A commenter recently linked to a post by Steve Goddard claiming that “GISS Shows No Warming Over The Last Decade.”



Goddard shows this graph:

and thinks that establishes his claim. So I asked the reader,



Suppose I characterize the global temperature trend by this graph: Is that a valid characterization of what to expect in the future? Why or why not?



The graph I showed (also from “WoodForTrees.org“) shows only a little more than 1 year’s data. Let’s get one thing out of the way: if you think that is a valid characterization of the trend, you’re wrong. If you insist on clinging to that belief, then reason cannot reach you.

Obviously a single year (and a few extra months) is too short a time span to separate the trend from the noise. After all, the noise is pretty sizeable. For monthly data, it’s typically about 0.135 deg.C, and can easily be as large at 0.4 deg.C above or below the existing trend. The trend is presently 0.017 deg.C/yr. You can’t expect to see a trend of 0.017 deg.C in a single year, when the noise is as much as 0.4 deg.C above and below that trend. So a single year isn’t enough — if you don’t admit that, then leave now because we’re not interested in arguing with fools.

But Goddard’s graph isn’t limited to a single year, it shows a bit less than 10 years’ data. Is that enough? Over 10 years, a trend of 0.017 deg.C will accumulate a net change of 0.17 deg.C. One can easily imagine that this could be swamped by noise which can extend as much as 0.4 deg.C above and below the trend. But it might at least be possible that 10 years’ data would have enough information to tease the trend out from the noise — after all, statistics is a powerful tool for finding real trends in spite of sizable noise. Is there a way to estimate the limits of what the actual trend might be, even for noisy data?

Yes, there is.

When you estimate the trend using linear regression on actual data, not only can you compute the trend estimate, you can also compute the uncertainty in that estimate. However, one must be careful because the default, “naive” uncertainty estimate assumes that the noise is white noise. White noise is noise for which different values aren’t correlated. We usually think of the different white noise values as being “independent” of each other (although it is possible for noise values to be uncorrelated, and therefore white, even when they’re not independent).

However, the noise in global temperature data isn’t white noise. Different values are correlated with each other, a phenomenon called autocorrelation. But we can overcome the difficulty induced by autocorrelation of the noise. It can be a bit tricky with global temperature because the noise isn’t even the simplest kind of autocorrelated noise. One often treats autocorrelated noise as “AR(1) noise“, but as it turns out even that model isn’t sufficient. A reasonable approximation is to treat the noise as being what’s called “ARMA(1,1) noise“. I won’t give all the details (although I’ve done so before), I’ll just apply this noise model to estimate the uncertainty in the trend.

Let’s consider the trend up to the present (through June 2011) from all possible starting years 1975 through 2002. I’ll use GISS monthly temperature data, and I’ll treat the noise as ARMA(1,1) noise when estimating the uncertainty in the trend. That will enable me to compute what’s called a “95% confidence interval,” which is the range in which we expect the true trend to be, with about 95% probability.

For each year, I’ll plot the estimated trend to the present as dots-and-lines, and the upper and lower limits of the 95% confidence interval as dashed lines. I’ll also plot the estimated trend since 1975, which is 0.017 deg.C/yr, as a horizontal dashed line in red. If at any time the upper limit of the 95% confidence inteval (upper dashed black line) dips below the level 0.017 (horizontal dashed red line), then we have evidence (not proof, but at least evidence) that the trend is no longer upward at the same rate. Here you are:

Does the upper dashed line dip below the horizontal dashed red line? No.

The fact is this: there’s no evidence that the rate of global warming (the trend, not the noise) for the last decade is any different than it has been since 1975.

But Steve Goddard thinks there is. It seems that he thinks so because when he fits a trend line to less than 10 years’ data, the line is horizontal. He utterly fails to estimate the uncertainty in that trend. Frankly, I doubt he really knows how. And he either ignores, or outright exploits, the existence of noise to give a false impression of the trend.

I’ve done posts like this before, many times. The reason is that this is one of the most common techniques used by fake skeptics to give a false impression — exploit noise to give a false impression of the trend. It’s not just one of their favorite techniques, it’s one of their most successful because most people don’t have the statistical savvy to see through it. You could even write a book about it. It seems that they do this whenever any global warming indicator dips because of noise, but when a global warming indicator peaks because of noise, the silence is deafening. Cold winter in England? Proof! Hottest ever April in England? Silence.

Last but not least, I’ll tell you why Goddard chose to start with 2002. You might think it’s because it has been almost 10 years since then, and 10 years is a nice “round number.” The truth is — whether Goddard will admit it or not, even to himself — that he did so because he’s cherry-picking. He’s deliberately starting with a year which had extra-high temperature due to noise rather than trend, so he could paint a false picture of the trend by exploiting that noise.

I’ll bet Steve Goddard thinks he’s a skeptic. I think he’s a fake skeptic.