In my ongoing quest to find a better way to align sea level records from tide gauges at different locations, I’ve tried a new strategy.

Different tide gauges are at different levels, so we need to offset them by a constant to *align* them before we *combine* them. But they don’t just show different base levels, they also have different *vertical land movement* (VLM). To put different tide gauge stations on a “global” scale we need to cancel that out, which means we need to remove a *trend* from the data — because the primary effect of vertical land movement is rise or fall at a *constant rate* which differs from place to place, sometimes dramatically.

Most of the time, one acquires an estimate of vertical land movement elsewhere, like a model of glacial isostatic adjustment, or GPS data if that happens to be available.

I’ve been experimenting with ways to use the data itself to compensate for VLM. What I’ve tried so far is to take the data over a baseline time period (I tend to use 1950-1989) and estimate its trend for each individual station. Then I subtract that trend from the station’s data, hoping it will subtract away the VLM as well. The hope is to bring all stations onto a scale where their 1950-1989 trend is zero, to get the most out of their alignment.

Doing so doesn’t actually estimate the rate of global sea level, but its difference from the 1950-1989 average. We have to add back the removed trend to get to actual sea level. But doing so *does* seem to improve detection and quantification of *how the rate has changed over time*, a worthwhile thing to know.

My newest method is to compute an offset for each station (as always), *and* choose a “trend offset,” or “tilt slope” for each station, selecting them to bring the data from all the different stations combined into best agreement. There are some undetermined parameters because we can increase each offset by the same amount, and we’ll just move every station up or down the same amount, not affecting their differences. Likewise, we can tilt every station by the same slope and not affect their differences. It’s easy enough to impose some constraints to make the problem well-determined. I decided on constraining the *median* overall slope to remain unchanged by the offsets.

This means of course I get an estimate of how much I have to “tilt” each individual station with a trend offset, which amounts to an estimate of its *local* sea level rate *relative to the other stations*. Let me plot a circle for each station on the U.S. east coast, with red for those where sea level is rising more slowly than the median, blue where it’s rising faster, larger circles for larger deviation:

Some things are clear right away. First, there are far more stations with available data from Cape Hatteras north, than from there south. Second, northward of New York City (the region I’ve called “New England (NE)”) is dominated by red, so that’s where local sea level is rising slower than the median, while the region from New York City to Cape Hatteras (which I’ve called “Mid-Atlantic North (MAN)”) is dominated by blue, that’s where local sea level is rising fastest. The differences in local sea level suggest differences in vertical land movement, with NE rising due to rebound from the melting of the great ice sheets, while MAN sinks for the same reason.

And when I put all the east coast stations together, using the data since 1950, what do I get? This:

I’ve added a trend line which allows for a change in 1989. The year is that which gives the best overall fit, but as it turns out when you do the statistics right it doesn’t reach statistical significance (due to the multiple testing problem).

But it did when we aligned the data the old way, by which I mean my original way without any slope offsets (neither the best-fit slopes like here, nor the 1950-1989 slope offsets like before). For that matter, the slope change is significant when using the 1950-1989 slope offsets too.

We can compare the new result (red circles) to the original method (blue triangles):

Sea level from the new method is a little bit lower early and late, a little bit higher in the middle. In fact the differences look like this:

The new method changes it only a little, but in just the right way to cancel out part of the 1989 trend change, robbing it of statistical significance.

Does that mean there was no trend change around 1989? Not necessarily. The two-slopes model shown above, the best-fit model, using the data from the new alignment method, gives a pretty sizeable slope change of 1.4 mm/yr at that time, but the truly interesting part is the uncertainty: +/- 1.6 mm/yr (95% confidence). So it could really have a slope change of +3 mm/yr, rather large (understatement), althought it could also have bent downward by -0.2 mm/yr — not likely but possible, given just the statistics.

And what about the different regions? Here are the reconstructed series:

Here are smooth versions of the same:

Further analysis and discussion will await another day …

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