A Peculiar Pause

Have you heard about the pause in global warming? If not, you should look at this figure taken from a recent paper by Ross McKitrick:


The pause is pretty obvious, but just in case you can't see it, I've decided to highlight it. McKitrick kindly provides his code online, and with a few changes, I was able to get it running (The URL he gave for downloading this data didn't work, but I had little trouble finding the correct file, such as here) With a few tweaks to the graphics parameters, I got:


Which is clearly the same as his. With two quick commands, I was able to add lines to indicate where the pause is according to McKitrick's analysis:


Yup. McKitrick's approach shows the global warming pause is exactly where I thought it would be.

Were you expecting something different? I understand. I can see why one wouldn't normally think of a "pause" as a period in which temperatures are visibly rising, and I know if you read McKitrick's paper, you'll see remarks like:

The IPCC has drawn attention to an apparent leveling-off of globally-averaged temperatures over the past 15 years or so.

Which are true. McKitrick's analysis finds a "pause" under the definition he provides:


Which sounds more complicated than it is. Basically, you find the greatest period where there is no statistically significant trend for any subset of the period in either (the northern or southern) hemisphere. The particular test for significance he uses is somewhat complicated, but otherwise, it's a simple approach.

But I left out one detail. With McKitrick's methodology, you always use 2014 as your last year. That means you can only find a "pause" which extends to current times. That ensures you will never find an earlier pause. It would also guarantee you find a modern pause except as the paper explains:

Table 1 presents the surface results. The data are monthly but we only consider annual increments for J, and only for durations of more than m = 5 years, as failure to reject the null of no trend in the vicinity of the end of the sample could, in the case of such a short interval, arise simply due to the small size of the subsample.

The paper never explains why a failure to find a trend over a five year period should be ignored but a failure to find one over a six year period should be considered. The number seems arbitrarily chosen to me. It's true a trend over a, say, two year period is almost certainly not going to be statistically significant, but why draw the line at five?

I'm not sure, but it's interesting to consider what would happen if you didn't. There is always going to be a period length short enough we can't find a statistically significant trend in it. If we considered every period, no matter how short, we'd always find a modern pause. Establishing a cutoff point, somewhere, is necessary so the methodology doesn't automatically build a "pause" into the results.

But that is just a peculiarity. We can examine the methodology without understanding why the value of five years was chosen. We should. A far more interesting issue is there is no particular reason to assume we are currently in a "pause." We could believe there really was a pause but it ended recently. This methodology could never hope to tell us that.

Obviously, it would be worth seeing what happens if we used the same methodology over a different set of periods. Instead of always ending our period in 2014, we should try ending it in other years. The year which immediately popped in my mind was 1998. It's often considered to be the start of the "pause." What would happen if we had used this methodology a year or so before the huge warming spike? Assuming the data set had the same values as today's, this is what we'd have gotten at the start of 1997:

J	Start	CI_L	Trend	CI_H
5	1991	-0.4476	0.0513	0.5501
6	1990	-0.5205	-0.0671	0.3863
7	1989	-0.2490	0.0343	0.3175
8	1988	-0.1896	0.0230	0.2355
9	1987	-0.1370	0.0272	0.1914
10	1986	-0.0764	0.0896	0.2557
11	1985	-0.0514	0.1521	0.3556
12	1984	-0.0194	0.1791	0.3777
13	1983	-0.0082	0.1332	0.2745
14	1982	0.0250	0.1453	0.2655

J stands for the length of the period. Start is obviously the start of the period. CI_L and CI_H are the lower and upper confidence intervals. As you can see, the first period with a statistically significant trend ending in 1996 begins in 1982. That means, according to McKitrick's methodology, there was a ~13 year "pause" prior to 1997. That's the pause I highlighted near the beginning of this post. You know, the one that happened in the period with the clearly visible warming trend.

(Caveat: I haven't tested the individual hemispheric data. I've left the values of that test out of my tables because they're in arbitrary units for which you need to convert critical values to compare. The code provided doesn't do this, and I haven't written code to generate the results yet. It seems unlikely the results will change much, but the possibility they might should be kept in mind.)

That "pause" does not exist, however, if we include data from 1998:

J	Start	CI_L	Trend	CI_H
5	1993	0.1394	0.6420	1.1445
6	1992	0.2146	0.5942	0.9739

In fact, we don't even need data from 1998's huge spike to erase that 14 year "pause." Just using 1997's data is enough:

J	Start	CI_L	Trend	CI_H
5	1992	0.0867	0.4367	0.7868
6	1991	-0.1804	0.2388	0.6579

That means this methodology can find a 10+ year pause today then come back in one year and say no pause ever existed. McKitrick says he found a 19 year "pause" in this data set, but if he redoes his analysis next year using the same methodology, he may find there was never a pause in the first place. That seems incredibly peculiar.

The idea a 19 year pause may vanish so easily may seem difficult to believe. I wasn't sure of it myself. To find out, I tested it. I created two years worth of artificial data modeled after the 1998 spike in temperatures and appended it to the current temperature series. You can see the results in the figure below:


I have no reason to expect such a huge spike in temperatures, but the paper claims its methodology is robust to a variety of effects. If the methodology is truly robust, it should certainly be robust to an outlier of a nature we know can happen. It isn't:

J	Start	CI_L	Trend	CI_H
5	2011	0.4971	0.8536	1.2101
6	2010	-0.0095	0.5609	1.1313
7	2009	-0.0898	0.4440	0.9777

In two years time, this methodology could find a statistically significant trend and conclude the "pause" never existed. It might not even take that long. I only tried one artificial series. There are thousands of other possibilities. Under some, the "pause" might completely vanish in as little as a year.

I haven't taken the time to see how much warming in what amount of time will erase the "pause" for good. I don't intend to. I think it's enough to note the 19 year pause McKitrick claims to have found in HadCRUT could vanish almost overnight.

That's not right.


  1. Thanks Brandon. You result doesn't surprise me. I suspect at least part of the immediate cause is that the CIs are inflated due to the Pinatubo eruption in the early 90s, and (for larger J) also the El Chichón eruption of the early 80s. McKitrick's definition of "pause" doesn't require a period of zero warming [as determined by OLS trend] but merely a sufficiently large CI relative to trend.

    The low-pass-filtered temperature curve suggests to me something which I haven't seen commented upon elsewhere. Namely, that the cooling periods (1880-1910, 1940-1970, 2000-present, to use round numbers) show discernibly less cooling progressively, while the warming episodes (1910-1940, 1970-2000) appear comparable. There's been a lot of discussion about the relative trends in Tmin vs. Tmax, or winter vs. summer, but not about cooling vs. warming periods. Perhaps it's a logical consequence of the greenhouse theory, but I don't recall this being mentioned.

  2. HaroldW, it wouldn't surprise me if we could find potential reasons for any number of aspects of the temperature record. I've always been suspicious of such though. That something "fits" doesn't mean it's right. That was well-demonstrated by the Foster and Rahmstorf approach to removing the "pause." I'm not sure how we can overcome the risk of spurious fits with things like volcanoes.

    On the other subject you mention, I think I remember people talking about that a bit, but I'm not sure. The diminished amounts of cooling in cooling periods wouldn't be surprising as that's pretty much what you'd get if you superimposed an increasing trend onto an internal cycle. That the warming periods wouldn't show a similar change is surprising though (at least, to me). I can't think of any particular reasons that should happen. I'd be curious to know if you're right about your impression. If so, it'd definitely be interesting to consider what's going on.

  3. Brandon -
    On looking more closely at it, I think my previous observation is just a visual illusion, and the smoothed curve is mainly superposition of a warming trend on a cycle. The peak 15- and 30-year OLS trends are increasing from cycle to cycle.

    So...never mind.

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