A recent blog post on RealClimate by Stefan Rahmstorf shows that when it comes to recent claims of a “pause” or “hiatus,” or even a slowdown in global surface temperature, there just isn’t any reliable evidence to back up those claims.

Yet for years one of the favorite claims of those who deny the danger of global warming has been “No global warming since [insert start time here] !!!” They base the statement on the observed data of earth’s surface temperature or its atmospheric temperature. Then they claim that such a “pause” or “hiatus” in temperature increase disproves, in one fell swoop, everything about man-made climate change.

They seem a bit worried lately because it is very likely that the data from NOAA (National Oceanic and Atmospheric Administration) will record this year as the hottest on record; we won’t know, of course, until 2014 is complete. A single year, even if the hottest on record, has only a little to do with the validity of such claims, but a lot to do with how hard it is to sell the idea. Perhaps they dread the prospect that if the most recent year is the hottest on record — in any data set — it will put a damper on their claims of a “pause” in global warming. If they can’t claim that any more, it deprives them of one of their most persuasive talking points (whether true or not). Still the claims persist; they’ve even begun preparing to ward off genuine skepticism spurred by the hottest year on record.

I seem to be one of very few who has said all along, repeatedly and consistently, that I’m not convinced there has been what is sometimes called a “pause” or “hiatus,” or even a slowdown in the warming trend of global temperature — let alone in global warming.

And it’s the trend that’s the real issue, not the fluctuations which happen all the time. After all, if you noticed one chilly spring day that all that week it had been colder than the previous week, you wouldn’t announce “No more summer on the way! No more seasons since [insert start time here]!!!” You’d know that in spite of such short-term fluctuations, the trend (the march of the seasons) will continue unabated. You wouldn’t even consider believing it had stopped without some strong evidence. You certainly wouldn’t believe it based on weak evidence, and if the evidence is far too weak …

Why am I not convinced? Because the evidence for claims of a “pause” or “hiatus” or even slowdown is weak. Far too weak.

Let me show you just how weak their case is.

Rahmstorf’s post is based on a mathematical technique known as “change point analysis” (with the kind assistance of Niamh Cahill, School of Mathematical Sciences, University College Dublin) applied to data from GISS (NASA’s Goddary Institute for Space Studies). The result is that the most recent change point (the most recent change in the trend) which is supported by the data happened back in 1970, nearly 45 years ago. As for a change in the trend more recently than that (which is the basis of claims about a “pause”), there’s just no evidence that passes muster.

Of course, the data from GISS isn’t the only well-known data for global surface temperature; there’s also the aforementioned NOAA data, the HadCRUT4 data (from the Hadley Centre/Climate Research Unit in the U.K.), the data from Cowtan & Way (an improved — in my opinion — version of the HadCRUT4 data), the CRUTEM4 data which cover only earth’s land areas (also from the the Hadley Centre/Climate Research Unit), and the land-only Berkeley data (from the Berkeley Earth Surface Temperature project). There’s also data covering, not earth’s surface but its lower atmosphere (often called “TLT” for “temperature lower-troposphere), one from UAH (University of Alabama at Huntsville), another from RSS (Remote Sensing Systems).

With so many data sets to choose from, sometimes those who deny the danger of global warming but don’t like the result they get from one data set will just use another instead, whichever gives the result they want. Then again, some of them might accuse Rahmstorf, in his blog post, of choosing the NASA GISS data because it was most favorable to his case; I don’t believe that’s true, not at all. We can forestall such criticism by determining the result one gets from different choices and compare them. In fact, it’s worth doing for its own sake.

Let me state the issue I intend to address: whether or not there has even been any verifiable change in the rate of temperature increase — and remember, we’re not talking about the up-and-down fluctuations which happen all the time, and are due to natural factors (they’re also well worth studying), we’re talking about the trend. If there’s no recent change in the trend, then there certainly isn’t a “pause” or “hiatus” in global warming. I’ll also apply a different technique than used in Rahmstorf’s post.

First a few notes. Those not interested in technical details, just skip this and the next paragraphs. For those interested, I’ll mention that to estimate the uncertainty of trend analysis we need to take into account that the noise (the fluctuations) isn’t the simple kind referred to as white noise, rather it shows strong autocorrelation. I’ll also take into account that the noise doesn’t even follow the simplest form of autocorrelation usually applied, what’s called “AR(1)” noise, but it can be well approximated by a somewhat more complex form referred to as “ARMA(1,1)” noise using the method of Foster & Rahmstorf. This will enable me to get realistic estimates of statistical uncertainty levels.

I’ll also address the proper way to frame the question in the context of statistical hypothesis testing. The question is: has the warming rate changed since about 1970 when it took on its rapid value? Hence the proper null hypothesis is: the warming rate (the trend, not the fluctuations) is the same after our choice of start year as it was before (basically, since 1970). Only if we can contradict that null hypothesis can we say there’s valid evidence of a slowdown.

Spoiler alert: there’s no chance whatever of finding a “slowdown” that starts before 1990 or after 2008. Therefore for all possible “start of trend change” years from 1990 through 2008, I computed the best-fit statistical model that includes a change in trend starting at that time. I then tested whether or not the trend change in that model was “statistically significant.” To do so, we compute what’s called a p-value. To be called “significant” the p-value has to be quite small — less than 0.05 (i.e. less than 5%); if so, such a result is confirmed with what’s called “95% confidence” (which is 100% minus our p-value of 5%). Requiring 95% confidence is the de facto standard in statistics, not the universal choice but the most common and certainly a level which no statistian would find fault with. This approach is really very standard fare in statistical hypothesis testing.

So here’s the test: see whether or not we can find any start year from 1990 through 2008 for which the p-value is less than 0.05 (to meet the statistical standard of evidence). If we can’t find any such start year, then we conclude that the evidence for a trend change just isn’t there. It doesn’t prove that there hasn’t been any change, but it does lay bare the falsehood of proclamations that there definitely has been.

I’ll also avoid criticisms of using some data set chosen because of the result it gives, by applying the test to every one of the aforementioned data sets, four for global surface temperature, two for land-only surface temperature, and two for atmospheric temperature.

I can graph the results with dots connected by lines showing the p-values for each choice of start year, with the results from different data sets shown in different colors. The p-values are plotted from highest (no significance at all) at the bottom to lowest (statistically significant) at the top, with a dashed line near the top showing the 5% level; at least one of the dots for at least one of the data sets has to rise above the dashed line (dip below 5%) to meet the “Statistical Significance for Trend Change” region in order to claim any valid evidence of that (think of it as “You must be this tall to go on this ride”). Have a look:

In no case does the p-value for any choice of start year, for any choice of data set, reach the “statistically significant” range. Therefore, for no choice of start year, for no choice of data set, can you make a valid claim to have demonstrated a slowdown in warming. As a matter of fact, in no case does the p-value for any choice of start year, for any choice of data set, get as low as the 10% level. To put it another way, there’s just no valid evidence of a “slowdown” which will stand up to statistical rigor.

Bottom line: not only is there a lack of valid evidence of a slowdown, it’s not even close.

But wait … there’s more! Imagine you roll a pair of dice and get a 12 in some game where that’s the only losing roll. You might suspect that the dice are loaded, because if the dice were fair then the chance of rolling a 12 is only 1 out of 36, or 2.8% (hence the “p-value” is 2.8%). You can’t prove the dice are loaded, but at least you’ve got some evidence.

Now suppose you roll the dice 20 times, and at least once you got a 12. Do you now have evidence the dice are loaded? Of course not. You see, you didn’t just roll once so that the p-value is 2.8%, instead you gave yourself 20 chances to get a 12, and the chance of rolling a 12 if you get to try 20 times is much much higher than the chance of rolling a 12 if you only get to try once. In fact the chance is 43%, so the p-value for all the rolls combined is 43%. That’s way way way higher than 5%. Not only do you have no valid evidence based on that, it’s not even close.

In the above tests, we didn’t just test whether there was valid evidence of a trend change for a single start year. We did it for every possible start year from 1990 through 2008, 19 choices in all. That means that the actual p-value is much higher than the lowest individual p-value we found — it’s just too easy to get results that look “significant” when you don’t take into account that you gave yourself many chances. The conclusion is that not only is there a lack of valid evidence of a change in trend, it’s nowhere near even remotely being close. Taking that “you gave yourself multiple chances” into account is, in fact, one of the strengths of change point analysis.

I repeat: not only is there a lack of valid evidence of a slowdown, it’s nowhere near even remotely being close. And that goes for each and every one of the 8 data sets tested.

A hottest-on-record for 2014 will dampen the enthusiasm of those who rely on “No global warming since [insert start time here] !!!” Yet, in my opinion, this never was a real issue because there never was valid evidence, even of a slowdown, let alone a “pause” or “hiatus.”

Based on the best estimate of the present trend, using the data from NASA GISS (as used in Rahmstorf’s post), this is what we can expect to see in upcoming years:

Of course there will still be fluctuations, as there always have been. But if future temperature follows the path which really is indicated by correct statistical analysis, then yes, Earth’s temperature is about to soar.

Does the data prove there’s been no slowdown? Of course not, that’s simply impossible to do. But the actual evidence, when subjected to rigorous statistical analysis, doesn’t pass muster. Not even close. Those who insist there definitely has been a “pause” or “hiatus” in temperature increase (which seems to include all of those who deny the danger from man-made climate change) either don’t really know what they’re doing, or — far worse — they do know what they’re doing but persist in making claims despite utter lack of evidence.

I will predict, however, with extreme confidence, that in spite of the lack of valid evidence of any change in the trend, and even if we face rapid and extreme warming in the near future, there’ll be no “pause” or even slowdown in faulty claims about it from the usual suspects.