UPDATE: A new post at RealClimate is very relevant, and well worth the read.

One day, a new data set is released. The rumor runs rampant that it’s annual average global temperature since 1980.

Climate scientist “A” states that there is clearly a warming trend (shown by the red line), at an average rate of about 0.0139 deg.C/yr. She even computes the uncertainty in that trend estimate (using fancy statistics), and uses that to compute what’s called a “95% confidence interval” for the trend — the range in which we expect the true warming rate is 95% likely to be; it can be thought of as the “plausible range” for the warming rate. Since 95% confidence is the de facto standard in statistics (not universal, but by far the most common), nobody can fault her for that choice. The confidence interval is from 0.0098 to 0.0159 deg.C/yr. She also adds that there’s no sign of any slowdown in the rate of warming.



Along comes a reporter for a London newspaper who proclaims, “Global warming has stopped! Call it a ‘pause’ or ‘hiatus’ or whatever you like, but the proof is in the fact that if we just look at the data since 2005 we find that the temperature in the most recent year (2014) is actually lower than it was in 2005!!!”

Climate scientist A and most of her fellow climate scientists (97% of them, in fact) declare that to be nonsense. You see, you can’t draw conclusions about a trend based on such a short time frame. Besides, the reporter didn’t even compute a trend, he just drew a line from one data point to another and drew a grandiose — and mistaken — conclusion.

Meanwhile, a popular website which focuses on denying global warming announces “Bomshell! Global Warming has stopped!! Hiatus lasts at least 10 years!!!” A U.S. senator from Oklahoma hails it as proof that the entire global warming thing is a hoax, a fraud perpetrated by hollywood liberal elitists to bring about socialism based on world government. Besides, the whole global warming thing is just a fraud so scientists can get more money for their “research”.

Numerous U.S. politicians say, “I’m not a scientist, but the pause in global warming shows that doing anything about it will only ruin the economy … especially since China and India won’t do anything.”

Along comes econometrician “B” who states that based on rigorous statistical analysis, the “pause” (or “hiatus” if you prefer) in warming hasn’t lasted 10 years, it’s lasted 12 years! Here’s his argument: test each possible start year from 1990 through 2010, use just the data from then on to estimate the trend (the warming rate), and estimate the uncertainty in the trend. Then compute a 95% confidence interval. Find out whether there’s some start year for which the plausible trend range includes zero. Here’s a graph of the result of applying that test; the dots (one for each choice of start year) show the estimated trend from that moment to the end, while bars extending above and below mark the 95% confidence interval. If any of the bars includes zero in the “plausible range” …

Note that starting in 2003 the “plausible range” includes zero. That means that you can’t prove it was warming using only the data since 2003 (“prove” meaning meet the standard of statistical significance). The same is true for every start year from 2003 to the final year tested. Voila! Pause since year 2003, has lasted 12 years. Heck, he even publishes his analysis in an obscure scientific journal.

The popular website lauds his efforts, pointing out that the result has actually been published in a scientific journal, and besides, econometrician B has a Ph.D. degree.

What do you think?

Perhaps you’re thinking that “Just because you can’t prove it’s been warming since 2003, that doesn’t prove it hasn’t been warming. From the look of the graph, the warming rate could plausibly be the same as it ever was. You certainly can’t prove there’s a pause at all, let alone claim that it has lasted 12 years.”

Enter statistician “C” who announces “Actually, those aren’t temperature data. They’re artificial data which I created with a known warming trend of 0.012 deg.C/yr plus random noise (which in this case is the simple kind known as “white noise”). The trend didn’t change, I’m sure because the data were constructed with a constant, unchanging trend.”

Now what do you think?

Perhaps you’re thinking, “Nothing even remotely like that could ever really happen.” I wish that were true.

Ross McKitrick recently published a paper in the rather obscure scientific journal Open Journal of Statistics in which he purports to show that the “pause” in the data for lower-troposphere temperature (TLT) from Remote Sensing Systems (RSS) has lasted nearly 26 years. His procedure was just as described for econometrician B, with some added complexity. For instance, he emphasizes that when computing uncertainty in a trend estimate you have to take into account something called autocorrelation, which means the noise isn’t the simple type called “white noise.” He also emphasizes (more than once) that the mathematical model for the noise which is most often used, a model called “AR1 noise,” is insufficient. Perhaps he isn’t aware that I’ve already pointed this out (see Foster & Rahmstorf).

For the RSS-TLT data set, he tries all start years from 1979 through 2009, applies his autocorrelation correction, and shows this graph:

I did the same thing using my method to correct for autocorrelation and got this (note that my units are deg.C/yr while McKitrick’s are deg.C/decade, and that I only tested start years as late as 2005 while McKitrick goes all the way to 2009):

The results are very similar, although McKitrick did make a mistake in his estimate of the uncertainty. Nonetheless, in my analysis the lower bound of the 95% confidence interval dips below zero in 1990, while in McKitrick’s it does so in 1989. That’s how he concludes that the “pause” is going on 26 years.

So, you wonder, would I protest that the “pause” in RSS-TLT has only lasted 25 years instead of 26? No.

Let’s add a dashed red line showing the estimated trend since the beginning of the data:

Every one of the 95% confidence intervals, for every choice of start year, includes the first trend estimate. None of them provides statistically valid evidence that the warming rate since any of the start years is any different than it has been all along. Bottom line: from this analysis, there’s no valid evidence that the warming rate (the trend, not the fluctuations) has changed at all.

Not only is there no valid evidence that the “pause” has lasted 25 years or longer, there’s not even any valid evidence that a “pause” happened at all. Heck, there’s not even any valid evidence that there’s been a slowdown — let alone a “pause” — in this data set.

What do you think?