# How is sea level measured?

In comments on Earth changes due to global climate change, sea level changes is a common topic. I hear quotes about sea level changes in the centimeter and even millimeter range and wonder how such precision is even possible. The sea moves a lot; way more than a centimeter in a given day. I have no understanding how the sea level is measured, and I also can't even imagine how to do it with that kind of precision. How exactly to oceanographers measure sea level?

Perhaps a different question, I also can't envision a way that a measurement of 1 cm change is pragmatically meaningful, even for just a single beach, never mind a global average. A 1 cm higher tide I don't think would be noticed at most places. Even 10 cm could go unnoticed at many places. Does a 1 cm global average change mean anything useful? I guess rates of change can be alarming. 1 cm per year would add up over the decades.

• I'm tempted to tackle this question (since I haven't looked at the explicit methods myself yet), but before allocating time to clarify this 'trope', I'm wondering whether you're actually interested in an answer. Not trying to antagonize you but these same simplified rationalizations (e.g. how can we aequately consider regional changes having any meaningful impact on global scales) are often used to discredit climate change as a whole and it's a bit tiresome to try convincing closed minds. – Trevor J. Smith Oct 16 '18 at 19:09
• @TrevorJ.Smith I'm trying to understand the measuring process. With my limited knowledge of it, I'm skeptical it's possible that "1cm global average change" is meaningful, but I'll readily admit that my skepticism may be from a lack of creativity. I can't imagine how it's done, so I have to ask how it's really done. I'm far from close-minded, but I'm very critically minded and won't take declarations as realities without personal understanding. Maybe to Oceanographers, it's a well settled question, but I'm not an oceanographer and I'm just getting around to personally settling the question. – 14070 Oct 16 '18 at 19:22
• I have removed the first two paragraphs (with assumptions and opinions) so that the question is now about the measuring process only. – Jan Doggen Oct 17 '18 at 7:28
• Regarding your latest estimate, you appear to be conflating statistical significance with cultural significance. A centimeter rise in sea level over the course of three years is quite observable; the uncertainty in the rate at which sea level is rising is less than half a millimeter per year. On the other hand, the cultural significance of that centimeter rise in sea level is nil. – David Hammen Oct 17 '18 at 16:47
• @David No, the whole point of my question is regarding instrument precision and statistical significance. In my final sentence I very much mean cultural and pragmatic significance. I can see how I may not have been perfectly clear. I'll edit again. – 14070 Oct 17 '18 at 17:52

There are two main approaches to measuring sea level (and thus its change): local and satellite-based.

To measure local sea level we can set up gauges on the coast that record the water level every so often - hourly is common. These use various methods, which have evolved over time, all aimed at having a very precise (sometimes down to millimetres) long-term record at that location. In the UK, the UK Tide Gauge network has records going back (in some locations) to 1915.

The mechanisms of tide gauges vary, and have improved over time. Early ones used floats inside a "stilling well" (a column of water that protects the gauge from waves). Some modern gauges work by sensing water pressure. If we have good measurements of temperature and salinity we can calculate density, and if we know density and the pressure at a location, we can calculate the amount of water above that location. Other modern gauges use ultrasound or radar transceivers located at a known vertical position above the water, and thus measure the distance to the water surface with very high accuracy.

These records of water level include the tides, of course, as well as other influences such as the effects of changing air pressure, wind driven currents, and so forth. They are also affected by the rising and falling of land over time. These effects can all be accounted for, and removed from the signal, and effort goes into doing this. You might some interesting reading on the topic from the National Tidal and Sea Level Facility.

However, no matter how good the record from fixed tide gauges, they can only tell us what is happening on the coast. While that's arguably the most important for mankind, it's hardly a global picture.

The other approach that we can take is satellite observations. Radar altimeters on satellites can, and do, measure sea level worldwide to a precision of a few centimetres or better. This is a recent mission for this purpose (there may have been others since - I'm not an expert). The level of accuracy here is not as good, but it can be improved statistically through a large number of measurements.

The greater difficulty with satellite altimetry is removing the tides, because the satellites are always moving over the earth's surface and so can only measure any one location at relatively infrequent intervals. Consequently, some sophisticated global tidal models are used with data provided by the satellites to (a) improve the models, for people who want to predict tides, and (b) use the tides from the models to remove the tides from the satellite measurements, leaving just longer-term changes in sea level.

I think part of the intent of your question is "people quote changes in sea level of millimetres or centimetres per year, yet surely the measurements are not this accurate?". Well, satellite measurements aren't, though local ones might be, but remember that we're measuring for more than just one year. One approach might be to look at a ten- or twenty-year trend, and work out the average change per year from that.

• Thank you for the answer. I have some follow up thoughts. For local measurements, you don't really explain how they take the measurement. Do they use rods, floats, radar? The sea moves a lot, so I still don't see how they can measure with a precision of millimeters. For satellite, I understand enough to see how they measure, but again, what exactly are they measuring since the sea moves so much? For example, you mention removing tides via "global tidal models". What is that exactly? Average over years mentioned at the end certainly makes sense for centimeter precision. Thanks. – 14070 Oct 17 '18 at 15:39
• @fredsbend I edited to add some info on how tide gauges work. – Semidiurnal Simon Oct 17 '18 at 19:33
• Thanks for the edit. This is very helpful to me now. A "stilling well" and calculating based on density and pressure are not things I would have thought of. Maybe a stilling well, eventually, but not in like a decade of wondering about this, so maybe not, lol. – 14070 Oct 17 '18 at 19:40

How exactly to oceanographers measure sea level?

By a number of mechanisms, some direct, others indirect.

Various government agencies such as NOAA operate coastal tidal stations that measure local sea level height. There are about a thousand of these worldwide. In addition to these official tidal stations, there are even more private stations such as those on offshore drilling platforms.

Other measurements come from buoys, some anchored, others adrift. There are almost 5000 drifting ARGO buoys alone. The ARGO buoys measure temperatures at various depths. Since warmer water is less dense than is cooler water, rising ocean temperatures are a key contributor to sea level rise, about 1/3 of the total.

Yet other measurements come from space. The remaining 2/3 of sea level rise results from added mass to the oceans. This added mass can be measured by high precision gravity experiments such as those by the GRACE satellites. Those precise measurements in the changes in Earth's gravity field enables precise orbit determination of other satellites, some of which carry radar altimeters. Those altimeter readings, coupled with high precision orbit determinations, provide yet another mechanism for assessing sea level change.

• Thank you for the answer, David, and here's an upvote for the effort. I'm afraid that I don't this as answering my question. You've mentioned some names of things, which I can certainly follow up on via Google, but you haven't really said more than "they take lots of measurements". I know that, but how is an individual measurement taken such that precision is millimeters? Admittedly, I'm seeking pretty technical information. Apologies if this wasn't clear. Should I edit my question again? – 14070 Oct 17 '18 at 19:24
• On ARGO buoys, I think I saw a display of one at Birch Aquarium at scripps in San Diego. They are pretty awesome, coming from a guy who greatly appreciates autonomous things. Are you saying that the temp data collected by ARGO bouys can be and is used to calculate sea level? That makes some sense and I can see how that works, so that definitely helps. If this is right, how much of sea level data (percentage) comes from ARGO temperature data? – 14070 Oct 17 '18 at 19:25
• @fredsbend - Re but how is an individual measurement taken such that precision is millimeters? It's not. Individual measurements don't need to be particularly accurate given a database of millions of measurements. Suppose the measurements are independent, identically distributed random variables (these are not), and suppose each measurement has an uncertainty of a meter. One hundred such measurements reduce the uncertainty of the mean down to ten cm. Ten thousand such measurements brings it down to a centimeter . A million, down to a millimeter. (continued) – David Hammen Oct 17 '18 at 23:09
• This is why data mining is such a powerful tool. Just as data mining takes advantage of the law of large numbers, so do estimates of sea level rise. Lots and lots and lots of somewhat sloppy measurements make for a rather precise mean. – David Hammen Oct 17 '18 at 23:14
• @fredsbend - Re Are you saying that the temp data collected by ARGO bouys can be and is used to calculate sea level? Yes. For example, see Closing the sea level rise budget with altimetry, Argo, and GRACE (DOI: 10.1029/2008GL036010), and many, many other papers along similar lines. – David Hammen Oct 17 '18 at 23:21

(adding this as a separate answer as it's answering a different part of the question - one that wasn't there when I did my first answer...)

To understand why a rise in sea level of as little as 10cm can be significant:

Imagine a place that floods occasionally. Maybe just once a year, or less. Now think about how often it almost floods - where the water stops just 5cm below the top of the wall. Those occasions don't get reported in the same way, but they are probably much more frequent than the times when it actually floods. So a modest increase in sea level could have serious implications for many coastal areas - especially in generally low-lying countries such as the Netherlands or Bangladesh (one of those can afford to raise its walls; the other can't)

Also, remember that while we're dealing with millimetres per year at the moment, the concern that many climate scientists have is not about a few centimetres - it's about a few metres. At that level, most of the coast cities in the USA are flooded.

• That makes sense. Thanks for the follow up answer. Also, a global average of 10cm increase might mean some places get more, while others less (because as we already know, the sea is not evenly distributed). I guess a major difficulty here would be predicting how individual regions would be affected. Since you target 10cm, in your opinion, would a 1cm global average increase likely cause problems? I haven't seen any source say meters worth of sea level rise. In what time frame is that? – 14070 Oct 17 '18 at 19:51
• @fredsbend any sea level rise will cause problems. All we're talking about is the severity. I don't know what effect 1cm globally might have, but bear in mind that many places in the world have had a few mm/year for decades now (not just due to climate change), so cm-level changes are not new (though the speed at which they happen matters). The multi-metre scenarios are what one gets if land-based ice sheets collapse (mostly Antarctica, but also Greenland, maybe some others). I'm not sure what timescales we would be talking about there. – Semidiurnal Simon Oct 17 '18 at 20:04