The Sea Level site of the University of Colorado has an interesting graph which shows quite plainly that there’s a relationship between global sea level and the el Niño southern oscillation:
I decided to see how el Niño might be related, not to global sea level, but to that of individual tide gauge stations. Like the U.Colorado graph, I too will use MEI (Multivariate el Niño Index) to characterize the el Niño southern oscillation.
It occurred to me that the strongest influence would probably be at tide gauges in the Pacific ocean and surrounding areas — after all, that’s where el Niño really happens. First I looked at a U.S. Pacific coast station, San Diego (Quarantine Station). I took the data from PSMSL (Permanent Service for Mean Sea Level), which goes through the end of 2015, and first removed the annual cycle. Then I de-trended the result, to remove the long-term sea level rise. Finally, I regressed the de-trended de-seasonalized sea level against MEI.
For San Diego, this indicated that a single unit of MEI causes sea level to rise by +28 ± 2 mm. The statistical significance is overwhelming. It’s also no surprise, since el Niño is Pacific ocean waters piling up in the east Pacific.
I could then remove the el Niño influence, to define a revised tide gauge record for San Diego which not only has the seasonal cycle removed, it has the el Niño influence out of the way as well (but the long-term trend is left in place):
The red line is a modified lowess smooth. It not only enables me to estimated the smoothed sea level, it also returns the estimated rate of change, and the uncertainty level of that (an autocorrelation correction is included in uncertainty estimates).
I also wanted to see how fast it was rising using a method simpler than my “modified lowess smooth,” so I decided to simply fit straight lines. One giant problem with doing that is that if you just fit a straight line to some time span in isolation, you’re essentially fitting a model with a broken trend, and that can really gum up the works of trend estimation.
I wanted to get at the rate of sea level rise on about a 30-year time scale, so I took the data and split it into sections 30 years long. Approximately: I actually split it into section 360 data points long, to avoid the difficulty when a big gap in the data makes some particular 30-year time span too sparse to give reliable results. I then fit a piecewise linear model, allowing a different slope in each 30-year segment, but to avoid the “broken trend” issue I constrained the model to be continuous, i.e. the endpoints of the 30-year time spans have to meet. For the San Diego data we get this:
I’m also able to compute the rate for each time span and its uncertainty (again including an autocorrelation correction). Finally, I can graph the estimated rate from the modified lowess smooth, and that from the continuous (unbroken) piecewise linear fit, on the same graph:
The very thick black line (actually, it’s closely spaced small circle) shows the estimate rate of sea level rise from the piecewise linear fit, the dashed black lines the uncertainty level (95% confidence) of that. The solid red line is the estimate from the modified lowess smooth, the dashed red lines its uncertainty envelope. Finally, the solid blue line shows the linear rate of change using the entire data set in one fell swoop. That’s what’s usually reported for a tide gauge station, but it assumes that the rise rate doesn’t change, which I regard as a capital mistake.
It’s abundantly clear that the rate of sea level rise at this station is not constant. In fact it shows a pattern which is quite common for long records: acceleration followed by deceleration followed by acceleration. The fastest rise occurred in the 1925-1955 period according to the linear fit, in the 1985-2015 period according to the lowess smooth, but neither outpaces the other with statistical significance. They do, however, outpace the remainder of the time span.
San Diego is on the eastern edge of the Pacific, but I also wanted to look at a station in the West Pacific. I chose another with long time coverage, Fremantle in Australia. This too shows a very strong response to el Niño, but out of phase with the east Pacific. An increase of MEI by 1 unit causes a drop in sea level at Fremantle, by about -40 ± 3.7 mm. Again, statistical significance is beyond question.
Again, I can remove the el Niño influence and estimate how the rate of sea level rise has changed over time, using the same methods as for San Diego. I get this:
We see the same pattern of acceleration followed by deceleration followed by acceleration, although at Fremantle the first acceleration doesn’t make statistical significance. The last one does; the fastest rise is definitely in the most recent 30-year period.
Finally, I wondered about stations in the Atlantic, so I chose a place in the western Atlantic ocean with a long record, Key West in Florida. This time, the estimated response to a single unit of change of MEI is a mere -0.15 ± 2.8 mm, which is definitely not statistically significant. Effectively, it’s zero. There’s no sign that el Niño is having an impact on sea level at Key West.
I did, however, repeat the computation of the rate of sea level rise by both methods, giving this:
We no longer see an initial acceleration, but we do see deceleration followed by acceleration. We do see once again, however, that the fastest rise has been during the most recent 30-year period.
It turns out that removing the el Niño influence doesn’t have much impact on estimates of the rate of sea level rise on 30-year time scales, even for those stations with a strong el Niño response (San Diego and Fremantle). One could say that it makes estimates a bit more precise, but doesn’t change them substantively. It doesn’t affect the Atlantic ocean station at all, although so far I’ve only looked at one of them. All in all, the response to el Niño by individual tide gauge stations is exactly as expected: an increase in MEI is accompanied by rise in the east Pacific, fall in the west Pacific, and no discernable change in the Atlantic.
Of course there’s a lot more to investigate because there are many, many more tide gauges than just three! Give it time …
This blog is made possible by readers like you; join others by donating at Peaseblossom’s Closet.