## The Foolish Line

Anthony Watts is on a very long list of those who ridicule the threat of sea level rise. As many others have done, he shows a tide gauge record (for Sewell’s Point, near Norfolk Virginia):

He also shows the data from Portsmouth, VA, although it is of shorter duration and doesn’t go past 1990. Then he claims that there is no discernable *acceleration* in either data set and declares that the rise is linear:

The most important thing to note is that unlike the steeply vertical graph in the WaPo article showing up to 8 feet of projected sea level rise, there is no acceleration visible in either of these two tide gauge graphs. They illustrate the slow, linear, subsidence that Nature has been doing for thousands of years.

Note that he also blames the rise on subsidence — the sinking of the land — which is a real factor in this area but is *not* the only reason sea level is rising so fast there. That’s “Uncle Willard” for you.

Then Watts declares that he’ll “do the math”:

So, let’s do the math to see if the data and claims match. We’ll use the worst case value from Sewell’s Point tide gauge of 4.44mm/year, which over the last century measured the actual “business as usual” history of sea level in concert with rising greenhouse gas emissions in the atmosphere. with no “mitigation” done in the last century of measurements.

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Their claim is for the “business as usual” scenario: “by the end of this century, the sea in Norfolk would rise by 5½feet or more.””

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1. At the year 2014, there are 86 years left in this century.*

2. 86 years x 4.44 mm/year = 381.84 mm

3. 381.84 mm = 15.03 inches (conversion here)

Apparently Uncle Willard’s idea of “doing the math” is: arithmetic. I’d say it’s rather revealing that one of the things he felt the need to “document” is how to convert mm to inches. Such mad math skillz!

One of the real shams behind his extrapolate-the-linear-trend-to-the-year-2100 method is that there *is* acceleration in this tide gauge record. But far too many people, including a lot of researchers, have missed it because there’s also *de*celeration.

Here’s the monthly average data for Sewell’s Point from the Permanent Service for Mean Sea Level, with the seasonal cycle removed by a 4th-order Fourier series:

We’ll start by converting monthly data to *annual averages*. This too will remove the seasonal cycle, and it will greatly reduce the autocorrelation of the data, making our statistical tests much more accurate.

I’ve included the best-fit straight line (by linear regression), which suggests an overall rise rate of 4.56 mm/yr. But — is the trend really linear?

Many have tried to find acceleration by fitting, not a straight line, but a parabola (a 2nd-degree polynomial). That suggests a very slight acceleration which is *not* statistically significant. Does that mean Watts is correct, that there’s no discernable acceleration?

The problem with a parabolic model is that it is a *constant*-acceleration model. Maybe the acceleration isn’t constant. Maybe we need a more complex model to find it with statistical significance. Let’s try all polynomial degrees from 1 (straight line) to 10 (10th-degree polynomial) and use AIC (Akaike Information Criterion) to estimate which is giving the best fit *when compensated for the extra degrees of freedom*:

The “winner” is the model with lowest AIC, which in this case is the 3rd-degree (cubic) polynomial. Here’s what it suggests is the trend in this tide gauge record:

Interesting! This model (which, by the way, *is* statistically significant even after correcting for autocorrelation) suggests *de*celeration early and *ac*celeration late. Of course it’s only a model and maybe (almost certainly in fact) not the best one, but it does *prove* (in the statistical sense) one thing: that **the trend is not a straight line**. It’s not. Claiming that it is, is foolish.

What’s far more foolish is using such a model to extrapolate, not just to next year or the next few years, but all the way to the end of the century. Foolish.

Suppose I used the cubic model (demonstrably better than the linear one!) to extrapolate to the end of the century? That model predicts that sea level will rise between now and the end of the century by over 2.6 meters. Yes, that’s meters. Over 2600 mm. Over 100 inches. Over eight and a half feet.

But, honestly, it’s *not* valid to extrapolate this statistical model to the end of the century. Prediction is hard — especially about the future — and extrapolating simple statistical models far into the future is a very poor way to go about it.

But it seems to be the favorite way to forecast future sea level rise by those who deny the reality, human causation, and/or danger of global warming. Not just Anthony Watts, but the North Carolina state legislature. It’s no surprise that when they do, they choose a statistical model which gives a low forecast: a straight line.

It’s the basis for the “line” that future sea level rise is not going to be much of a problem. I suspect that despite scientific evidence to the contrary, despite the best efforts of actual *experts*, they will continue to toe the line. A foolish line.