Tag Archives: Change Point Analysis

The alleged hiatus in global warming didn’t happen, new research shows.

There are two new scientific research papers looking at variation over the last century or so in global warming. One paper looks at the march of annual estimates of global surface temperature (air over the land plus sea surface, not ocean), and applies a well established statistical technique to ask the question: Was there a pause in global warming some time over the last couple of decades, as claimed by some?

The answer is, no, there wasn’t.

The paper is open access, is very clearly written so it speaks for itself, and is available here. One of the authors has a blog post here, in German.

The other paper looks at the so called global warming “pause” and interrogates the available data to see if the pause is supported. It concludes that it isn’t. The paper is written up in a blog post by one of the authors, here.

I’ll give you an overview of the findings below, but first, a word from the world of How Science Works.

It’s the variation, stupid

No, I’m not calling you stupid. Probably. I’m just paraphrasing Bill Clinton to underscore the importance of variation in science. The new paper examines variation in the global surface temperature record, so this is an opportunity to make this point.

Much of the time, science is about measuring, understanding, explaining, and predicting variation. This is a point non-scientists would do well to grasp. One of the reasons non-scientists, especially those engaged in policy making (from voter to member of Congress to regulatory agent to talking head) need to understand this better is because variation is one of the most useful tools in the denier tool kit. If your objective is to deny or obfuscate science, variation is there to help you.

Global warming, the increase in the Earth’s surface and ocean temperatures caused by the human caused increase in greenhouse gas, is a system with plenty of variation. The sources of variation are myriad, and the result is that the measurement of air temperature, sea surface temperature, and deeper ocean temperature appears as a set of squiggly lines.

In many systems, variation exists at more than one scale.

So, at the centennial scale, we see global surface temperatures not varying much century by century for a thousand years, then the 20th century average is higher than the previous centuries, and the 21st century average, estimated by 15% of the years of a century, is higher still. That is the effect of industrialization, where we shift from using energy from human and animal work, together with a bit of wind and water power, to using energy stored in carbon bonds in fossil fuels. This combined with population increase and increasing demands to support a consumer-driven comfort-based lifestyle have caused us to release fossil carbon into the atmosphere at an alarming rate.

At the decadal scale, we see a few recent decades that stick up above the others, and a few that are lower than others or at least don’t go up as much as others. Over the last 100 years, the decadal average temperatures have gone up on average, but with variation. The primary explanation for this variation is two fold. First, there is an increase in the absolute amount of greenhouse gas, and the rate at which we are adding greenhouse gasses to the atmosphere, so over time, greenhouse gasses have become the main determinant of temperature change (causing an increase). Earlier on, when greenhouse gas concentration was lower, other factors had a bigger impact. The second (and related) explanation is variation in aerosols, aka dust, in the atmosphere from various industrial processes, volcanoes, and such. Decadal or multidecadal variation over the last century has been mainly caused by aerosols, but with this effect diminishing in its importance as it gives way to the increasingly important role of greenhouse gas.

At a finer scale, of a year or a few years, we see variation caused mainly by the interaction of the surface (the air and the sea surface) and the upper ocean (this is sometimes examined for the top, say, 700 meters, other times, for the top 2000 meters, etc.) When we look at just ocean temperatures or just surface temperatures, we see a lot of squiggling up and down on an ever increasing upward trend. When we look at both together, we note that the squiggles cancel out to some extent. The ocean warmed considerably during recent years when the surface warmed more slowly. This is because heat is being exchanged back and forth between the surface and the deeper sea in a away that itself varies.

That is the simple version. In reality things are more complex. Even though ocean and surface temperatures vary from year to year, with the major variations caused by El Nino and La Nina events in the ENSO cycle, there are longer term variations in how this exchange of heat trends. This time scale is in the order of several decades going in one direction, several decades going in the other direction. (see this post) Then, this sort of variation may have much larger scales of change, at century or even millennial time scales, as ocean currents that facilitate this exchange, undergo major changes, which in turn alters the interaction of the surface and the sea. And, of course, both sea and ocean temperature can affect the major ocean currents, so there is a complex causal interaction going in both directions between those two sources of variation.

This is not a digression but it is annoying

Have you ever been annoyed by someone who makes a claim about the health benefits, or negative effects, of some kind of food or other ingestible substance? You know, one of those totally non-scientific “findings” from the usual internet sources. Here is a little trick you can do if you want to challenge such a claim.

In order to truly evaluate a health related claim, and have that evaluation be credible, you have to be able to do one of the following things, depending on the claim. Being able to do this is not enough to validate your expertise, but it is a starting point. It is a gate-keeper thought experiment. If you can’t do this, then you can’t really make the claim you are making with any credibility.

  • Name all the parts of a cell and what they do (for many health claims, especially those that have to do with diet, energy, metabolism, etc.)

  • Name all the different components of the immune system and explain how they work in detail (for many disease or illness related claims).

  • Describe, in detail, the digestive process, i.e., the process of food sitting on a plate being ingested and eventually being used by a human body, at the molecular level (for many claims about the beneficial or negative effects of certain foods, or the benefits of various dietary supplements).

You might be a climate scientist if …

All that stuff I said above about variation is the very simple version of what happens in the climate with respect to global surface temperature imbalance and global warming. If you read what I wrote and the whole time were thinking things like “yeah, but, he’s totally glossing this” or “no, it isn’t that simple, what really happens is…” then you might be a climate scientist.

If, on the other hand, this extensive tl;dr yammering on variation seemed senseless or a waste of time, or you didn’t find it interesting or don’t get the point, the you may not be prepared to evaluate claims like the one about the so-called “pause” or “hiatus” in global warming. More importantly, there is a good chance that a person making the claim that there has been such a pause is unprepared to do so, just as the person claiming that wearing a $50 fragment of a discarded circuit board around their neck will protect them from EMF can not really make that claim because they are a total dumb-ass when it comes to energy fields and cell biology.

Or, the person making the claim (most common in the area of global warming) is just trying to fool somebody. They are like the person who sells the fragment of the discarded circuit board.

Change Point

The first paper is “Change Points of Global Temperature” by Niamh Cahill, Stefan Rahmstorf and Andrew Parnell, published in IOP Science Environmental Research Letters.

A long series of data may demonstrate the outcome of a set of variables where all the variables act in similar ways over time, and any trend plus or minus variation will be clear. But if the variables change in their level of effect over time, it may be that parts of the long term data series need to be treated separately. This requirement has led to the development of a number of statistical techniques to break a series of data up into different segments, with each segment having a different statistical model applied to it.

The statistical approaches to this problem initially arose in an effort to better understand variation in the process of making key electronic components in the telecommunications industry. An early method was the “Control Chart” developed by Walter A. Shewhart at Bell Labs. The method allowed engineers to isolate moments in time when a source of variation contributing to mechanical failure changed, perhaps because some new factor came into play.

More recently, the statistical method of “Change Point Analysis” was developed to provide a better statistical framework for identifying and assessing the statistical significance of changes in sources of variation. The process involves determining whether or not a change in the sources of variation has occurred, and also, estimating if multiple change points have occurred. The process is pretty complicated, numerically, but is automated by a number of available statistical tools.

The new paper attempts to assess the reality of a “pause” or “hiatus” in global surface temperature increase using change point analysis. The change point analysis used four of the major commonly used data sets reflecting surface temperature changes. In each case, they found three change points to be sufficient to explain the medium to long term variation in the data. Most importantly, the most recent detectable change point was in the 1970s, after which there is no detectable change in the trend of increasing global temperature.

The results of the analysis are summarized in this graphic:


Figure 1. Overlaid on the raw data are the mean curves predicted by the three CP model. The grey time intervals display the total range of the 95% confidence limits for each CP. The average rates of rise per decade for the three latter periods are 0.13 ± 0.04 °C, ?0.03 ± 0.04 °C and 0.17 ± 0.03 °C for HadCRUT, 0.14 ± 0.03 °C, ?0.01 ± 0.04 °C and 0.15 ± 0.02 °C for NOAA, 0.15 ± 0.05 °C, ?0.03 ± 0.04 °C and 0.18 ± 0.03 °C for Cowtan and Way and 0.14 ± 0.04 °C, ?0.01 ± 0.04 °C and 0.16 ± 0.02 °C for GISTEMP.

Those who claim that there was a pause in global warming point to certain dates as the origin of that pause. The authors tested that idea by forcing the change point analysis to assume that this was correct. The alleged starting points for a global warming hiatus failed the statistical test. They are not real. The authors determined that the change point analysis “…provides strong evidence that there has been no detectable trend change in any of the global temperature records either in 1998 or 2001, or indeed any time since 1980. Note that performing the CP analysis on the global temperature records excluding the 2013 and 2014 observations does not alter this conclusion.”

In addition, even though the alleged starting points for a global warming hiatus were found to be bogus, they were found to be more bogus in one of the four data sets, that developed by Cowtan and Way, which in turn is generally thought to be the data set that eliminates most of the biases and other problems found in this sort of information. In other words, using the best representation available of global surface temperature increase, the so called hiatus is not only statistically insignificant, it is even less significant!

But that wasn’t enough. The authors took it even a step further.

Finally to conclusively answer the question of whether there has been a ‘pause’ or ‘hiatus’ we need to ask: If there really was zero-trend since 1998, would the short length of the series since this time be sufficient to detect a CP? To answer this, we took the GISTEMP global record and assumed a hypothetical climate in which temperatures have zero trend since 1998. The estimated trend line value for 1998 is 0.43 °C (obtained by running the CP analysis on the original data up to and including 1998). Using this, we simulated 100 de-trended realizations for the period 1998–2014 that were centered around 0.43 °C. We augmented the GISTEMP data with each hypothetical climate realization and ran the four CP model on the augmented data sets. This allowed us to observe how often a fourth CP could be detected if the underlying trend for this period was in fact zero. Results showed that 92% of the time the four CP model converged to indicate CPs in approximately 1912, 1940, 1970 and a fourth CP after 1998. Thus, we can be confident that if a significant ‘pause’ or ‘hiatus’ in global temperature did exist, our models would have picked up the trend change with a high probability of 0.92.

Climate change deniers are always trying to make the graphs go down. The graphs do not cooperate.
Climate change deniers are always trying to make the graphs go down. The graphs do not cooperate.
One is forced, sadly, to think about what deniers might say about any new climate change study. In this case, I think I know what they might say. Look again at the graph shown above. We see two periods when temperatures seem to be going down, and two periods when temperatures seem to be going up. So, half the time, they are going down and half the time they are going up, right? So, what happens if, as suggested by some climate deniers, we are due for a downward trend? Maybe there will be enough multi-decadal downward trends over the next century or so to significantly attenuate the overall trend. Hey, we might even see cooling. Right?

Well, no. For one thing, as mentioned above, the overall pattern has been an increase in the importance of greenhouse gasses as the variable controlling surface temperatures. Whatever factors caused the flattish or downward trends many decades ago may still be in place but are relatively less important from now on, even if we quickly curtail CO2 output. Also, one of those factors, aerosols, is reduced permanently (we hope). Industrial pollution, in the past, caused a lot of aerosols to be released into the atmosphere. This has been reduced by changing how we burn things, so that source attenuation of surface temperatures is reduced. Also, as noted above, there are multi-decadal changes in the relationship between the surface (air and sea surface) and the ocean, and at least one major study suggests that over coming decades this will shift into a new phase with more surface heating.

I asked author Stefan Rahmstorf to comment on the possibility of a future “hiatus.” He told me that one is possible, but “I don’t expect that a grand solar minimum alone could do it (see Feulner and Rahmstorf ERL 2010). Maybe an exceptionally large volcanic eruption could do it but it would have to be far bigger than Pinatubo, which did not cause one.” He also notes that some IPCC climate models have suggested a future slowdown, and the possibility of cooling in not non-zero. The key point, he notes, is “it just has not happened thus far, as the data analysis shows.”

Author Andrew Parnell noted, “I think anybody who claims that these current data demonstrate a hiatus is mistaken.”

Think there is a global warming hiatus? Slow down a second…

The second paper is “Lack of evidence for a slowdown in global temperature” by Grant Foster and John Abraham. Foster and Abraham start out by noting that there is a widely held belief, even among the climate science community, “…that the warming rate of global surface temperature has
exhibited a slowdown over the last decade to decade and a half.” They examine this idea “…and find no evidence to support claims of a slowdown in the trend.”

The authors note that most of the discussion of global warming involves reference to “ the relatively small thermal reservoir of the lower atmosphere” (what I refer to above as the “surface”), but since this is only a small part of the planets heat storage, this can be misleading. When the ocean is taken into account, we see no slowdown in warming. The paper by Foster and Abraham refers to the above discussed paper on change point analysis, so I’ll skip that part. The remaining thrust of the paper is to apply some basic statistical tests to the temperature curves to see if there is a statistically valid slowdown.

They derived residuals, using the GISS data set, for the last several decades, indidating the divergence of each year from an expected value given an upward trend. This looks like this:

Screen Shot 2015-08-04 at 10.38.58 AM

They then took sets of adjoining residuals, and tested the hypothesis “This set of numbers is different from the other numbers.” If there was a statistically significant decrease, or increase, in temperature change for several years it would show up in this analysis. The statistical test of this hypothesis failed. As beautiful as a pause in global warming may seem, the idea has been killed by the ugly fact of ever increasing temperatures. To coin a phrase.


As a last attempt to find evidence of a trend in the residuals, we allowed for models in which not only the slope (the warming rate) changes, but the actual value itself. These are discontinuous trends, which really do not make sense physically … but because our goal is to investigate as many possible changes as is practical, we applied these models too. This is yet another version of change-point analysis, in which we test all practical values of the time at which the slope and value of the time series change. Hence it too must be adjusted for multiple trials.

Again, no statistical significance. If you look at the global temperature curve, and see a pause, what you are really seeing is noise.

Foster and Abraham conclude:

Our results show that the widespread acceptance of the idea of a recent slowdown in the increase of global average surface temperature is not supported by analytical evidence. We suggest two possible contributors to this. First, the natural curiosity of honest scientists strongly motivates them to investigate issues which appear to be meaningful even before such evidence arrives (which is a very good thing). Second, those who deny that manmade global warming is a danger have actively engaged in a public campaign to proclaim not just a slowdown in surface temperature increase, but a complete halt to global warming. Their efforts have been pervasive, so that in spite of lack of evidence to back up such claims, they have effectively sown the seeds of doubt in the public, the community of journalists, and even elected officials.