For years, the Dave Burtons and Judith Currys of this world have shown a graph (from NOAA) of sea level measured by a single tide gauge at one location, followed by proclamations of “no acceleration” and/or “sea level rise has been steady.” They choose one for which the visual impression given by the graph supports that idea, whether the numbers do or not, especially since NOAA conveniently adds a best-fit straight-line to their graphs of tide gauge sea level, and putting a straight line on the graph plants the idea of straight-line trend (i.e. constant rate of sea level rise).
If you do the math, you often find that “steady rise” just ain’t so — demonstrably, the evidence contradicts the visual impression. That’s the way statistics is, and I’ve often emphasized that “visual impression” can err in either direction, suggesting a false positive or obscuring a true one. As for the straight line plotted on their graphs, NOAA makes it clear that they do not do this to claim or imply that sea level is following a straight line, it’s just to show what the best-fit straight line is — still, it’s hard not to get the idea anyway.
Then there’s the fact that the noise level in the data from a single tide gauge is very high, compared to the noise level in global mean sea level (GMSL). That makes it harder to detect and confirm acceleration even when present; the signal (in this case, change in the rate) has to be strong enough to achieve a sufficient signal-to-noise ratio for “statistical significance,” and that usually requires either a very big rate change, or persistence for a long time, for the accumulated signal level to compete with such a big noise level.
The noise itself is not the simplest kind (white noise). It’s strongly autocorrelated, which must be compensated for when testing for statistical significance and computing the uncertainty of estimated parameters. This is an issue which features prominently on this blog, and while NOAA uses an AR(1) model for the noise (it’s the usual approach in science today) I’ve championed the use of a more complex ARMA(1,1) noise model, because I think even the AR(1) model makes it too easy to think you’ve got statistical significance when you don’t, and gives you too much confidence in your parameter estimates.
Some statistical models — including some of my favorites — involve a change which happens at a particular moment. It complicates the statistics rather extremely, because there are so many moments to choose from, it dramatically increases the chances of finding one that makes your sought-after pattern look good (even to statistical tests) but it’s only dumb luck because you tried (or could have) so many times. In fact, the “moment” is usually deliberately chosen because it suggests itself — which is truly begging the question. The issue is sometimes called “selection bias,” sometimes referred to as the “multiple testing problem,” and figured prominently in the debate over the non-existent “pause” in global temperature. It can be compensated for — that’s the essence of change-point analysis — and if it’s too messy to compute what you need theoretically, celebrate living in the high-speed-computer era when Monte Carlo simulations make that easy.
And let’s not forget that the way the data are graphed, and the scale chosen, has a profound effect on the visual impression. It’s usually straightforward to choose the view which gives the impression you want to give, or confounds the one you don’t like.
So why, some might wonder, did I choose in my last post to show the data from a single tide gauge station (Wilmington, NC), do no analysis at all, but manipulate the graph to give a distinct visual impression? It wasn’t much of a manipulation — all I did was plot the pre-2012 data in black and the post-2012 data in red — but it did the job.
True answer: because I thought it had the best chance to make Dave Burton say (to himself), “Ouch.”
I had already “done the math.”
The blue line shows the best-fit parabola, the red line the best-fit PLF (Piece-wise Linear Fit). I tested both models as the “alternate hypothesis” against the “null hypothesis” that it follows a straight line (constant rate of sea level rise). Yes I compensated for autocorrelation and selection bias. Both tests return a clear result: statistically significant.
By no means does this demonstrate that the data are following either of these models, parabola or piece-wise linear. Statistical significance doesn’t confirm the alternate hypothesis, it rejects the null hypothesis. The real result of both tests is: sea level is not rising at a constant rate, rather it has accelerated, at Wilmington NC.
I’ll address some other issues that came up in comments to my previous post.
First of all, I didn’t “hand-pick” the very limited time span to show in red (rather than blue) in my graph of sea level at Wilmington, NC. It was dictated by the North Carolina state legislature passing HB-819 in 2012. The station was hand-picked — but not by me, by Dave Burton.
The nearby tide gauge station at Beaufort, NC, shows the same response to the same statistical tests:
As for satellite data, I used it to estimate the straight-line trend using only the data prior to 2011, then I subtracted that trend from all the data, leaving these deviations from the pre-2011 trend:
I don’t think that increase post-2011 is just fluctuation caused by el Niño. I do think that some people, especially Dave Burton, try to blame el Niño for most things they can’t explain.
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