How one plots the data can have a big impact on whether or not one can “see” acceleration or deceleration of sea level in tide gauge data. Here, for instance, is a plot of sea level at Boston (data from PSMSL, and I’ve removed the annual cycle):
It’s similar to (and on the same scale as) the plot provided by NOAA.
One can easily get the impression the data follow a straight line (plus noise of course). One reason is that the y-axis scale covers 1.2 meters while the data only cover about 0.5 meters. Another reason is that the plot includes a straight-line fit, which to most people is highly suggestive of a straight-line pattern.
NOAA has good reasons for those choices. They want to plot all tide gauge records on the same scale, so they need a wide-range y-axis to accomodate them all. They also want to report the linear trend rate (whether the trend is linear or not), although as I’ve said before they make no attempt (and no pretense) to detect or to rule out departures from linearity. For their purpose, their scale choices and inclusion of the straight-line fit make good sense.
But for “seeing” acceleration and deceleration, this is a better plot:
It’s exactly the same data, but this plot makes it a lot harder to say “See — no acceleration.”
Despite the effect plot choices have on what we think we “see,” the real test is analysis. In fact I’ve often emphasized that we too often think we see meaningful patterns when it’s really just noise — that’s not the Mona Lisa next to the sistine chapel, it’s really a bunch of clouds that look like it.
I’ll start by computing annual averages, which reduces autocorrelation without sacrificing the precision of trend analysis. The annual averages are still autocorrelated, so I’ll still inlude an autocorrelation correction in analysis, but the annual averages make things a bit easier to “see.” Here they are for Boston:
Now it’s even harder to say “See — no acceleration.”
Nobody disputes that it’s rising. But is it really doing something else? It “looks like” there was deceleration early and acceleration later. Let’s try fitting a cubic curve, in order to accomodate such a pattern. It looks like this:
More to the point, the cubic term is statistically significant. Strongly. So no, it’s not following a straight line. According to this model it shows deceleration early and acceleration later.
That model is fine for testing departure from linearity. But we don’t really expect it to follow a cubic curve. Let’s fit a “modified lowess smooth” to these data, which doesn’t assume a particular form for its changes, to get this (dashed lines show 2sigma ranges):
That looks more like it slowed down around 1950, then sped up around 1990. We can sharpen our estimates of when those might have happened by fitting a continuous piecewise-linear model, and that will also test the statistical significance of those changes. The best model is this:
And yes, the changes are statistically significant. That doesn’t mean it’s following the continuous piecewise-linear model exactly — but it did decelerate early and accelerate later, and this model is at least a good approximation. It’s also very similar to the model from smoothing the data, obvious when we plot them both together (piecewise linear in blue, smooth in red):
Both models also provide an estimate of the rate of sea level rise over time (of course the piecewise linear model has a constant rate over each piece). Here they are (piecewise linear in black, smooth in red, again with 2sigma ranges above and below):
We can see that they agree overall (although the piecewise-linear model is constrained to constant rate over each piece). We can also see that the current rate of sea level rise is around 5 mm/yr, faster than the global average rate.
One of the things I’ve mentioned many times is that not only does sea level not follow a straight line, it also doesn’t show constant acceleration. It shows a much more complex pattern, and deceleration early followed by acceleration later is a feature of global reconstructions (e.g. that of Church & White), not just of individual tide gauges. For some reason, deniers just can’t seem to wrap their heads around that. They seem to insist on the simpleton’s view of sea level rise — that if it isn’t showing constant acceleration through all time, then global warming is just a fraud and we have nothing to worry about.
Such a pattern also agrees with empirical models of past sea level change, particularly those of Vermeer and Rahmstorf. The observed pattern not only shows in the data, it also matches models! For some reason, deniers just don’t want to acknowledge that.
As for Boston, one of the reasons it shows such a fast rate of increase may be the slowdown of the AMOC (Atlantic Meridional Overturning Circulation, sometimes called the “Gulf stream”). What the AMOC does in the next few decades can affect the U.S. east coast profoundly. It’s unlikely that AMOC will “shut down,” but if it does that will be incredible trouble for a lot of places. Let’s hope it doesn’t happen.
As for J. Richard Wakefield’s comment saying that “Sat data shows sea level rise doubled in rate in 1990, 100% acceleration in one year. And not one surface station shows this? Explain.” Perhaps Mr. Wakefield will explain how the satellite data show sudden acceleration in 1990 when they don’t even begin until 1993.
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