Marcel Crok asked me to comment on the peer-reviewed paper “Tide gauge location and the measurement of global sea level rise” Beenstock (yes) and others in the journal Environmental and Ecological Statistics. From the Abstract:
The location of tide gauges is not random. If their locations are positively (negatively) correlated with sea level rise (SLR), estimates of global SLR will be biased upwards (downwards). Using individual tide gauges obtained from the Permanent Service for Mean Sea Level during 1807–2010, we show that tide gauge locations in 2000 were independent of SLR as measured by satellite altimetry. Therefore these tide gauges constitute a quasi-random sample, and inferences about global SLR obtained from them are unbiased.
Random means unknown, therefore it is true the gauge locations are not random since we know where they are. But they obviously mean random in the classical mysticism sense where “randomness” is a (magical) property of a system and which must be present to bless statistical results. The authors are right to insist that if gauges are placed only in locations where the sea is likely to rise, and none where it isn’t, then the gauges will only show sea level rise. So what is wanted is control of gauge placement, not “random” placement, such that the gauges accurately estimate overall changes in sea level. I mean control in the engineering sense and not the incorrect sense used by most users of probability models, where “control” isn’t control at all.
So the authors gathered a subset of gauges where the control appears better. They call this a “quasi-random sample”, but that’s the old magical thinking and it can be ignored. About real-control, the authors say:
Although coverage has greatly improved, especially in the second half of the 20th century, there are still many locations where there are no tide gauges at all, such as the southern Mediterranean, while other locations are under-represented, especially Africa and South America. The geographic deficiency of tide gauge location is compounded by a temporal deficiency due to the limited number of tide gauge with long histories. Indeed, the number of tide gauges recording simultaneously at any given period is
So measurement error is with us. No surprise to any but activists. Yet here comes a dodgy move: “To mitigate these spatial and temporal deficiencies, data imputation has been widely used.” By “imputation” they mean “guesses without their predictive uncertainty (and where parametric uncertainty is of no interest).” Imputation in this sense is smoothing, and we all know what happens when smoothed data is input into downstream analyses, right? Yes: over-certainty.
Okay, whatever. Did the sea rise or didn’t it?
To estimate SLR in specific locations over time we use statistical tests for non-stationarity. A time series is non-stationary when its sample moments depend on when the data are measured. Trending variables must be non-stationary because their means vary over time. Therefore, if a time series, such as sea level, happens to be stationary it cannot have a trend by definition…”augmented Dickey-Fuller” test (ADF) for stationarity…
No. This is the Deadly Sin of Reification. To tell if the sea has risen at any gauge, all you have to do is look. If last year the gauge read “low” and this year it said “high”, then the sea has risen no matter what any model in the world says. All that mumbo-jumbo about Dickey’s Fuller and stationarity apply to fictional mathematical objects and not reality itself. Hence reification.
And there is nothing in any statistical model which says what caused a change, in one or any number of gauges.
“Trends”, if they exist, merely depend on the definition—and nothing more. Trends exist if they meet the definition, else they don’t. Just look! The remainder of the methods section is given over to various tests and models to determine if a reified trend occurred. Wait. Isn’t showing a trend conditional on a model a definition of a trend? Yes. But then we must ask: is the model any good at making skillful predictions? If not, then this definition of trend is not useful. Is the model used here good at making predictions? I have no idea. The authors never made any.
Some interesting just-look statistics of the number of gauges and missing data through time are shown. Then the findings:
The Augmented Dickey-Fuller statistics (ADF) show that in the vast majority of segments and tide gauges sea levels are not rising…
The number of tide gauges with statistically significant trends is even smaller using Phillips-Perron tests, according to which as few as 5 segments and 5 tide gauges have trends.
By “trends” they mean reified and not real.
Look. Gauges are usually placed where they are useful in some decision-making activity. Harbormaster or the Army Corps of Engineers wants to know what’s happening here or there. What happens at these gauges is what is useful, and not what happens in some model. Unless that model can be used to skillfully predict what will happen (or what is unknown, such as what happened in times historical), and that means forecasts with predictive bounds.
I have no idea whether the models developed by the authors are useful for forecasting. They didn’t make any predictions. All they said was whether or not some model dial was in some place or other. They present some actual data plots, and some of these, by eye, look like they have positive trends, some negative, and some bounce around. One is at the head of this article.
The definition I used for trend was “by eye.” I have no idea if that’s the right definition for any decisions made at any of these locations. That’s what really counts.