Author: Willis Eschenbach / Source: Watts Up With That?

**Guest Post by Willis Eschenbach**

There’s a recent and good post here at WUWT by Larry Kummer about sea level rise. However, I disagree with a couple of his comments, viz:

(b) There are some tentative signs that the rate of increase is already accelerating, rather than just fluctuating. But the data is noisy (lots of natural variation) and the (tentative) acceleration is small — near the resolving power of these systems (hence the significance of the frequent revisions).

(c) Graph E in paper (5) is the key. As the world continues to warm, the rate of sea level rise will accelerate (probably slowly).

This question all revolves around whether the rate of sea level rise is relatively steady, or whether it is accelerating … so how do we tell the difference?

Well, how I do it is to fit two models to the data and see which one works better. The first is a straight-line model (a linear fit), and the other is an accelerating model (a “quadratic” fit). Figure 1 shows an example of some pseudo-tidal data which in fact has an accelerating rate of sea level rise. I’ve created it by simply adding an accelerating trend to an actual tidal record.

As you can see, the blue line showing an accelerating (quadratic) fit matches the data much better than the linear fit (red). How much better? Well, that’s measured by something called “R-squared” (R^2). This is a value between zero and one which measures how well the given line explains the dataset.

The R^2 for the blue line (0.88 ± 0.02) is much larger than the R^2 for the red line (0.77 ± 0.02). And since the difference between the two values is greater than the sum of the standard errors of the two values, we can say that the difference between them is statistically significant. In other words, in the Figure 1 case we can say that there is a statistically significant acceleration in the dataset.

So that is what I planned to look at—whether the difference between the R^2 for the linear and the quadratic fits is greater than the sum of their standard errors.

With that as prologue, let me discuss my methods. I took the full tidal dataset from the Permanent Service for Mean Sea Level. It has 1,505 tide station records in it. However, as with most historical datasets, there are lots of gaps and stations with short or spotty records.

So I had to use a subset of the data. Because the long lunar tidal cycle is just over fifty years, you need at least that much data to get a serious estimate of the rate of sea level rise. And we are interested in any recent acceleration. So I limited my analysis to tidal stations with data starting before 1950 and ending after 1915. This cuts the list down to 171 stations which cover the period of interest.

However, some of these are missing a lot of data, some with over half of the data gone. I wanted enough data to have faith in the analysis, so I further limited the dataset to those stations having 95% or more of the data during 1950-2015. This further reduced the number of tidal stations to 63. Figure 2 shows a sample of 10 of these.

Now, my Mark 1 Eyeball says that if there is acceleration there, it is minor … but let’s look at the numbers. Here is a scatterplot of the R^2 values of the linear fit versus the R^2 values of the quadratic fit:

*Figure 3. Scatterplot, R^2 of the linear fit vs. the R^2 of the accelerating (quadratic) fit. Dots above…*

Editor for @MotherNatureCo @DogCoutureCNTRY | Love my outdoors, environment activist and climate change advocate, health & yoga | Family, friends and of course puppies and dogs. Go figure! Social media geek at heart #cmgr all night and day.

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