I’ve made a new estimate of global sea level based on a subset of all the tide gauge data in PSMSL (Permanent Service for Mean Sea Level). I’m just doing the 20th century, and I’ve used only those data sets with a decent amount of data, at least 360 monthly values since the year 1900. That leaves a “mere” 723 tide gauge stations to work with. Here’s where they are located:
And here’s the estimated global average sea level since the year 1900:
We can map the estimated corrections for vertical land movement (VLM), with upward-pointing blue triangles showing stations where sea level is rising faster-than-average because the land is sinking faster-than average, and downward-pointing red triangles showing stations where sea level is rising slower than average because the land is rising faster than average. Bigger triangles indicate farther from average:
One thing to note is that many of the stations with slower sea level rise due to rising land, are those in the far north. This region is where the great ice sheets used to weigh down the continents but disappeared during the last deglaciation, so the land is now rebounding (glacial isostatic rebound).
I corrected each individual station record for its estimated VLM and aligned it with the other records. Then I computed the difference between this aligned, VLM-corrected data and the estimated global signal shown above. This gives a residual sea level time series for each station, one which represents its departure from the global-average pattern which is unrelated to VLM.
I wanted to find which stations show similar patterns of changes, so I thought to apply principal component analysis (PCA). The problem is that “straight” PCA requires that each station report a data value at each time — missing values aren’t allowed. For sea level time series, it’s not just a case of stations missing a few values, many stations have large gaps or cover only a brief time span. The missing data problem is severe.
There’s a decent literature on PCA with missing data, much of which utilizes infilling — substituting estimated values for missing data. I’ve never cared for infilling, so I used a different technique. It has its strengths and weaknesses, but that’s a subject for another post.
I applied this PCA method to the residual series, and here’s the time series for the first PC:
It’s not a pattern of trend but of the fluctuations, which turns out to be the most prominent one which isn’t related to the global pattern or to vertical land movement.
Here’s how different stations match this pattern, with upward-pointing red triangles stations which show this pattern, downward-pointing blue triangle stations which show the opposite pattern, larger triangles for a stronger match:
The vast majority of the big triangles are the downward-pointing blue ones in the area of the Baltic Sea. Here’s another version of the same map, but for stations with values less than two standard deviations from the mean (which is most of them) I’ve replaced colored triangles with black x’s:
This makes it clear that mainly, the pattern shown in the time series (actually, it’s negative) matches the fluctuations shown by stations in the Baltic Sea area, as well as a few stations in odd locations.
For the 2nd PC the time series pattern looks like this:
The map looks like this:
All but a few of the triangles are small, the exceptions being a group of stations in North America. I can once again replace triangles within two standard deviations of the mean with black x’s, and zoom in on North America, giving this:
This shows that the 2nd PC is really a pattern of fluctations in stations along the St. Lawrence river in Canada, where water levels are strongly managed by human activity; these stations are a poor representative of global sea level. In this case, principal component analysis succeeded not only in identifying a genuine coherent pattern, it also defined a set of stations which should be excluded from a “best” estimate of global sea level.
The time series for the 3rd PC shows an interesting trend pattern, a decline since around 2005:
The map has most of its big triangles in far northern regions:
Again, let me replace triangles with x’s for stations within 2 standard deviations of the mean, to highlight where the strong activity is concentrated:
The pattern is mainly found in stations around the Arctic ocean, especially the coast of Siberia. A possibility, one I regard as speculative but interesting, is that the recent severe melting of glaciers has caused nearby sea levels to fall because there’s so much less ice that the local gravity in the area is reduced.
The fourth PC is the one I find most interesting. Here’s the time series as a blue line, and I’ve added a red line which is proportional to MEI, the Multivariate El Niño Index:
The match is outstanding; clearly the 4th PC in sea level deviations is the pattern induced by the el Niño southern oscillation.
The global pattern of response confirms what is expected:
Here’s another version, in which I’ve replaced triangles with x’s, not for stations within 2 standard deviations of the mean, but for stations within the interquartile range:
We see that during a strong el Niño, sea level is higher in the east Pacific, while it’s lower in the west Pacific and the Arctic ocean.
I was surprised, and pleased, by the results of this exploratory analysis. Finding the imprint of el Niño on sea level was an unexpected but especially satisfying result. There’s more to be done to understand quite what the results mean.
I think, that next I’ll re-do the global analysis but omit those stations along the St. Lawrence river in Canada — they just don’t belong in an estimate of global sea level. There are other individual stations which should be omitted too (e.g. stations which show a strong shift due to earthquake activity). Some might say there’s a lot of work to do on this. I might say, ain’t we got fun?
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