I’m skeptical. In particular, about this idea that the rate of global warming at Earth’s surface has recently exhibited a slowdown.



Even more extreme claims have been promoted, such as an actual “pause” or “hiatus” in warming of earth’s surface (i.e. that surface warming actually came to a halt). But those ideas are fading away, not just because we’re setting new temperature records, but also because it has finally dawned on people that actual statistical evidence for a pause just isn’t there. Never was. The longer and louder deniers continue the “pause” narrative, the more foolish they show themselves to be.

But to some people (not everybody), some of the graphs (not all of them) made it look so much like something different happened recently, that the idea of a slowdown took hold. Naturally climate scientists want to understand it — so they have searched for reasons and causes and explanations. But skepticism about the idea seems lacking. My guess is that a majority of climate scientists consider it established (it’s certainly mentioned in the IPCC reports).

On another forum I was recently part of a very brief discussion about the subject (one which mainly amounted to expressing our opinions). At least one very distinguished climate scientist stated that he considered a slowdown to be a genuine feature of the modern surface temperature record, while I stated that I didn’t see enough evidence to draw that conclusion.

This is exactly one of those subjects about which climate scientists can, and do, disagree. Not that I count myself among that august body, but in the spirit of the most convivial disagreement, with some whom I greatly respect and even like (without ever having met in person), I’d like to lay out the evidence for my claim that when it comes to claiming a slowdown, there isn’t enough evidence yet. If others can provide a cogent contradiction, then we’ll all have learned something.

So let’s get down to brass tacks.

A recent analysis by Stefan Rahmstorf with assistance from Niamh Cahill used a form of change-point analysis to look for exactly what we’re discussing: changes in the rate of surface warming. It does so by fitting piece-wise linear functions to the data, and determining how many changes from one piece to another are needed, and justifiably so, to get an “optimal” model. It demonstrated that there were no statistically significant changes in the warming rate after 1970. At least, not according to that test.

Of course that doesn’t prove there hadn’t been some change, a “slowdown” even — but there just wasn’t enough evidence to claim there had been either. One conclusion we can rely on is that the real question is this: has the warming rate changed since 1970? Let’s begin by isolating the data since then, using the global temperature data from NASA GISS:

I’ve superimposed a line showing the linear trend (by least squares), which of course has a constant warming rate. One of the difficulties we’ll face in trying to find changes of the warming rate is that the data show such strong autocorrelation. We can reduce its impact, and simplify things considerably, if we use the monthly data as shown to compute annual averages, and work with those.

Annual averages will still show autocorrelation, but it’ll be much weaker and we’ll simply ignore it. Incidentally, that will make it easier to show a change in the warming rate, so this errs on the side of confirming the trend has changed rather than stayed the same.

Here are yearly averages of the GISS data:

The two most recent (and hottest) data points are circled in red. We’ll omit the final one because it’s for 2015, which is only three months old (but off to a toasty start). We’ll also omit 2014 because, on another forum, it was suggested that we should look for a slowdown without using 2014 data. I consider that a capital mistake — but I’m gonna do it anyway. This too will therefore err on the side of confirming the trend has changed rather than stayed the same. Since I’m genuinely looking for evidence of a slowdown, I’m just going to give it every possible chance, even if that means leaving out the most recent data, consisting of the hottest year on record followed by the hottest three-month start to a year on record.

That leaves us with this (again, a linear trend superimposed):

If you want to claim a change in the trend (meaning, a change in the warming rate), then you should be able to show it in this data set.

In fact, if you want to claim a change in the trend, then you need to show that there’s something significant other than just that linear trend. Here’s what’s left over after we subtract the linear trend from the data, leaving what are usually called “residuals”:

To show a change in the warming rate since 1970, you need to show there’s something in these residuals other than just noise. If you can’t do that, then I say you’ve failed to provide solid evidence of a slowdown.

I originally started trying (long ago in a galaxy far away) by fitting continuous piecewise linear functions, essentially reproducing the change point analysis of Rahmstorf and Cahill. In doing so we try all reasonable change points (did the trend change in 1998 or 2006? or 2002? or last Thursday?) and we need to take that into account. After all, if you’re aiming at a target, it’s not so impressive to hit the bulls-eye when you’re allowed a dozen tries! Traditional change-point analysis adjusts how we compute the p-value for each statistical test to compensate for our making multiple trials, often doing so by Monte Carlo simulations. I used a different (but equivalent) method, of computing p-values the single-trial way but using Monte Carlo to determine how those should be adjusted. After each change-point try, if it gave a seemingly significant result, meaning a naive p-value of 0.05 or less (the de facto standard for statistical significance), I still needed to adjust that for multiple trials. As a result, most of the apparently significant change points will turn out to be simply not so.

The real kicker is, that when I got to that final stage of adjusting for multiple trials, I didn’t have to because there weren’t any seemingly significant results to adjust. We got our dozen shots at the target and still couldn’t hit the bulls-eye. So it not only fails to demonstrate any trend in these residuals, it doesn’t even come close.

Maybe piecewise linear functions turn corners too sharply, while the changing trend has been more curved. Let’s try polynomials. That of 2nd degree (quadratic) fails statistical significance. So does a 3rd-degree (cubic) polynomial, and a 4th and 5th, and all the way up to degree 10 it still fails. No demonstrable polynomial trend in these residuals.

By the way, we tried lots of polynomial degrees so we should adjust those too for multiple trials. It’s part of the complication involved in stepwise regression. But once again we don’t have to adjust the seemingly significant results, because there aren’t any. Not only is there no demonstrable polynomial trend, it’s not even close.

Maybe it’s some different kind of trend change altogether. Maybe the last decade, the residuals have just been cooler than they tended to be in prior decades. Or maybe it was hotter. Or maybe the decade before this most recent one, is the decade that “stands out” and shows something significant, something different from the others. Can we look for that kind of change?

There is a way to look for differences between groups, a standard and strong way called ANOVA (ANalysis Of VAriance). Let’s split the residuals into 10-year segments, the most recent of which will culminate with 2013, then run the ANOVA analysis to see whether or not we can detect a difference among any of the segments (the first segment, as it turns out, will only have four years rather than 10 like the others, but that doesn’t bother ANOVA):

Result: no. With a p-value 0.45 it falls into the “not even close” category, there’s no evidence from that analysis that any of these 10-year stretches of residuals is different from any of the others. Well, maybe 5-year spans shows this? Again applying ANOVA, again it’s not even close with p-value 0332. Well, it kinda looks like the final six years (2008 through 2013) are on the low side, what does ANOVA say? It says “no.” Does my eye deceive me, or does the final 3-year span (2011 through 2013) look different? What if we split it into 3-year segments? Again, not significant, not even close.

What if we just took those last three years, when the residuals are all nearly the same and below zero, and compared them to the rest of the years 1970-2010 using a plain old t test instead of ANOVA? We have to recognize the null hypothesis is that the last three years aren’t really different from the preceding except for random fluctuation, so our t-test should use the null hypothesis of equal mean and equal variance, which calls for the equal-variance version. It says, once again, there’s no statistically significant evidence that the residuals during the 3-year span from 2011 through 2013 were any different from those which preceded it.

What if … and I think this sounds crazy … the trend has changed in a discontinuous way? What if, instead of just changing its rate (the warming rate), it also changed its value, making a sudden jump? After all, if we’re to believe what the deniers say about the trend “since year whatever” without taking into account what came before that, then we’d have to believe in a “trend” in the residuals that looked something like this:

Frankly, I think such a trend would be unphysical. But crazier things have happened, so let’s find out if this kind of model can give us solid evidence of a trend change.

So, I fit models which allowed for a sudden change in both rate and value, at some change point. I tried all possible change point times which gave at least 5 years of data on both sides. I computed the p-value for each trial, and if any of them were seemingly significant I was prepared to adjust for multiple trials. I applied the proper F test, including accounting for the fact that I had already subtracted a linear trend. The residual fit shown above gave the strongest result, and corresponds to modeling the data (not residuals) like this:

When the results are adjusted for having made so many multiple trials, this really amounts to a form of the Chow test. But, once again, statistics says this strongest model isn’t even seemingly significant so we don’t even need to compute that refinement.

One last note: just in case you think there might be a slowdown if I did include data from the year 2014, you’re mistaken. I’ve run all the same tests on that too, and still no trend change can be demonstrated.

Bottom line:

Even allowing for a rather crazy-seeming trend with discontinuity, no slowdown can be confirmed. Even cherry-picking (actually) the final 3-year span for a t-test can’t do it (I only picked a 3-year span because it looked like it might give me the result I was looking for). I only tried a t-test because the ANOVA test gave no significant result. I tried lots of other grouping intervals for ANOVA besides just 3 years and 5 years and 6 years and 10 years, without even bothering to account for multiple trials. I did the ANOVA because I couldn’t find any significant polynomial pattern, although I pushed the polynomial degree all the way up to 10. I tried polynomials because the original change point analysis found no trend change after 1970. And I did all of that after first chopping off the most recent data, consisting of the hottest year on record followed by the hottest three-month start to a year on record. I also did all of that without chopping off the most recent year’s data.

I think I gave it a fair shot. More than a reasonable chance. I still I found no reliable evidence of a slowdown.

Maybe there has been one. Really. Maybe not. Really. If you think the slowdown is real and you want to study why it happened, that’s a great idea because we’re likely to learn more. I suspect we may learn more about the fluctuations than we do about the trend — but either way we learn.

Still, don’t say there is a slowdown as though it were a known fact; when you publish your hypothesis in Geophysical Research Letters, refer to the slowdown as purported or possible. ‘Cause I’ve tried to show it a dozen ways from Sunday, but it’s just not there, and I have yet to see anybody else show it either.