Willis gets it right? Not.
Willis Eschenbach has a post at WUWT claiming to show that sea level rise is not accelerating. What he actually demonstrates is that he doesn’t know how to tell.
His method is to fit a straight line to sea level data (from tide gauges) and to fit a quadratic, then compare their “R^2 values.” R^2 is not a test of statistical significance, and neither is the difference from two models. Willis doesn’t know this. He thinks he does — but he’s wrong. I’ll leave it to Willis to figure out why that is (I don’t expect him to be able to do that either).
Evidently Willis also doesn’t know that there are perfectly good, and well-known (for a long time), ways to test the quadratic fit vs. the linear fit statistically. My advice to Willis: crack a book.
Willis uses tide gauge data from PSMSL (Permanent Service for Mean Sea Level), and accepts only data ranging from 1950 through 2015. He then isolates the data since 1950, and further insists that it must be at least 95% complete, i.e., less than 5% of monthly values are missing. He tell us this leaves him with 63 data records, and he is kind enough to provide a link to the data itself. His conclusion, from his analysis, is:
… in every single case the accelerating fit was NOT statistically better than the linear fit.
“NOT ONE of these 63 full tidal datasets shows statistically significant acceleration …”
Let’s take a look, shall we?
Here’s the data from Boston:
The red line is a quadratic fit by least squares. When we test the quadratic term for statistical significance the p-value is 0.0006. That’s statistically significant at the 99.9% level. Of course I corrected for autocorrelation. If I hadn’t — and I suspect Willis doesn’t know how — the estimated p-value would be 2.2 x 10^-11.
Boston isn’t the only example. Willis isn’t just wrong, he’s so wrong, that he reveals he is not qualified to do this kind of analysis. Not even close.
There’s another case worth noting, Juneau, Alaska:
Again, the red line is the quadratic fit. With a p-value of 0.002, it’s significant at 99.8% confidence. But this time, it’s statistically significant deceleration!
Before you declare “Aha — no global warming” be advised that we know why it’s decelerating: because of global warming.
Glaciers are melting so fast that the total mass on land areas is decreasing … the mass of all that water leaves the land and ends up in the ocean. That means the gravity from that ice is no longer pulling the sea closer with its gravity. Because of that, sea levels can actually fall near regions with much land ice melt. So yes, Juneau sea level is decelerating because of global warming.
I wonder whether Willis will dispute that too?
Let’s perform an experiment. Go to the WUWT post and leave a comment referring to this post. Be as polite as you can, stick to facts, don’t get mired in mud-slinging, just point out that Willis is mistaken and link to this post. Let’s find out whether or not your comment appears.
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