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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