A Very Informative Post — but not the way they think it is

And that very informative post is at the Watts Up With That blog. It’s even the “recommended” post there.

The title is “NOAA shows ‘the pause’ in the U.S. surface temperature record over nearly a decade.” It’s based on monthly average temperature anomaly for the 48 conterminous states of the U.S., using data from the USCRN (U.S. Climate Reference Network), which probably is the highest quality temperature data for the U.S., for climatological purposes. The theme of the post is that data since 2005 show a cooling trend, albeit not statistically significant, so it shows “the pause.” After all, it certainly doesn’t show a statistically significant warming.

Here’s the data together with a trend line estimated by least-squares regression:

The estimated trend is -0.06 deg.F/yr (or, -6 deg.F/century). Here’s what uncle Willard has to say about it:

It is clear there has been no rise in U.S. surface air temperature in the past decade. In fact, a slight cooling is demonstrated, though given the short time frame for the dataset, about all we can do is note it, and watch it to see if it persists.

Likewise, there does not seem to have been any statistically significant warming in the contiguous U.S. since start of the new USCRN data, using the average, maximum or minimum temperature data.

There’s one thing I’ll have to agree with: that the time frame is short. The total time span is less than 10 years. For climate purposes, for determining the actual, relevant trend, it’s not nearly long enough — especially since this is for the 48 states of the U.S. only (not the whole world), and the noise level in that regional time series is a lot bigger than the noise level in global temperature.

How meaningful is the purported “trend”? To answer that question we’d have to know the uncertainty associated with the trend estimate. Of course (!) Watts doesn’t provide that. But one of his “reviewers” does, in what is perhaps Watts’ most “informative” graph, one provided by Willis Eschenbach, after Watts “… asked three people who are well versed in data plotting and analysis to review this post before I published it …“:

It clearly indicates that the estimated trend is -0.6 +/- 0.68 deg.F/decade, which is the same as -6 +/- 6.8 deg.F/century. I get the impression that Willis Eschenbach is uncle Willard’s “go-to guy” for data analysis.

Problem is, that uncertainty range of -6 +/- 6.8 deg.F/century is a 1-sigma error range. That means it’s not a 95% confidence interval, it’s only a 68% confidence interval. Which doesn’t inspire a lot of confidence. If I claimed there was a trend based on 68% statistical confidence, what do you think the WUWTers would say? Of course, if we go by the 95% confidence interval (the de facto standard in statistics) then the actual trend could be as high at 7.6 deg.F/century. That’s a helluva lot! Which makes me wonder why Watts is so convinced that these data show an indisputable “pause.” (Just kidding)

Other problem is, even for a 1-sigma error range it isn’t correct. The residuals show distinct autocorrelation, a phenomenon which makes the estimated uncertainties from standard statistical software too low. To get a realistic estimate we’d have to correct for autocorrelation. I estimate that the corrected standard error (the corrected “1-sigma” error range) is actually +/- 13.1 deg.F/century. That means that even within the 68% confidence interval the actual trend might be as high as 7 deg.F/century. That too is a helluva lot. And within the 95% confidence interval, the trend might be as high as 20 deg.F/century. You read that right. Twenty degrees F per century.

What’s the bottom line here? If you analyze it correctly, you discover that using just this set of data, the actual trend could be as low as -32 deg.F/century or as high as +20 deg.F/century. That doesn’t exactly narrow things down, does it? In fact, for an honest estimate of whether or not the trend has (since 2005) been any different, faster or slower, than the trend leading up to 2005, using just this data set gives you an answer which is useless.

And that, ladies and gentlemen, is the truly informative aspect of Watts’ post. His analysis is useless but he still touts is as a clear demonstration of “… ‘the pause’ in the U.S. surface temperature record over nearly a decade.” I’d say it is very informative indeed — not about climate (!) but about about Anthony Watts’ blog — that he (and most of his readers to boot) regards a useless trend estimate as actual evidence of “the pause” they dream of so much.

Incidentally, there’s yet another problem with Willis Eschenbach’s “error bars” which are plotted on the graph (the yellow lines above and below the trend line, let’s call that the “error envelope”). They too aren’t right. Here is an error envelope for the trend line without bothering to apply the autocorrelation correction, just using the white-noise model:

Let’s zoom in the y-axis so you can see the shape of the upper and lower limits:

Note that the upper and lower limits are curved lines. Now let’s magnify the y-axis on Eschenbach’s graph:

Notice that Eschenbach’s upper and lower limits are not curved lines, they’re bent straight-line segments? I think it’s safe to conclude that Willis Eschenbach doesn’t know how to do this calculation. Which makes him the perfect choice to be Anthony Watts’ “go-to guy” for data analysis.