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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Open Mind 
Neat.
Curious how you calculated the power spectrum, whether via transform, or my preferred way, the multitaper method. (See also van Drongelen (2014) and Mathworks. There’s also an R package.)
I ask, not because I want to be picky, but because the transform approach has high variance per bin, and doesn’t address spectral leakage well.
Specifically, I ask because:
https://tamino.files.wordpress.com/2019/01/dft.jpg?w=500&h=333
looks a bit spikey to be a taper product. I could be wrong, of course. The typical Thomson multitaper looks more like
although it is possible to lower the time-bandwidth product to improve resolution and get more variance in each point.
You don’t discuss ENSO in any of your sea level series but the spike just before 2000 in your first figure immediately suggests an effect. There are papers out there discussing this. E.g https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2017GL073926
Have you accounted for this ? Perhaps I missed something.
I would also want to see an estimate from the physics that the Chandler effect could cause sea level variation of 100mm. I think there is a danger here that you may be on to a red herring. Could it be that the wobble is influenced by sea level? I suspect this given I found this. https://www.jpl.nasa.gov/releases/2000/chandlerwobble.html
The effect of the wobble should also be present in the southern hemisphere and likely out of phase with the US east coast. I think you need to review other coastline data before running with this. Australia might be a good spot to compare with.
[Response: I wasn’t aware I was “running with this.” I thought I was playing with data in speculative fashion, including phrases like “play fast and loose with statistical significance” (which may be a surprise to some regular readers).
The level of variation possibly associated with polar motion, isn’t as high as 100mm. And it’s not all the Chandler effect, in fact it’s mainly the interplay between the Chandler wobble and the annual solar influence — or, it’s a look-alike from red noise (we’re playing fast and loose).]
@MDenison,
I have not looked at the others, but I did take a look at Valle-Levinson, Dutton, and Martin (2017).
First, their construction of Empirical Orthogonal Functions (EOFs) appears sound, but it is bothersome that whatever correlations between SLR modes 1 and 2 only appear when using 7-year filtered cumulatives both for the modes and for ENSO and NAO. They found no correlation in the modes themselves, whether as correlation coefficients or as p-values. That they had to resort to something as obscure as 7-year cumulatives filtered in a manner not specified in the text suggests p-hacking, or, in other words, massaging data as in data mining until an effect is found. I don’t put much weight on such shenanigans.
Second, the explanation they offer purports to be that this kind of thing happened frequently over the last 95 years. Yet they do no explain why there has only recently been tangible evidence of Sunny Day Flooding.
Third, whether it is in meteorological or climate papers, or symposia, I have never quite understood how and why people are happy and content to ascribing to fluctuations in NAO or ENSO causation of physical phenomenon. This is ignoratio elenchi or at least complex question because the causation appeals to other phenomena whose causes are not explained. Sure, there are oscillations in climate, but these do not create energy out of nowhere. They are fed by the same thermal forcing everything else is. They might modulate its application or store it for a time. They certainly don’t store it as long as oceans do.
I’m willing to buy that AMOC deceleration might not be the cause of SLR hotspots, although I think that analysis remains incomplete. Such analyses do not account for large eddy effects in oceans because eddy formation and maintenance is not causally linked to global climatic parameters.
Even if AMOC has nothing to do with these, appealing to specious correlations with ENSO and NAO is unconvincing and seeking another explanation rather than settling for having somehow disproved an AMOC connection appears appropriate.
Beautiful work with complex data sets. I understood some of it. Thank you.
@Tamino, this and the original are, as @smallbluemike says, nicely done, and beautifully explained.
I should say that if someone pours cold water on the 432 Chandler Wobble tone, it seems to me their scholarly responsibility to find an alternative explanation for it, and not merely dub it some kind of noise. I’m thinking that if an MTM taper were done instead of whatever was done — and, as I noted, maybe it was and so, this is inoperative — a broader peak would emerge there roughly coinciding with it, perhaps even combining the energy in the three separate ones below 0.25.
[Response: But the below-0.25 stuff is a known effect, according to the Wikipedia article, and I expect it would persist (along with its spectral energy).]
Hotspot of accelerated sea-level rise on the Atlantic coast of North America
Rate increase after 2010 is worrisome. The impact of significance on coastal flooding might get lost in the discussion of statistical significance. Most reports cite the global rate of about 3.2mm/per year. Post-2010 rate if 7mm per year on the East Coast shown in this post adds up to 2.8 inches per decade. For locations already dealing with sunny day flooding, an additional 2.8 inches in a single decade would be hugely significant.
1) About how many more years of data required to determine if the post 2010 rate is statistically greater than 1980-2010 rate vs. being temporary noise?
2) Does influence of polar motion with peak in 2023 suggest that rate post-2010 is likely to stay high or go even higher at least through early 2020s?
3) Sea level rise through thermal expansion should remain linear as I understand it, but fresh water additions from Greenland and Antarctic ice sheet melt are accelerating in nonlinear fashion. How much Is that likely to add to recent acceleration of East Coast SLR rates suggested here?
4) While variation within the solar cycle is a relatively weak forcing, it is a real and reliable one. With solar cycle bottoming out in 2019-2020, and roughly 2-year lag in solar cycle effect on global average surface temperatures (according to Hansen), then 2021-2027 could see accelerated surface warming. Is that likely to show up in annual East Coast SLR rate, or does even longer lag in ocean response smooth out any affect of solar cycle on global average surface temps on SLR?
Even without an immediate SLR effect, the early 2020s appear set to provide dramatic evidence for the costs of disrupting the climate and the need to reduce greenhouse gas emissions. Not that we haven’t see that already, at least those willing to look. ‘Elections have consequences’ has never been so true.