I’ve been looking more closely at the result from my new alignment method for tide gauge data, applied to the U.S. east coast. In particular, I’ve been studying the data since 1950, which very nearly follows a straight line:
We noted in the last post that the trend-rate change about 1990 that we had found with the old-fashioned alignment method, no longer reached statistical significance with data from the new method.
I took the residuals from the straight-line fit shown above, and computed their power spectrum:
The dashed lines show estimates of statistical significance levels (at 90%, 95%, and 99%), but they’re not flat lines because the data show pretty strong autocorrelation. They’re really just a guide, particularly to how significance varies at different frequencies.
Only one peak actually reaches any statistical significance level, corresponding to a period of 432 days. This is the Chandler wobble, which is known to affect local sea level with a sort of “tide” of period a little over a year. It’s due to a nutation of the Earth, the fact that it wobbles on its axis as it spins (hence the title of this post). Here’s what Wikipedia has to say about it:
The Chandler wobble or variation of latitude is a small deviation in the Earth’s axis of rotation relative to the solid earth, which was discovered by American astronomer Seth Carlo Chandler in 1891. It amounts to change of about 9 metres (30 ft) in the point at which the axis intersects the Earth’s surface and has a period of 433 days. This wobble, which is a nutation, combines with another wobble with a period of one year, so that the total polar motion varies with a period of about 7 years.
There is, in addition to the Chandler wobble, a peak around 7 years (more like 6.5 really), but it’s not statistically significant, and it looks to be a harmonic of an even stronger peak with period 13 years. It’s even possible that there are three harmonics of that longer period.
The Chandler wobble is there. The other factors might well be, but I don’t consider them established. Even so, I’m going to use them to model the part of sea level change due to nutations. Step 1 is to determine the best frequencies precisely.
Then we can use them to construct our model:
It actually looks pretty good — but I’ll say again what many of you expect me to say because I keep saying it again and again, that “looks like” is a great way to get ideas but a lousy way to confirm them. But hey, we’re playing fast and loose with statistical significance anyway, so let’s have some fum.
I’m finally ready to remove the nutation part of the signal (or at least, my estimate of it), leaving this:
Now let’s see what we can find out about these data.
One positively fascinating thing is that the trend-rate change around 1990 that loses its statistical significance when we use the new alignment method, gets it back (with best estimated change time 1989) when we remove the nutations from that same new-method data:
At the change point, the slope (rate of sea level rise) increases by 1.6 +/- 1 mm/yr above its preceding rate. That’s a pretty substantial “+/-” figure so there’s plenty of uncertainty, but the change is still there. This, of course, is the average rate since 1989, which doesn’t preclude further acceleration.
A model consisting of straight lines is one possibility; another is a smooth curve like this lowess smooth:
Either way, it doesn’t seem to be following a straight line. We can use the smooth to estimate the rate of sea level rise (with uncertainty ranges as dashed lines):
The uncertainty ranges are 95%, but I caution that they are very precarious estimates, though they do at least get us “in the ballpark.” We can compare them to the estimated rate of sea level rise from the straight-lines model (plotted in blue):
There is at least some evidence of further trend change (more acceleration, to be specific) after 1990, but I’m not ready to call it conclusive based on these data alone.
Another interesting approximation comes from fitting a piecewise-linear function (where all the pieces are connected), but instead of using two straight lines let’s use seven if them. I’ll allow for a different slope over each 10-year period, but of course insist that the pieces meet at their endpoints. The best such model is this:
It too provides an estimate of the rate of sea level rise, this time for each 10-year time slot:
Both the 10-year-pieces model, and the smooth-fit model, suggest the possibility of recent further sea level acceleration along the U.S. east coast, particularly since 2010.
The effects of total polar motion are still clear in the data (by the new method) for the New England (NE) and Mid-Atlantic North (MAN) regions, but not really present for the Mid-Atlantic South (MAS) or Florida (FL) areas. Basically, it’s clearly present north of Cape Hatteras but not south of.
Another interesting aspect is that the basic period of the polar-motion effect is just about 13 years. That means that the coastal sea level sees a “surge” from the polar motion cycle, with that period. The last such surge was around 2010, so we should expect the next about 2023. This will be the surge due to polar motion only, which is in addition to any change in global sea surface height.
In spite of the high level of variability in sea level on the U.S. Atlantic coast, and in spite of the fact that we may not “see” a big surge until the next polar-motion peak joins forces with the global-warming-induced trend around 2023 (north of Cape Hatteras at least), we’re already suffering plenty of problems on the U.S. east coast from the higher sea levels we already have.
Tidal flooding — sometimes called “sunny-day flooding” since there’s no wind or rain or storm — has become so common in some places that it’s costing huge amounts of money to try stopping the sea from coming on the streets. When storms do come, whatever storm surge threatens life and property is bigger than it would have been before, and a little extra height of storm surge means a lot of extra distance flooded inland. And the rates of sea level rise on the U.S. east coast are higher than the worldwide average, because of land subsidence.
As global sea level accelerates, so too will local sea level, including along the U.S. east coast. What is already a serious problem will keep getting worse, and for us, it will do so faster than for others.
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