About that disappearing pause

Is it, as Chris Kenny says:

indisputable that the warming trend has disappeared over the past 15 years or so.

No, it isn’t.  First of all, note that the ‘past 15 years or so’ probably means ‘since the extremely hot El Nino year of 1998’. It’s pretty standard for climate agnotologists like Kenny to use 1998 as the break year, since comparing trends before and after 1998 will naturally give the kinds of numbers most favourable  to the ‘global warming has stopped’ line of thought.

Nonetheless, let’s allow Kenny to pick his own time periods of comparison and see whether ‘the warming trend has disappeared’. So what question are we asking, statistically? Well, since Kenny is conceding that there was a warming trend before 1998 or thereabouts, the natural statistical hypothesis to test is, ‘is the current temperature trend statistically different from the historical trend that Kenny acknowledges exists’? In slightly more technical words, our null hypothesis is that the warming trend continued. Let’s see if there’s sufficient statistical evidence to conclude that that hypothesis is wrong.

I calculated the trend over our whole time period (I’ve chosen 1979-2013, but you can do this for whatever time period you like.) Then, I calculate time trends over the subperiods (in this case, 1979-1998 and 1999-2013). These look like this—the trend since 1979 is in red, while the subperiod trends are each in blue:

Screen Shot 2014-08-31 at 6.00.30 pm

It sure looks like the trends are different, doesn’t it? But are they different in a statistical significant way? Actually—no, they’re not. The p-value from a Chow test (which, in short, tells us if there’s statistical evidence for a structural break in the trend of a time series) is 0.28. Usually we don’t reject the null hypothesis (in this case, that there was no structural break 15 years ago) if the p-value is greater than 0.05. So we don’t reject the null hypothesis. No structural break in 1998. So, actually, there’s insufficient statistical evidence to conclude that the warming trend over the past 15 years has changed from the warming trend that preceded it. 

Of course, as is now known by just about everyone there’s also not enough statistical evidence to show that the trend over the past 15 years or so is different from zero. (Can Kenny seriously think that this so-called ‘pause’ has been underreported? My second cousin, a farmer in northwest Victoria, was telling me authoritatively about the ‘pause’ a few months ago, and she’s not exactly sitting on her computer every night reading Anthony Watt’s blog).

But that doesn’t mean there’s no trend. There’s a lot of noise in temperature series, and over short time periods of one or two decades, it can be difficult to separate the underlying trend from the noise. But just as we don’t have enough statistical evidence to say that the temperature trend is different from zero, we also don’t have enough evidence to confirm that it’s different from the the warming trend that preceded it. We don’t have enough evidence to say a lot of things about temperatures over a short time period. In fact, just about the only thing we can say is that from 1999-2013, our best guess is that the trend was positive (I get a value of +0.007479 Celcius a year) but that it could be quite a bit above or below this:

Screen Shot 2014-08-31 at 6.13.46 pm

UPDATE: A good way of thinking about what this regression tells us about warming since 1998 is by looking at a 95% confidence interval, which gives us an idea of the range of warming trends that are consistent with the data. In this case, the interval is (-0.00166; 0.01662). In other words, we can be confident that the ‘true’ warming trend since 1998 has been somewhere between -0.16 a century and 1.6 degrees a century. In other other words, a warming trend is quite a bit more likely than a flat or cooling one.

Of course, you might quibble with some of my regression choices. I’ve used annual temperature means because this helps to address the fact that the monthly data are autocorrelated. You could also fit a trend that explicitly models the autocorrelated error structure of the HadCRUT series. You might also calculate your trends from different years. But it is, I think, false to say that it is indisputable that the warming trend has disappeared.

 

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