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Has sea level rise accelerated since 1880?

Posted on 7 April 2011 by Tamino

Many thanks to Tamino from Open Mind for allowing SkS to republish his post So What? as the rebuttal to "sea level rise is decelerating".

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, Nature, 453, 1090-1094, doi:10.1038/nature07080). 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.

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Comments 101 to 106 out of 106:

  1. Scaddenp - I think the point is that Stern does not cost positive effects in the same way he costs harmful effects. I didn't see any evidence that Stern had (a) costed value of additional crop yields and (b) incorporated such costings into the overall cost-benefit analysis. Tom Curtis - You're wrong. We're sinking in the South where I live(Scotland is on the up). But even so I have not noticed any serious effects. Of course, there must be effects and we must be reacting to them...I am just pointing out they haven't been catastrophic.
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  2. 101, daniel maris,
    ...costed value of additional crop yields...
    I'm not sure where you get this, but in the long run, globally, everything I've seen says that crop yields will be down. Unlike much of the world, the USA is expected to benefit in the short term, as precipitation and temperature increases in the center of the continent are expected to be more mild, however, the southwest will eventually be hard hit by both drought and extreme temperature ranges, and the fact that climate zones move north does not necessarily translate into "let's just farm farther north." You need to take into account length of day, precipitation, quality of soil, irrigation sources, etc. And if the weather becomes more erratic, even the better areas may be subject to crop killing droughts as often as not. Changing the temperature of the planet also dramatically changes the distribution of water and precipitation patterns in not entirely predictable or useful ways. Crop yields may rise fractionally for a decade, maybe two, then things go way, way down. And it only gets worse if biofuels are one of the more serious solutions to getting away from fossil fuels (i.e. if we need to use productive land to produce fuel instead of food). Of course, that may not matter much if it pushes us into WW III by 2050 or so -- over food and arable land (the climate losers may not take kindly to the USA using its meager climate benefits to produce biofuels instead of helping to feed a starving world).
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    Moderator Response: Everybody, please get back to the topic of this thread.
  3. I won't respond to the detail in view of the moderator's comment but I will say that I think you have a lot more to fear from population rise than temperature rise.
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  4. I am not, in any case, entirely convinced there has been any increase in seal level. What about this article featuring the views of an eminent expert. Why don't Dr Morner's views count for anything?
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    Moderator Response: [Dikran Marsupial] Funny you should mention that. I'd be happy to discuss Morner if you like, but first I suggest you look into it in a bit more detail, starting with using Google scholar to look up his papers on this topic and then the responses which completely refute his accusations. Then ask yourself why Morner doesn't mention this in his Telegraph artcle.
  5. daniel #104 - indeed, funny timing mentioning Morner, since I just published a post (linked by Dikran) which discusses his claims. The short answer is that opinions are like a-holes, everybody's got one. What Morner doesn't have is any data whatsoever to back up his claims. Calling him an "eminent expert" is also not warranted.
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  6. I posted this originally to Tamino's blog, but it didn't show up for some reason. So I am reposting it here The reason Houston and Dean are using a quadratic fit is that they are trying to ascertain the long term average rate of acceleration. They note that Douglas (1992) has determined that it is necessary to analyze upwards of 50-60 years of continuous data in order to determine a significant trend, because decadal scale oscillations in the acceleration are common in the observed record. By significant I do not mean “statistically” significant: rather, I mean significant with respect to the determination of the type of long term trend that the climate models forecast in response to the increase in atmospheric greenhouse gases. If we had thousands of years of data, this could be done by first decomposing the data with a Fourier series analysis, and then analyzing the low frequency signals for statistics on acceleration. But we don’t have enough data to do that, so the next best thing is to fit the data to a quadratic curve, which by definition yields the “average” acceleration rate of the entire sample space. Houston and Dean are explicit with respect to their reasons for starting the analysis at 1930. Quoting from the paper: “A review paper on sea-level acceleration by Woodworth et al. (2009) notes that the analysis by Church and White (2006) shows a positive acceleration, or ‘‘inflexion’’ point, around 1920–30. They do not use the mathematical definition of an inflexion point as the point where the curvature (second derivative) changes, but instead define it as a change in sea level trend. They say that the inflexion point around 1920–30 is the main contributor to acceleration from 1870 to 2004. Woodworth et al. (2009) concluded there was consensus among the authors that acceleration occurred from around 1870 to the end of the 20th century; however, with the major acceleration occurring prior to 1930, the sea-level rise (Figure 1) appears approximately linear from 1930 to 2004. Church and White (2006) did not separately analyze this specific period.” So, Houston and Dean analyze from 1930 forward to determine if the acceleration is a persistent (long term) trend or not. If the acceleration is a response to atmospheric greenhouse gas emissions, the trend should in theory be persistent and observable in the record since 1930. Tamino's method of analysis consists of averaging over shorter and shorter time scales as one moves along the time axis. This effectively weights higher frequency signals more and more as one approaches the present time. This method ensures that such a plot will look more “active” on the right hand side of the plot.(i.e. the left hand side of such a plot will always have less high frequency events than the right hand side) Since the most recent data indicate a short term increase in acceleration , this ensures that Tamino's plot will appear to show this acceleration as if it were a novel event, which is misleading. Houston and Dean acknowledge that there is a recent trend showing increased acceleration, especially evident in the satellite altimetry data. They discuss this observation at length. They conclude that this type of higher frequency event is not unique in the observational record, and that although it may represent a long-term change in the rate of acceleration, it is not possible to determine this with the limited amount of data available (again, 50-60 years of data is needed) They speculate that it is more likely just another decadal oscillation ,for several reasons they give in the paper, but they do not form any definite conclusions on this point. The Houston and Dean analysis is appropriate for use in determining the long term trend of acceleration in the 20th century (at least since 1930) . Whether this is important information or not depends on the results of the hindcasting verification runs of the climate models . If the climate models hindcast a significant positive 20th century long-term acceleration, and if, as Houston and Dean demonstrate, such an acceleration is not present in the observational record, it gives good reason to be concerned that the process descriptions that govern the models are in error. I don’t know enough about the climate models to know what their hindcasts indicate, so I can’t asses the relative significance of these results with respect to climate modeling.
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  7. Attn Steve Case, the correct topic for your comment was here. Learning to stay on topic at Skeptical Science can require a sharp learning curve for those used to a more laizez faire moderation style. The correct procedure is to find an appropriate topic and make your comment. You then link back to your comment in the comments of the original post for your discussion. Although following the correct procedure can be a pain, it pays of in terms of far more orderly discussions which can focus on genuine scientific points of interest or misunderstanding. It can also help you understand, as in this case, why certain comments might be considered cherry picking. You are of course welcome to argue the "no-acceleration" hypothesis for the full period of 1880- current above, but on the face of it, that period shows acceleration. Choosing a shorter period to dispute the claim on the Morner thread which is linked to this topic, is therefore cherry picking.
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  8. muoncounter@55 and scaddemp@60...methinks you reference this, in your comments... 'Twas a dangerous cliff, as they freely confessed, Though to walk near its crest was so pleasant; But over its terrible edge there had slipped A duke and full many a peasant. So the people said something would have to be done, But their projects did not at all tally; Some said, "Put a fence 'round the edge of the cliff," Some, "An ambulance down in the valley." But the cry for the ambulance carried the day, For it spread through the neighboring city; A fence may be useful or not, it is true, But each heart became full of pity For those who slipped over the dangerous cliff; And the dwellers in highway and alley Gave pounds and gave pence, not to put up a fence, But an ambulance down in the valley. "For the cliff is all right, if you're careful," they said, "And, if folks even slip and are dropping, It isn't the slipping that hurts them so much As the shock down below when they're stopping." So day after day, as these mishaps occurred, Quick forth would those rescuers sally To pick up the victims who fell off the cliff, With their ambulance down in the valley. Then an old sage remarked: "It's a marvel to me That people give far more attention To repairing results than to stopping the cause, When they'd much better aim at prevention. Let us stop at its source all this mischief," cried he, "Come, neighbors and friends, let us rally; If the cliff we will fence, we might almost dispense With the ambulance down in the valley." "Oh he's a fanatic," the others rejoined, "Dispense with the ambulance? Never! He'd dispense with all charities, too, if he could; No! No! We'll support them forever. Aren't we picking up folks just as fast as they fall? And shall this man dictate to us? Shall he? Why should people of sense stop to put up a fence, While the ambulance works in the valley?" But the sensible few, who are practical too, Will not bear with such nonsense much longer; They believe that prevention is better than cure, And their party will soon be the stronger. Encourage them then, with your purse, voice, and pen, And while other philanthropists dally, They will scorn all pretense, and put up a stout fence On the cliff that hangs over the valley. Better guide well the young than reclaim them when old, For the voice of true wisdom is calling. "To rescue the fallen is good, but 'tis best To prevent other people from falling." Better close up the source of temptation and crime Than deliver from dungeon or galley; Better put a strong fence 'round the top of the cliff Than an ambulance down in the valley. -- Joseph Malins (1895)
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  9. For sphaerica@66...>;-) Head bangingly good!
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