Guest Post by Willis Eschenbach (NOTE UPDATE AT END)
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.
Figure 1. Artificial pseudodata of a tidal gauge recording an accelerating rate of sea level rise.
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 2015. 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.
Figure 2. Typical records which fit the criteria of the ex-ante data selection process (95% data coverage from 1950-2017)
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 the diagonal line are stations where the R^2 of the accelerating (quadratic) fit is larger than the R^2 of the linear fit.
As you can see, in almost all cases the gain in the goodness of fit when we go from linear to quadratic fits is trivially small, invisible at this scale. And when I examined the gain in R^2 versus the standard errors for each of the 63 stations, in every single case the accelerating fit was NOT statistically better than the linear fit.
In other words, not one of these datasets shows statistically significant acceleration.
And that is why at the top I said that I disagree with the following statement from the other post, viz:
There are some tentative signs that the rate of increase is already accelerating …
Simply not true. Figure 3 shows clearly that the tidal gauges contain no such “tentative signs”. NOT ONE of these 63 full tidal datasets shows statistically significant acceleration, and more to the point, most of them show only a trivially small difference between acceleration and a simple linear fit.
The other statement I disagreed with was:
As the world continues to warm, the rate of sea level rise will accelerate (probably slowly) …
Look, this is just the same nonsense that the alarmists have been peddling for the last thirty years, that in the future the sea level rise will accelerate, that New York will be underwater, and the like … but it has been thirty years since the first bogus prognostication was made, and there is still no evidence that the sea level rise is accelerating.
Look, I’m all in favor of taking care about the future … however, call me crazy but I need EVIDENCE before I start hyperventilating about Miami sinking into the ocean.
5 PM, the dreaded global warming has cooled down now. Me, I’m going to post this and then go outside to lay some pavers in the new level space I just made with my own sweat. Plus a rented backhoe. I could have hired someone, but why should illegal immigrants have all the fun? I like living in the hills … but this is the first and only flat spot on my land, so I’m making it nice.
What a universe!
Best to everyone,
PS—The Usual: When you comment, please QUOTE THE EXACT WORDS YOU ARE DISCUSSING, so that we can all be clear about your precise subject.
DATA—I’ve put the 63-station data here, as a CSV file so that anyone can use it in Excel or any other program.
[UPDATE] Over at Tamino’s website, where since about 2009 I’m barred from commenting because I was asking inconvenient questions, he points out that there is a simpler and more accurate method for finding out if a dataset contains acceleration. This is to see if the squared term in the quadratic equation is statistically significant after correction for autocorrelation, duh … he is correct.
My thanks to him for pointing this out, although I do have to deduct points for his repeated ad hominem attacks on me in his post … haters gonna hate, I guess.
Using his method I identified seven of the sixty-three stations as having statistically significant acceleration and three stations with statistically significant deceleration. However, the average value of their acceleration is 0.015 ± 0.012 mm/yr2 … which is not statistically different from zero. Here are the stations and their accelerations:
VLISSINGEN BALTIMORE SMOGEN KEY WEST KETCHIKAN 0.0605 0.0542 0.0676 0.0477 -0.0543 WEST-TERSCHELLING SANDY HOOK JUNEAU SITKA KWAJALEIN 0.0979 0.0510 -0.1052 -0.0573 0.1258
I note that one station he says has significant acceleration doesn’t appear in this list (Boston). I find that the p-value of the acceleration term for Boston is 0.08, not significant. I suspect the difference is in how we account for autocorrelation. I use the method of Koutsoyiannis, detailed here. I don’t know how Tamino does it.
I would also note that the average acceleration of the entire 63-station dataset is 0.014 ± 0.008, still not statistically significant. And if this turns out to be the long-term acceleration, currently the rate of rise is on the order of a couple of mm/yr, or 166 mm (about 7 inches) by the year 2100. IF this increases at 0.014 mm/yr2, this will make a difference of 48 mm (under two inches) this century.
Curiously, in the previous fifty-year period 1900-1950 there are only three sites with significant acceleration out of 38 datasets covering the period, and none are in the first list:
NEW YORK (THE BATTERY) HARLINGEN SEATTLE 0.0976 -0.1182 0.0959
Whatever any future sea level acceleration turns out to be, it is very unlikely to put the Statue of Liberty underwater anytime soon …
Man, I love writing for the web. All my errors get exposed in the burning glare of the public marketplace of ideas, I get to learn new things, what’s not to like?