding".
    I can see your point, but you shouldn't be surprised. After all they're writing on a scientific journal and readers are supposed to know the science.
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  25. Berényi Péter:

    "Since observed sea level data are taken from IPCC AR4 WG1 where twentieth century sea level rise is estimated to be 14±10 cm"

    The Church and White (2006) paper, used by Vermeer & Rahmstorf (2009) and the IPCC, estimates 20th century rate of sea-level rise at 1.7 ± 0.3 mm/yr, so, unfortunately, you fail at quoting, among other things.
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  26. #48 rocco at 22:55 PM on 25 February, 2010
    "you fail at quoting, among other things"

    Yes, I am evil. I have quoted Siddall 2009 on the IPCC thing in a disguised form. Had been curious if anyone noticed.

    "Our model [...] estimates 4–24 cm of sea-level rise during the twentieth century, in agreement with the Fourth Assessment Report of the Intergovernmental Panel on Climate Change"

    BTW, IPCC AR4 WG1 says "we assess the rate [... ] for the 20th century as 1.7±0.5 mm/yr". It is 12-22 cm. One can argue ad infinitum about if it is "in agreement" with a 4-24 cm model output or not.
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  27. Berényi Péter,
    no need to argue on this, a linear extrapolation over one century has no bases whatsoever.
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  28. As satellite measured recent sea level rise is faster than estimated 20th century average, it is often cited as proof of acceleration.

    Some acceleration is to be expected, simply because the density of water decreases with temperature in a way that is not linear. I found a calculator for the density of water given temperature and salinity here:

    One divided by density will give you relative volume.

    I've put that in a graph already. Here's a formula that gives near-1.0 correlation coefficient:

    V = 3.96E-3 T^2 + 8.36E-2 T + 973

    V is volume of 1000 Kg of water (salinity=3.5%) in liters. T is temperature in Celsius.
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  29. Yes, I am evil. I have quoted Siddall 2009 on the IPCC thing in a disguised form.

    The fact that Sidall came up with numbers consistent with the IPCC AR4 was coincidence. AR4 left out any enhanced contribution by glacial melt altogether, as was pointed out near the top of this thread. Siddall didn't, yet got similar numbers. This immediately raises "sniff test" questions about the validity of the paper's result.
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  30. #43 AndrewY at 21:14 PM on 25 February, 2010
    "Returning to the topic, it does seem the Siddall abstract is very easy to misinterpret (unless you are careful to find the definition of sea level response)"

    The issue is not made less difficult by the fact that "definition of sea level response" is nowhere to be found in Siddall 2009 either.

    However, usege is consistent with that found in retraction letter.

    "Over the twenty-first century, projected sea-level rise reaches a maximum of 0.82m in response to warming from the upper estimate of the A1FI emissions scenario (6.4°C)"

    Finally let me confess I've made an error in calculating sea level rise acceleration for New York and Stockholm. The acceleration of sea level rise is actually positive for both places.

    I have found 32 tide gauges in the PSMSL database, having data for the 1900-2006 interval. To make up for my error, I have calculated sea level rise acceleration for each, including the two above.

    First column is acceleration in mm/yr^2, then latitude, longitude and name of station.

    -0.0152 43 18 N 05 21 E MARSEILLE
    -0.0128 51 27 N 00 45 E SHEERNESS
    -0.0065 57 26 N 10 34 E FREDERIKSHAVN
    -0.0059 55 00 N 01 26 W NORTH SHIELDS
    -0.0034 54 34 N 11 56 E GEDSER
    -0.0034 48 23 N 04 30 W BREST
    0.0002 40 42 N 74 01 W NEW YORK
    0.0010 53 58 N 10 53 E TRAVEMUNDE
    0.0023 53 54 N 11 28 E WISMAR 2
    0.0035 55 34 N 09 46 E FREDERICIA
    0.0041 45 53 S 170 30 E DUNEDIN II
    0.0044 55 20 N 11 08 E KORSOR
    0.0048 64 00 N 20 55 E RATAN
    0.0058 54 11 N 12 05 E WARNEMUNDE 2
    0.0074 55 17 N 10 50 E SLIPSHAVN
    0.0077 37 48 N 122 28 W SAN FRANCISCO
    0.0102 56 09 N 10 13 E AARHUS
    0.0108 57 22 N 17 06 E OLANDS NORRA UDDE
    0.0109 57 36 N 09 58 E HIRTSHALS
    0.0117 30 41 N 81 28 W FERNANDINA
    0.0129 55 28 N 08 26 E ESBJERG
    0.0142 65 02 N 25 25 E OULU/ULEABORG
    0.0145 59 19 N 18 05 E STOCKHOLM
    0.0165 55 41 N 12 36 E KOBENHAVN
    0.0166 47 36 N 122 20 W SEATTLE
    0.0169 58 45 N 17 52 E LANDSORT
    0.0194 56 06 N 15 35 E KUNGHOLMSFORT
    0.0221 56 06 N 12 28 E HORNBAEK
    0.0307 60 09 N 24 58 E HELSINKI
    0.0328 53 52 N 8 43 E CUXHAVEN 2
    0.0425 42 10 N 41 41 E POTI
    0.0490 55 42 N 21 08 E KLAIPEDA

    Looks like at some stations sea level has got rather large upward acceleration. But even 0.049 mm/yr^2 at KLAIPEDA means less than 1 m in two centuries.

    The average acceleration of sea level rise across stations is a better candidate for being a global indicator. In this timespan it was 0.0102 mm/yr^2. It is 20.4 cm in 200 years. From 2006 to 2100 it means an additional 14.7 cm sea level rise.

    Of course, there is a steady linear rise as well due to geophysical processes (like glacial rebound), but it can hardly be more than 10 cm/century.

    To get a sea level rise during 21st century substantially higher than 25 cm, not only rate of rise should increase, but acceleration as well. In other words, there should also be non-vanishing third or higher derivatives of sea level.

    It can happen, if the underlying dynamics is exponential. However, a dynamics like this makes the system very unstable. Not likely scenario. With no major icesheets left on Northern continents, sea level has not changed much during last eight millenia. Ice albedo feedback must be weaker than during deglaciation for two reasons.

    1. Remaining ice sheets are closer to poles, don't get much sunshine anyway
    2. No long ice sheet margin on land exists

    Substantial sea level rise can only come from land ice melt, not sea water thermal expansion, since latter requires almost a hundred times more energy to produce same rise.

    I would rather watch out for black carbon (soot), not carbon dioxide. It accelerates ice melt by a well understood process (makes it dark). Also, it is WAY cheaper to filter it out from industrial smoke (it is done in Europe). Not only cheaper, possible as well.
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  31. Berényi Péter at 04:25 AM on 26 February, 2010

    Thanks for doing all that work. Was that the result of hand calculation, or something you could conceivably pour downloaded data into?

    Finally let me confess...

    I wouldn't term it a "confession", or at least I hope you don't feel mournful about it. You're putting more effort into this than a lot of other folks. Me, for instance.
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  32. Interesting. As i am trying to understand all this and follow the conversation it appears to me a sort of an example of a peer reviewed process has happened. In #18 Berényi Péter provided data and his conclusion. In a later post he gave his process for coming to that conclusion. Someone else reviewed that process and found an error. Berényi Péter acknowledged the error and came back with a revised and expanded conclusion.
    If i am in error or simplifying too much please correct me.
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  33. With all that mass moving off the poles, the Earth should slow down a little to conserve angular momentum. Days should get longer.

    Ocean salinity should also decrease just a tad.
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  34. #53, Berenyi Peter, your last post shows you are making progress. In particular, you fixed your computational error that gave you the wrong sign, and you are averaging over many tide gauges. Now it gets a bit harder. Some general advice:

    Not every acceleration estimate is going to be equally good. You need to weight them appropriately. A simple way would be based on the formal uncertainty of the quadratic fit, scaled by the misfit of each quadratic fit. You should also assess the statistical correlation between the linear and quadratic terms so that you can determine whether that needs to be considered in weighting the quadratic terms. A more accurate measure of the uncertainty in the quadratic terms would explicitly estimate the temporal noise character of each time series.

    You'll have to carefully pore over the station history information, just to make sure that there are no discontinuities in the series (PSMSL should note that), or anything else (earthquakes, etc) that might affect the series. Some of your extreme values might be outliers due to something other than sea level changes, or they might just be far from the mean due to random variations.

    You might then be able to refine your estimate. You also need to determine the uncertainty in your estimate, and evaluate how that projects into the range of sea level rise you would predict. This last bit is a little trickier than you might think, because you have to combine your acceleration estimate with the appropriate linear rate, and you have not addressed that yet.

    But all in all, I suspect by going through this process you will get a range of rates fairly similar to the IPCC AR4 projection. In projecting to the future, you are assuming that nothing will happen in the 21st century that is fundamentally different from the 20th century. That may or may not be true, and to assess that you need to consider projected future temperature trends, and some glaciology.

    So your next question should be, is your assumption that you can extrapolate correct? If temperature rises faster in the 21st century, will your extrapolation still be valid? Will rising temperatures trigger the beginning of new processes affecting sea level that were not captured in your analysis of (mainly) 20th century sea level?

    Look more carefully at the work of people like Rahmstorf and Vermeer to get at the first question. (And I mean carefully, skeptically, not with a "what are these guys trying to pull on me" attitude). Go to a library and look things up when they reference papers you can't get online -- most university libraries I have been associated with do allow you to enter even if you are not a student, and there are xerox machines so "paywalls" are not really an issue because you can copy journal articles for personal research use like everyone had to do when I was a student.

    For my second question, John has postings on this site that deal with the recent significant increases in mass loss in Greenland and Antarctica. I'm betting his postings are quite good, and will point to the original sources. Fact is, both Greenland and Antarctica have started to lose significant mass, and this is a recent change (within the last decade). This appears to be dominated by the speedup of glaciers.

    Finally, your two numbered points near the end of the post are not very accurate, and you really just need to do some more reading and research to learn more about those topics. Starting with the sources on this website is a good way to go.
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  35. #56 RSVP, yes. Search for "Earth Orientation Parameters" (EOP might do). Both rotation pole and rate (length of day) are monitored, and most variations are well explained. Also, the shape of the earth changes (although glacial isostatic adjustment may be the bigger factor). Search on "J2" or "J2 + oblateness" or "J2 dot" to find information about how the oblateness of the earth is changing.
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  36. Berényi Péter (53) wrote:
    "Finally let me confess I've made an error in calculating sea level rise acceleration for New York and Stockholm. The acceleration of sea level rise is actually positive for both places."

    You have my respect for that correction.

    "The average acceleration of sea level rise across stations is a better candidate for being a global indicator. In this timespan it was 0.0102 mm/yr^2. It is 20.4 cm in 200 years. From 2006 to 2100 it means an additional 14.7 cm sea level rise."

    0.0102 mm/yr^2 x (200yr)^2 = 408 mm, not 20.4 cm

    But this only deals with the x^2 component. There's also a significant linear trend. Using the New York guage as an example, the trend line I calculated was:

    y = 0.0036x^2 + 2.2337x - 5.087
    {Note: I adjusted all the data so that 1856 was year=0 and level=0}

    The trend line in 2008 (x = 152) shows:
    y = 0.0036(152^2) + 2.2337(152) - 5.087 = 417.61 mm (above the 1856 level).

    In the year 2100 (x = 244) you'll get:
    y = 0.0036(244^2) + 2.2337(244) - 5.087 = 754.3 mm
    This is 328 mm above the 2008 level (which is 426 mm above the 1856 level).

    If I take this out another 100 years to 2200 (x = 344) I'll get a sea level of about 1.189M above the 1856 level.

    But as you pointed out, some of the guages show a much higher rate of acceleration than the New York one. So I would have to conclude that if I averaged the trend-lines of the 32 tide guages you posted, the increase would be higher.
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  37. I wrote:
    "In the year 2100 (x = 244) you'll get ... This is 328 mm above the 2008 level"

    I should have noted that this 32.8 cm estimated rise by 2100 falls within the IPCC range for all 6 emission scenarios.
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  38. #59 kwinters79 at 07:15 AM on 26 February, 2010
    "not 20.4 cm"

    s(t)=a/2*t^2, v(t)=s'(t)=a*t

    Kinematics, uniform acceleration. You've forgotten to divide by 2.

    Linear component is trivial, does not add much, depends on place. No accelerating acceleration (i.e. no jolt, snap, crackle, pop, etc.), no scare.

    In the long run (>> 100 years) even this tiny acceleration can't possibly persist. Also, in a century, if some silly war or neoluddite takeover would not kick us back to stone age, climate engineering is quite possible.

    I did the average, this is the 10 micron/yr^2 figure.

    However, Klaipeda, Lithuania looks like an outlier. Something must have happened to the tide gauge during the war. According to docu old name Memel (used to belong to Third Reich).

    Black sea (e.g. Poti, Georgia - not the one enduring general Sherman's March) also problematic. See comments for Bourgas

    You can look up any PSMSL station here:
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  39. #56 RSVP at 06:25 AM on 26 February, 2010
    "With all that mass moving off the poles, the Earth should slow down a little to conserve angular momentum. Days should get longer"

    Part of the reason it does. Moon is a major player (tides, friction, angular momentum transfer).

    You can find everything & much more here:

    IERS (International Earth Rotation & Reference System Service)

    Stuff GPS is based on.
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  40. If the function you fit to the sea level height is h0 + v*t + (1/2)*a*t^2, then you need to report that your function had that form so that your coefficient can be interpreted. Otherwise, if you just say you fit a quadratic function the assumption would be h0 + v*t + a*t^2, that is, straight polynomial coefficients. "Fit an acceleration" leaves an ambiguity.
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  41. Berényi Péter
    Thank you.
    On the home page, the graph, "Excess of the Length of day for the last years", it is interesting to see the deviation on the order of what appears to be nano seconds. This is kind of humbling.
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  42. Looks balanced, puts things into perspective, makes you feel small (a good thing). Unfortunately it's behind a (mild) paywall.

    Oxford Companion to Global Change
    Sea Level
    By Michael J. Tooley
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  43. Thanks to satellites we can be confident that sea levels have risen 55 mm in the last 17 years. That works out at about 320 mm/century.

    The 20th century rise was <220 mm so it seems plausible to suggest that the 21st century will see a rise in sea level greater than the last century. However, the 750 - 1,900 mm predictions by 2100 sound high given the current rate of rise.

    We may be in danger of missing the big picture by agonizing over what may turn out to be small, short term fluctuations. My understanding is that sea levels have risen by ~360 feet in the last 9,000 years. That works out at an average of 4 feet/century or 1,200 mm/century.

    My conclusion is that the rise in sea level is a good thing because it will be accompanied by longer growing seasons in the high latitudes and eventually the de-glaciating of the poles as in the Eocene.

    I don't buy your sea level "Catastrophe".

    Rapidly falling sea levels on the other hand will constitute a "Catastrophe" as they will be accompanied by famines on a horrific scale.
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  44. Berényi Péter (61) wrote:
    "Kinematics, uniform acceleration. You've forgotten to divide by 2."

    I see the confusion. As Jeff (63) pointed out, I took your statement about fitting a quadratic function to be in the form: h0 + v*t + a*t^2
    All my computed data is in this form.

    Berényi Péter (61) wrote:
    "Linear component is trivial, does not add much, depends on place. No accelerating acceleration (i.e. no jolt, snap, crackle, pop, etc.), no scare."

    The linear rise rate is actually the dominant part of the sea-level rise projection in my polynomial equation of the NY data. If the acceleration term were dropped, you're still looking at 20.5 cm rise by 2100 and over 42.8 cm by 2200 (the acceleration term only adds an additional 12.3 cm by 2100 or 33.4 cm by 2200).

    However you look at it, the current trend line from NY guage data shows an expected sea-level rise of an additional 32.8 cm by 2100 and 76.2 cm by 2200. I'd call those extremely low-ball estimates, since the ice sheet dynamics haven't yet really come into play and there was very little global warming during the early part of the NY tide guage dataset. If I start my NY guage data projection fit from 1950 or 1960 (vs. 1856) there's a significantly more rapid acceleration component. I'll gladly post the data, if anyones interested.

    Though my analysis here is much too simplistic, it certainly helps convince me that Siddall's results appear quite reasonable.
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  45. @53, Berenyi Peter wrote:

    "Of course, there is a steady linear rise as well due to geophysical processes (like glacial rebound), but it can hardly be more than 10 cm/century."

    Surely post-glacial rebound, the process by which landmasses rise after removal of the weight of glaciers which had rested upon them and caused them to sink into the mantle, causes sea levels (as measured with respect to those land masses, and ceteris paribus) to *fall* and not to rise.

    It is my understanding that the linear rise component you observed in these data is in fact attributable to warming (some of it an extremely delayed response to the warming experienced as we emerged from the last ice age) and not to "geophysical processes" (as distinguished from warming).
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  46. #68 Douglas McClean at 19:24 PM on 27 February, 2010
    "the linear rise component you observed in these data is in fact attributable to warming"

    The linear component can have any sign, is highly variable over locations, not just at sites close to former ice sheets. Shape of Earth is changing all the time, has nothing to do with temperature, usually a slow process (having minuscule acceleration on century time scale) except at plate boundaries.

    Mediterranean seas like Black sea can also have weird behavior for a number of reasons.

    All in all the quadratic component is much more reliable than the linear one, depends less on the particular choice of tide gauge set considered. It also dominates over longer time scales.

    Just to make things clear, the line fit I used was (a/2)*x^2+b*x+c.
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  47. #67 kwinters79 at 07:49 AM on 27 February, 2010
    "If I start my NY guage data projection fit from 1950 or 1960 (vs. 1856) there's a significantly more rapid acceleration component. I'll gladly post the data, if anyones interested"

    Post it please.

    However, this acceleration thing is not so simple.

    In PSMSL we have two time series for each station, monthly & annual ones.

    For the New York tide gauge they are:

    The corresponding text files:

    Some measurement points are flagged "XX" at end of line, meaning database collectors found them suspicious. I have left them out in this analysis.

    I have calculated acceleration term for relative sea level change at NY gauge for a number of time spans. Here it is.


    1900-1920: +0.7263 mm/yr^2 +0.7899 mm/yr^2
    1900-1930: -0.1316 mm/yr^2 -0.1158 mm/yr^2
    1900-1940: +0.1065 mm/yr^2 +0.1160 mm/yr^2
    1900-1950: +0.0976 mm/yr^2 +0.1011 mm/yr^2
    1900-1960: +0.0675 mm/yr^2 +0.0701 mm/yr^2
    1900-1970: +0.0320 mm/yr^2 +0.0338 mm/yr^2
    1900-1980: +0.0097 mm/yr^2 +0.0083 mm/yr^2
    1900-1990: -0.0098 mm/yr^2 -0.0095 mm/yr^2
    1900-2000: -0.1244 mm/yr^2 +0.0005 mm/yr^2
    1900-2008: -0.1123 mm/yr^2 -0.0010 mm/yr^2
    1910-2008: -0.1390 mm/yr^2 -0.0093 mm/yr^2
    1920-2008: -0.1650 mm/yr^2 -0.0164 mm/yr^2
    1930-2008: -0.1807 mm/yr^2 -0.0187 mm/yr^2
    1940-2008: -0.1392 mm/yr^2 +0.0117 mm/yr^2
    1950-2008: -0.0339 mm/yr^2 +0.0283 mm/yr^2
    1960-2008: +0.3291 mm/yr^2 +0.0679 mm/yr^2
    1970-2008: +1.5011 mm/yr^2 +0.1345 mm/yr^2
    1980-2008: +5.0428 mm/yr^2 -0.1557 mm/yr^2
    1990-2008: +7.4565 mm/yr^2 -0.6288 mm/yr^2

    The large discrepancies toward the end are due to measurement problems after 1990. Annual series misses data for years 1992, 1994 & 2001, 1997 flagged suspicious.

    Metadata does not have explanation.

    Monthly dataset misses three months for 1992, two for 1994, one for 1997 and four in 2001.

    Data after 1990 are unusable. I don't know why it is so, one would fancy some technical improvement, not deterioration for recent times.

    Also, according to docu "Data 1922-1926 interpolated".

    Looks like only period 1927-1991 is reasonably intact.

    1927-1991: -0.0908 mm/yr^2 -0.0901 mm/yr^2

    Someone should visit (or call) NY tide gauge station, ask them and report findings.

    BTW, the station must be The Battery, downtown Manhattan (ID: 8518750), even if PSMSL ducu lacks station ID (!).,%20NY&type=Tide%20Data
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  48. You can have a look at sea level trends here:

    Unfortunately they neither compute acceleration term nor have data in text files.
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  49. Sure, sea level changes can have either sign. Sure, there are movements of landmasses in both directions. My point was only that sea level *rise* cannot be caused by post-glacial rebound.
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  50. Berényi Péter,
    The data quality issue is indeed a problem. But since I'm not working to publish any results and since these are only hobby calculations, I'll just stick with the simplistic approach of using the annual data, as is, except for the 2 years flagged with XX.

    I subtracted out of all my level measurements the 21-year average tide level from 1856 to 1876. The levels were left in mm. And my Time-0 is 1856.

    I computed a h0 + v*t + a*t^2 least squares equation for the 3 periods: 1856 - 2008, 1950 - 2008, and 1970 - 2008. The equations I got are:

    Period 1 => -20.524 + 2.269t + 0.0033t^2
    Period 2 => 190.2 - 0.787t + 0.0142t^2
    Period 3 => 1133.5 - 14.99t + 0.0672t^2

    Projecting these out to 2100 I get the following sea-level rise (relative to the average from 1856 - 1876):

    Period 1 => 75 cm
    Period 2 => 88 cm
    Period 3 => 1.58 m

    So what can I conclude from this little exercise? Not much, as it's far too simple and only dealing with a single tide gauge. But along with all the recently published papers, the ice sheet dynamics, and the fact that Siddall withdrew his low estimate paper, I'd have to conclude that the IPCC estimate was indeed too low. A 1M rise may actually turn out to be a conservative estimate. It will be interesting to see what additional papers are published over the next year or two.
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