Not long ago I posted about how multiple factors, including in particular the use of “broken trends,” can lead us astray about what the trend really is by allowing distinctly non-physical changes. It also amounts to ignoring evidence about the trend, namely all the data that comes before a chosen start time. Let me illustrate.
Let’s use annual average global temperature data from HadCRUT4 (the Hadley Centre/Climate Research Unit in the U.K.) for the period from 1970 through 2013. It looks like this:
Of all the global surface temperature data sets, this is the one which most “looks” like it may have shown a slowdown, especially from 2001 through 2013. If we fit a straight line to the data using only that time span, we get this:
That certainly gives the visual impression of no warming, covering a period of 13 years.
However that impression quite ignores all the data which came before. It amounts to this model of the “trend”:
In addition to the un-physical nature of such a “broken trend,” the model does not pass statistical muster; there’s insufficient evidence that the change of trend in 2001 is real. The broken trend only accomplishes one thing: it gives the visual impression of a trend which is much lower than what came before, by completely ignoring what came before.
If all we had was the data from 2001 through 2013, then that’s all we could do — you can’t include information from data you don’t have. But we do have data on what came before. Ignoring that data is a mistake. Ignoring that data specifically because 2001 is the starting point of the strongest visual impression of trend change, is cherry-picking. Doing so because you want to believe, or to make others believe, that the trend is lower than reality, is dishonest.
I know that fitting a trend line to a limited time span is very common. Most of the time, it’s an innocent mistake, not a deliberate one. If one suspects that the trend changed in 2001, then estimating it separately and independently for the “before” and “after” data is a very natural thing to do … but unless you have evidence that there was a “jump discontinuity” as well as a trend change, it’s a mistake.
It also, far too often (perhaps even most of the time), includes a purely statistical mistake. When comparing those “before” and “after” trends, the usual way is to allow for the fact that the “two different trends rather than just one” model includes a single additional degree of freedom: the trend difference between the two time spans. But in fact it includes two additional degrees of freedom: the trend difference and the jump discontinuity. This is rarely accounted for, but must be for a valid treatment (it’s one of the reasons the Chow test was devised).
There is a way to include a trend change at a particular time but avoid a non-physical jump discontinuity. We simply fit a model which allows for a trend change but is still continuous, i.e. no discontinuity (jump or otherwise). We can, for example, do that with the HadCRUT4 data 1970-2013 with a trend change in 2001. That yields this model (in blue, compared to the “broken trend” model in red):
Suddenly the estimated trend change isn’t nearly so impressive, and no longer gives the visual impression of 13 years with no increase. And it still doesn’t pass muster statistically; there’s just no solid evidence of a trend change at that time.
Another extremely important statistical consideration is that if one goes searching for a trend change, there are a great many places at which it might have happened. This means we have many, many “changepoint” times to choose from. And that means we have many, many more chances to get an apparently significant result just by accident. It’s like buying a lot of lottery tickets; your chance of getting a win, just by accident mind you, are much improved because you have so many more chances. All of which drives home the lack of evidence for a recent trend change … the test models don’t pass muster, even before we compensate for the large number of chances we have from the free choice of when to start.
And then there’s the issue of when to end a purported “trend change” period. So far, I’ve ignored (I haven’t even shown) the data after the potential “trend change” interval. When we include information from what came after, as well as what came before (when we include real context about claims of trend change), the case for a “slowdown” or “pause” or “hiatus” is even more paltry:
In order to claim a “slowdown/pause/hiatus,” we have to believe in broken trends, ignoring what came before and after, followed by the trend taking off like the proverbial bat out of hell. And, of course, we kinda have to ignore the data from NASA, from NOAA, from Cowtan & Way, and from the Berkeley Earth Surface Temperature project, all of which show nowhere near as much visual impression of a “slowdown” as the HadCRUT4 data.
If you look at nothing but 2001-2013, from HadCRUT4 data only, then it’s easy to get the idea that global temperature showed a recent slowdown. But what’s really impressive is the array of things you have to hide from view to maintain that impression. Such a limited perspective is not very scientific. Neither are the claims from those who deny the danger of man-made global warming.
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