# Sea Level Stations with a Long Record

Tide gauges measure local sea level, the difference between sea surface height (SSH) and the height of the land. If the sea surface gets higher — what we usually think of as “sea level rise” — local sea level won’t necessarily go up because the land itself might also be getting higher. Although tide gauges are generally fixed to solid rock (the more solid the better), the land itself can still move up or down, a process called vertical land movement (VLM).

One of the main causes of VLM is glacial isostatic adjustment. When the last ice age ended, the great ice sheets covering much of north America and northern Europe melted away and their immense mass no longer pressed down on those areas. They have since rebounded, but the rebound proceeds at a “glacial” pace (pun intended). More useful is the fact that on time scales of the last few centuries they have done so at a constant rate. This means that the rate of vertical land movement due to glacial isostatic rebound has been roughly constant, faster at some locations and slower (even negative) at others, but not changing from year to year fast enough to worry about. If we can figure out what that constant rate is at a given location, we can compensate for it and get a good estimate of how fast the sea surface height itself is changing (which is what we’re really interested in, on a global scale).

There are factors which can change local VLM on shorter time scales (years to decades), such as pumping groundwater and/or oil out of the earth, or sediment accumulating, or earthquakes. But the main influence on large scales is glacial isostatic adjustment. To correct for it we need to know its rate, but that’s not so easy. We can use models based on geophysics to estimate how it varies from place to place — for instance, the regions where the great ice sheets used to be are rebounding upward fastest. Lately some places have attached GPS (global positioning system) sensors to their tide gauges for direct measurement, but they haven’t been in place long enough to make estimates of VLM very precise. All in all, measuring or estimating VLM is tricky business.

Yet estimates of global sea level depend on them. To combine and average data from different locations, we need to remove the influence of local VLM or we’ll be averaging differences in VLM rather than the common changes of sea surface height. Much research has focused on allowing for VLM, but its uncertainty remains a sticky issue. It really is tricky business.

Although there are over a thousand tide gauges around the world which contribute their data to the study of sea level, many of them don’t have data stretching very far back in time. But some do; I looked at the data available from PSMSL (the Permanent Service for Mean Sea Level) and found 125 tide gauges with at least 80 years’ data which include at least some data as modern as 1970. My goal is to align and average these long records to get a global sea level estimate.

But what to do about VLM? Estimates of their rates are available, but I’ve tried a new idea. Instead of estimating it from a model, or from a brief record of GPS data (which is only available for a fraction of stations anyway), I decided to let the tide gauge data itself tell me the rate of VLM at a given place — or at least, how different it is from other locations.

Specifically, for each station I estimated the rate during a “reference period” from 1950 through 1989. Then I subtracted that trend from the entire record, so the revised data will necessarily have a rate of zero for that time period. Finally, I’m prepared to align and average the revised records to form a global composite. The idea is that they should all have roughly the same rate of rise for sea surface height during the “reference period” so subtracting their different local rates will cancel out that rate plus their local rate of vertical land movement. No model or GPS needed.

The aligned revised records will of course be “tilted” by the actual global rate during the reference period. To get actual global sea level that rate should be restored, so I took the aligned composite values and added back an estimate of the global rate during the reference period, 1.6 mm/yr. That’s the rate indicated by the global composite from Church & White (which I consider the best), so the final result should be a new estimate of global sea level, based on tide gauge stations with at least 80 years of data.

Where are the stations with long records? There are a few scattered about the globe, but most of them are in Europe and North America:

It’s worth noting that far north stations (especially in Europe) show very strong glacial isostatic adjustment, rebounding strongly from the disappearance of the great ice sheets, so a large fraction of these stations can be expected to show large upward VLM, leading to strong underestimates of how the sea surface height is rising. This emphasizes the need to correct for VLM when using such a limited, and geographically biased, sample.

If I align and average but don’t correct for VLM with the 125 long-record stations, I get this:

But when I apply my new method of correcting for VLM I get this:

That’s different! It emphasizes just how strongly the result is affected by the different values of VLM at different locations.

I smoothed the new estimate (with a modified lowess smooth), and for your edification I’ll compare it to two other global sea level estimates, from Church and White (shown in blue) and from Jevrejeva et al. (shown in green):

My new estimate agrees exceptionally well with the data from Church & White, although at least in part that’s because it’s constrained to have the same average rate of increase during the reference period 1950 through 1989. Mine shows less sea level rise during the 1930-1950 period, but overall agrees quite well during the wole period covered by both. The Jevrejeva data, however, are in considerable disagreement with my own estimate (as well as that of Church and White) prior to 1950, yet do agree with my estimate pretty well during the very early time span from 1800 to 1850.

One of the virtues of the smooth is that it enables a reasonable estimate of how the rate of sea level rise has changed over time. Using a 30-year time scale, I get this:

This belies claims that decades ago, sea level rise showed a rate comparable to today’s. It also shows a present rate in reasonable agreement with the satellite data, considering that these are roughly 30-year rates, while the satellite data only cover about 25 years and sea level has been accelerating during that period.

My new reconstruction also illustrates yet again (as do all good estimates in fact) that sea level has shown both acceleration and deceleration over the last couple of centuries. One of climate deniers’ favorite claims is that sea level hasn’t accelerated at all, so its rise will be modest this century. Such claims are terribly misleading for at least two reasons: first, that the sea level rise we’ve seen already (let alone what’s to come) isn’t modest and certainly isn’t harmless, it’s costing millions from increased flooding during storm surge and flooding even without storms (“sunny-day” flooding); second, that their basic premise (no acceleration) is just plain wrong.

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### 16 responses to “Sea Level Stations with a Long Record”

1. Jeff

One of the tide gauges you include is Fort denison, Sydney, Australia (closest to me)
The Sonel GPS shows a subsidence over 8 years of -0.33 mm/year.
http://www.sonel.org/spip.php?page=gps&idStation=2405
The tide gauge data give a trendline rise of about 100 mm in 100 years.
http://www.psmsl.org/data/obtaining/stations/196.php
Giving about 70mm if you extrapolate the subsidence over 100 years.
So about 0.7mm/year sea level rise.
“I estimated the rate during a “reference period” from 1950 through 1989. ”
What estimate for the rise did you use ?

[Response: The GPS station in Sydney isn’t at the same place as the tide gauge, they’re about 11 km apart. The two locations can have different VLM due to groundwater extraction or other local effects (the difference can be substantial, as is know e.g. for Fremantle).

And that GPS station estimates the rate of VLM based on less than 9 years of data, hardly representative of the last century+. The quoted standard error (from SONEL) is 0.25 mm/yr, so the 95% confidence interval is from -.83 to +.17 mm/yr.

But Australia sea level (based on 80 tide gauge stations) does seem to show change different from other parts of the world. Uncorrected for VLM, Oz shows notably less increase than the global average prior to 30 years ago, but over the last three decades has risen at about 3.2 mm/yr. And, let’s not ignore the rest of the world.]

2. John Nielsen-Gammon

Seems promising. I wonder whether there might be an issue with aliasing of basin-scale natural variability of sea level onto the estimated VLM. The chosen reference period corresponds to a substantial positive trend in the Pacific Decadal Oscillation, for example. Unfortunately, the PDO and Atlantic Multidecadal Oscillation are not in sync, so it’s hard to find a good reference period that minimizes trends in both of them. Perhaps 1958-2002?

4. JCH

This belies claims that decades ago, sea level rise showed a rate comparable to today’s.

Just to remind, this is a center-piece claim of Curry and Koonin. I suspect they know it is not true, and yet, they just keep saying it.

[Response: Bear in mind that this is a new way to correct for VLM, and that other reconstructions (e.g. Jevrejeva et al. and Douglas et al.) do show earlier rates comparable to the last three decades. I suspect that Curry and Koonin might believe that, but refuse to acknowledge that they could be wrong.]

5. B Buckner

Just to note here that the satellites measure something completely different that the tide gages – a measurement of the entire ocean surface versus the point where water meets land – and they really shouldn’t be directly compared. The satellite reported sea level rise rates are higher than tide gages for two reasons. First, a major component of sea level rise is the thermosteric effects of the oceans warming. Much of the added heat is stored in the upper 2000 feet of the ocean, largely in areas such as the tropical Pacific. Where oceans warm the water expands and the surface bulges, where cooling occurs the ocean surface drops. The oceans are not exactly flat like a bathtub, but rather vary plus or minus 3 feet or so based on these thermal effects as well as wind and currents. At the shoreline, the thickness of water approaches zero, so no bulge occurs.

Second, the glacial isostatic adjustment is not limited to the shore land rising. When the 2-mile thick ice sheets covered portions of the northern hemisphere, the weight of the ice did indeed depress the earth crust. Correspondingly, the crust at the ocean floor rose as the magma beneath the crust was displaced and moved to the ocean areas. So now as the shore land rises, the ocean floor is dropping. The satellite data counts the dropping ocean floor as sea level rise as the column of water is thicker, although the actual sea level stays the same. Think of it as more water being poured into a larger glass, so the water level at the shore is not effected.

6. Two questions:

(1) What are the uncertainty envelopes about your lowess, and then then Church & White and Jevrejeva, et el sea level height plot?

(2) Is the span between the dashed lines in the rate plot? $1\sigma$?

[Response: I’ll have to check the uncertainties, a plot would be good. The dashed lines are 2-sigma but I’m not sure I really trust them.]

7. Neil White

In response to B Buckner’s point on GIA, the satellite altimeter data can and often is corrected for the GIA effect on the ocean floor. Most of the plots you see around the place are the ocean height w.r.t a fixed reference (e.g. the geoid), but corrections are available and are usually applied to turn the altimeter data into a measure of ocean volume.

There is some discussion of this here:

https://physicstoday.scitation.org/doi/full/10.1063/1.1472392

and here:

https://eprints.soton.ac.uk/365254/1/1-s2.0-S0012825214000956-main.pdf

Neil

• Let me be sure I understand this bit:

Most of the plots you see around the place are the ocean height w.r.t a fixed reference (e.g. the geoid), but corrections are available and are usually applied to turn the altimeter data into a measure of ocean volume.

It sounds as though using the geoid as reference would eliminate the issue of water column depth change due to submarine GIA–the altimetry for that only needs to look at the surface. Which brings up another point: radar altimetry *can* only look at the surface, since radar does not penetrate seawater well–that’s the flip side of strong reflection that gives you the good signal in the first place. (And hence, looking at the question from another angle, the historic use of expensive and inefficient Extremely Low Frequency (ELF) radio to communicate with submarines.) So fundamentally, Topex et al are measuring their own altitude above sea level, and all the software wizardry on top of that is error correction and conversion to SL height relative to (usually) the geoid–as discussed here:

https://research.csiro.au/slrwavescoast/sea-level/measurements-and-data/sea-level-measurements/

So ocean basin GIA adjustments don’t even come into the picture until one needs to infer depth of water column/ocean volume. And, I would think, such things must be inferred by combining altimeter data with seabed maps constructed (I would presume) primarily from sonar data collected over decades.

Have I got this something like right?

• Neil White

Firstly, I should have said something like “(e.g. a reference ellipsoid)” instead of “(e.g. the geoid)”. A reference ellipsoid (e.g. WGS84) is a fixed reference surface which approximates the blobby ellipsoid shape of the Earth.

Yes, satellite altimeters give heights referenced to a fixed surface, which is equivalent to measuring heights relative to the centre of the Earth.

If the ocean floors weren’t (in general) sinking then the GMSL measurements from the satellite altimeters would be equivalent to measurements of ocean volume. But, as the ocean floors are (in general) sinking in response to the dumping of huge quantities of water into the oceans during the last deglaciation, the satellite altimeters measurements as they stand underestimate the changes in ocean volume. To get the best estimate of changes in ocean volume from satellite altimeters you need to correct for this effect using “basin GIA” from geophysical models. There is no other practical way of doing this.

Neil

• Neil, thanks for elaborating. Interesting bit about the response to LGM.

8. Bob Loblaw

At the shoreline, the thickness of water approaches zero, so no bulge occurs.

Yet I swear I’ve seen waves and tide move water towards and away from the beaches I have visited. Water has the peculiar characteristic of moving horizontally when the pressure gradient favours it. Yes, bulges occur where density variations change the pressure gradient, and and wind pressures offset the pressure gradient, but they’re not some magical effect that stops water from moving around horizontally.

So now as the shore land rises, the ocean floor is dropping.

Not everywhere. the crustal movements are limited to a certain distance from the edge of the ice. Geologists have long mapped this during glacial periods by examining beach deposits and rates of vertical movement (ages of the beaches). The area of upward crustal movement (during the glacial period) is call the peripheral bulge. You can even look this stuff up using Da Google.

https://pubs.geoscienceworld.org/gsa/geosphere/article/13/5/1555/353716/toolbox-for-analysis-of-flexural-isostasy-tafi-a

• B Buckner

We have 10-foot tides where I live. These bulges do not flatten out despite water “moving around horizontally.” Water expands where it warms. Sure there will be some minor level of horizontal flow, but please calculate the pressure gradient and tell me how much sea level rises on the California coast from a 1-foot bulge in the middle of the Pacific Ocean.

Regarding GIA and the ocean floor, of course vertical movements vary relative to the locations of previous ice sheets. The adjustment however is for the entire ocean, and makes up roughly 20 percent of the sea level rise reported using satellite methods. So what was your point?

• Bob Loblaw

1-foot bulge? Absent density differences? About 1/33 of one atmosphere of pressure. Or about 30mb. This is trivial stuff to look up.

Tell me: is the drop in pressure in a hurricane a factor in the size of the storm surge? Does your magical “it doesn’t flatten out” prevent horizontal water movement tied to hurricane storm surges due to low atmospheric pressure?

As for isostatic adjustment: not it’s not for “the entire ocean”. It’s for each local tidal station record, to remove the local effects that are not part of global ocean height changes. It’s required so that local tidal gauges can be used to estimate sea level change without including errors/biases due to purely local effects.

• B Buckner
• Bob Loblaw

So, two references, with no indication what you expect me to see there. Let’s try the second one first. Part of the IPCC 2007 report, section titled “Global Average Sea Level Rise Due to Thermal Expansion”. Not a word about glaciers or isostatic effects. Nothing about magical mid-ocean bulges that can’t find their way to shore.

Maybe the second supports B Buckner’s argument.It’s titled “What is glacial isostatic adjustment (GIA), and why do you correct for it?”. Much more promising. Does it say GIA is “for the entire ocean”. Let’s look.

Oh, here it is. It says “currently some land surfaces are rising and some ocean bottoms are falling relative to the center of the Earth”. Hmm. Doesn’t seem so “entire ocean” to me – different parts moving in different directions?

Maybe this is it. “To understand the relative sea level effects of global oceanic volume changes (as estimated by the GMSL) at a specific location, issues such as GIA, tectonic uplift, and self attraction and loading (SAL, e.g., Tamisiea et al., 2010), must also be considered.”. Oh, drat, It says “specific location”. I don’t think “the entire ocean” is a “specific location”.

This must be the one: “When studying local sea level rates, which is important for policy planning, one definitely needs to account for the fact that in areas where GIA is causing an uplift, this somewhat mitigates the ocean volume change.” Oh, crap. It’s local sea level rates again. and they wouldn’t need to say “in areas where GIA is causing uplift” if GIA was for “the entire ocean”, would they?

Last try. They say “For example, large parts of New Orleans are subsiding more than 10 mm/year”. New Orleans is “the entire ocean” isn’t it? What? There not even talking about all of New Orleans – just large parts of it?

Oh, here’s your confusion. They close with “Including the GIA correction has the effect of increasing previous estimates of the global mean sea level rate by 0.3 mm/yr.”. So, when all the local GIA adjustments are made to individual tidal records, and then those sea level changes are integrated to a global level (“the entire ocean”), it changes that global estimate by 0.3mm/yr. That does not make the GIA an “entire ocean” adjustment though.

Perhaps you want to try extracting your own sections of those links and making an actual argument?

9. Jeff said:

“One of the tide gauges you include is Fort denison, Sydney, Australia (closest to me)”

The Sydney harbor tidal gauge series is interesting in the fact that it reveals a strong ENSO signal upon a data transformation. If the difference of the average SLH reading is taken at a separation of precisely two years (i.e. a biennial differencing), then the ENSO signal emerges. The ENSO signal is otherwise buried.
http://contextearth.com/2017/05/10/enso-and-tidal-slh-a-biennial-connection/