Reader Question On Sea Level Data Precision — Help Requested

From reader Kip Hansen comes a long but good (and slightly edited) question on sea level data. I can only answer part of it, because I have no expertise in the dataset at hand. Perhaps some other reader does.

The data in question:

The red trace is Global Mean Sea Level (anomaly over and under the 20 year mean) — with what appears as grey shading being the +/- 1 SD for each data point on the red trace.

This data set is more often shown only as

what I have often called “Errorless Sea Level”—NASA only gives a error bar for the long term trend. Nothing on the data itself.

I’ve dug in to get the original data, available as a text file…and I find that though NASA doesn’t provide any estimate of measurement error or CIs, they do, in the data file, provide a column which they describe as: “standard deviation of GMSL (GIA not applied) variation estimate (mm)”.

That is what is used in the first chart — +/- 1 SD on each data point — and appears to be solid grey shading.

Your question: “The dots are the data? Or are they themselves the result of a model, which is why individual dots have their own SD?”

The dots are the data—one dot for each calculation of the GMSL for that time period. I believe they are at ten day intervals—some 35 or so for each year. The SDs are for each individual data point (dot).

They are deriving the GMSL from (column 4 “number of observations”) approximately 46,000 observations for each data point. Yes, they must be using a model to turn “time for signal to return” and “scatter” into some idea of sea surface height for each observation. (There are many “corrections” and “adjustments” — each with acknowledged measurement errors, many of which which are more than one order of magnitude larger than the quantity being measured). So, yes, I’d say that each data point has its own SD because they are using a model to get a single number from the 46,000 observations.

I think that they are parametric SDs–and are specifically called “standard deviation of ….variation estimate (mm)” and the data points themselves are described as “GMSL … variation (mm) with respect to 20-year TOPEX/Jason collinear mean reference.”

So, we have the approximately 1,000 data points, GMSL variation from 20-yr mean, described themselves, by inference, as “estimates”, each has its own SD.

My question is what is the meaning that we can derive by the hugeness of the SDs compared to the long-term delta—long-term change—in the GMSL estimates?

I understand that Standard Deviations are NOT (necessarily) an indication of uncertainty in the measurement—not Measurement Error estimates, not Confidence Intervals, not Standard Errors.

It makes me uneasy to see those Wide Wide Wide SDs attached to tiny changes in GMSL proudly given to the world in hundredths of a mm (as 45.68 mm)—but truthfully, I can’t say what it tells me! But I can see why NASA doesn’t normally show them.

The part in bold is by me, and is the only thing I can talk about, since I’m still uncertain how this dataset is constructed.

Rule of thumb would say the parameter has about a 70% chance of being in the +/- SD interval. The actual observation, the sea level itself, has a smaller chance of being in that interval. Experience shows predictive intervals—the only ones that count, or should count—are anywhere from 4 to 8 times wider.

That doesn’t seem to make sense here. The +/- parametric intervals are already wide; the predictive interval would be mighty indeed.

The parametric interval already shows that anything might have happened from the 1990s to now. There could have been a decrease, increase, or anything in between. Any line you could draw in the gray envelope could have happened.

I wonder, though, how these SDs are constructed, and what they mean exactly. It appears to be ridiculous in the extreme to make pronouncements of observations to hundredths of millimeters. Anything even to the whole millimeter is ballsy. Yes, lots of observations go into each point, but those measures themselves must have some error.

This must be some kind of model, which must have seen much massaging. First is TOPEX Alt A, married to Alt B, married to Jason-1, married to Jason-2, married to et cetera. Those are always shotgun marriages. Models are always involved.

The second graph is therefore absurd. There is 0 indication of uncertainty, and therefore it cannot be taken seriously.

The first graph I just don’t understand enough; but I can say that if these SDs are what we thought they are, then the best we can say is “We really don’t know what’s going on with sea levels.”

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12 Thoughts

  1. GMSL is a largely irrelevant statistic that is used primarily by Climate Change of Doom cult leaders to frighten their members. At any specific coastal location on earth, changes in the measured sea level are dominated by sedimentation and land mass movements at that location, not by GMSL. Globally, over the past 30 years, net land area displacement of water area has actually increased by about(173,000 km2 – 115,000 km2) = 58,000 km2.
    https://www.deltares.nl/en/news/how-the-earth-has-changed-over-the-past-30-years/

  2. Just a guess because I don’t have time to research it, but I think the 46,000 altimeter readings encounter a huge range of wave heights at the sea surface. Likely that variation contributes somehow to the error calculations.

  3. Briggs ==> Thank you for taking up my question. Perhaps someone with a deeper insight into the working of NOAA’s calculation methods can offer additional information.

    My [limited] understanding is that they have a model that does something similar to what is done with Global Surface Temperatures using a grid of some specific size, finding an “average” sea surface height for that grid, then “averaging” those on some [weighted?] basis into a single global number.

    Readers: Please weigh in here if you have any particular insight.

  4. I have done a lot of looking as to how they determine sea level and sea level rise using these satellites. There are nine parameters that change with each orbit such as cloudiness, sea state as in rough or smooth, a parameter for sea spray, an adjustment for tides and currents. The accuracy of these satellites is approximately 3 cm over fixed objects such as the top of the mountain. It is my opinion that the sea level that is determined by satellite merely reflects the opinions and biases of those that write the programs to process the data.

    These satellite systems were never designed to measure global average sea level but rather to see changes in large-scale patterns such as ENSO events or changes in time over Gulf Stream flow. R. Steven Nerem is one of the principles behind trying to adapt this data for use as an indicator of sea level rise.

  5. Pardon my naivety, but why do we need satellites for this when we have sea levels recorded at lighthouses, harbors, island shorelines worldwide, accounting for tidal activity?

  6. Ed ==> Tide gauges record only Relative Sea Level — sea surface height where it hits the land. Relative Sea Level between differing locations is not, well, level. The sea is bumpy, as in lumpy, higher here than there.

    Tide gauges tells us important things — but almost nothing reliable about global or even regional sea surface height changes.

    I wrote a series about Sea Level at WUWT titled SEA LEVEL: Rise and Fall. (You can use WUWT’s search function to find it this comment section does not accept links.)

  7. Given that a tenth of a millimeter is roughly the limit of human eye resolution (and happens to be roughly a hair’s width), yeah a hundredth seems a stretch. I have done mass measurements in the microgram range and they, I think, can be done now in the nanogram range and maybe the picogram range. An altimetry measurement by satellite? That really seems to be a stretch.

    I’ve read some of Kip’s WUWT articles. They’re good. There are others who post articles there that have/do work in fields where actual measurements are done. One such article blasts our ‘friends’ in climate science on their handling of propagation of error. Yeah, they stink at it; even the better ones conflate the central limit theorem’s use when you are making multiple measurements of the same object using the same instrument with making multiple single measurements of many different objects with single instruments once each. That’s not counting mistaking extensive physical properties with intensive ones (and one of my beefs with things is that IR is light, not heat; though energy is mutable, that does not mean that the mutation is lossless nor that the conversion must result in loss of internal kinetic energy, unlike state changes such as evaporation which by definition removes the fastest moving fraction first).

  8. According to this:
    https://science.nasa.gov/earth-science/oceanography/physical-ocean/ocean-surface-topography

    The Jason satellites measure ocean topography accurate to 3.3 centimeters relative to the center of the Earth. By averaging measurements, the claimed precision is several millimeters. (Yes, they mixed accuracy and precision in the same paragraph).

    The accurate determination of ocean topography is made by first measuring the precise height of the spacecraft above the center of the Earth. …

    The height is determined by GPS, DORIS tracking combined with models of the forces on the craft.

    The second component of the ocean height measurement is the range from the satellite to the ocean surface. To take a measurement, an onboard altimeter bounces microwave pulses off the ocean surface and measures the time it takes the pulses to return to the spacecraft. The highly accurate altimeter range measurements are subtracted from the satellite orbital height, resulting in ocean topography measurements that are accurate to 3.3 centimeters (1.3 inches) relative to the center of the Earth. By averaging the few-hundred thousand measurements collected by the satellite in the time it takes to cover the global ocean (10 days), global mean sea level can be determined with a precision of several millimeters.

    How they get from several millimeters to hundredths of a mm isn’t mentioned.

  9. The military has similar (classified) data no doubt. Imagine how important sea level change is to the military, in just a very practical no politics way. Ask the Pentagon what they think GMSL is doing. Would you believe the Pentagon?

  10. @DAV ‘…How they get from several millimeters to hundredths of a mm isn’t mentioned….’
    Better satellites. I believe it was around 2006 that the data collection of this type via satellites was improved. I would really pay attention to the data coming from that time on. The beginning and the end of that graph most likely have different levels of precision, with the latter being more precise.
    10-14K years ago the sea levels were about 400ft lower, but now we are denying that it’s been rising for a few cms lately :-))). Some folks just need to pick a lane and drive in it (CHP highly recommends that).

    @Ed
    Yes, those are good records, but very local. Lighthouses and such are only at some select places. There are too many variables to account for. Even in the middle of the ocean there are dips (indentations) when you look it over a few 1000s of miles scale. Near the coasts it gets much more complicated. However, satellite data (not sure if the are developing lidar for that specifically) is too damn precise these days.

  11. @Kalif,

    Better satellites. I believe it was around 2006 that the data collection of this type via satellites was improved.

    Umm, Jason-2 was launched in 2008 and Jason-3 was launched in 2016. The orbit determination doesn’t depend on the spacecraft outside of requiring a GPS receiver. The Jason-3 orbit altitude can be resolved to 1 cm (0.4 in) but the radar altimeter is still only 3.3 cm — the same as Jason-2. Doesn’t account for 0.01 mm precision.

    https://directory.eoportal.org/web/eoportal/satellite-missions/j/jason-2
    http://spaceflight101.com/jason-3/jason-3-spacecraft-and-instruments/

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