It is said that global warming has taken a break over the last decade or so. This is not true. Surface temperatures (air, sea surface, and ice) have increased over this period of time, though less so than previous years. Also, there are various indicators that the coming year or so may be extra warm, depending on what happens in the Pacific Ocean. Perhaps more importantly, deep sea temperatures seem to have gone up, and since most of the effects of anthropogenic global warming are seen in the ocean (over 90% of the extra heat goes there), changes in the rate of global warming at the surface can easily be the result of short term changes in exactly where the heat goes. (I discuss this in detail here: The Ocean is the Dog. Atmospheric Temperature is the Tail and About That Global Warming Hiatus… #Fauxpause.)

Recent research has suggested that part of the recent slow down in global surface warming, and other fluctuations, have resulted from the fact that the Earth’s surface is not as evenly sampled as one would like, and certain areas that have heated up quite a bit lately such as the Arctic and interior Africa are underrepresented in the data.

Some of the variation in surface warming has been attributed by some researchers to a phenomenon known as the Atlantic Multidecadal Oscillation (AMO). “Oscillations” are a common phenomenon in climatology. Generally speaking, this is where a major variable (temperature or air pressure) in a given area or between two areas shifts back and forth around a mean. The AMO in particular has been a bit difficult to figure out, or for that matter, to prove that it really even exists. Part of the problem is that a single oscillation, which involves seas surface temperatures over the Atlantic Ocean, may have a period of forty or even eighty years. For this reason, the high quality record of surface temperature change allows us to only see a couple of full oscillations, and this makes it hard to characterize and even harder to explain causally.

According to Michael Mann, lead author of a paper just out addressing the pause and its relationship to the AMO, “Some researchers have in the past attributed a portion of Northern Hemispheric warming to a warm phase of the AMO. The true AMO signal, instead, appears likely to have been in a cooling phase in recent decades, offsetting some of the anthropogenic warming temporarily.”

One application to understanding recent changes in the rate of warming in the context of the AMO is the so-called “Stadium Wave.” This is an actual Stadium Wave, a phenomenon seen at sporting events:

The climate Stadium Wave idea as proposed by Judith Curry suggests that certain changes in surface conditions related to the AMO result in swings in surface temperature that actually explain the long term “global warming curve” enough to discount or reduce the presumed effects of global warming. Curry’s Stadium Wave is a kind of emergent property of climate, where this and that thing happens and results in a large effect because of compounding variables.

It’s complicated. Here is an abstract from a paper by MG Wyatt and JA Curry explaining it:

A hypothesized low-frequency climate signal propagating across the Northern Hemisphere through a network of synchronized climate indices was identified in previous analyses of instrumental and proxy data. The tempo of signal propagation is rationalized in terms of the … Atlantic Multidecadal Oscillation. Through multivariate statistical analysis of an expanded database, we further investigate this hypothesized signal to elucidate propagation dynamics. The Eurasian Arctic Shelf-Sea Region, where sea ice is uniquely exposed to open ocean in the Northern Hemisphere, emerges as a strong contender for generating and sustaining propagation of the hemispheric signal. Ocean-ice-atmosphere coupling spawns a sequence of positive and negative feedbacks that convey persistence and quasi-oscillatory features to the signal. Further stabilizing the system are anomalies of co-varying Pacific-centered atmospheric circulations. Indirectly related to dynamics in the Eurasian Arctic, these anomalies appear to negatively feed back onto the Atlantic‘s freshwater balance. Earth’s rotational rate and other proxies encode traces of this signal as it makes its way across the Northern Hemisphere.

This led to a number of statements and predictions by Curry, which have been parsed out here.

For the past 15+ years, there has been no increase in global average surface temperature…
The stadium wave hypothesis provides a plausible explanation for the hiatus in warming and helps explain why climate models did not predict this hiatus. Further, the new hypothesis suggests how long the hiatus might last.
The ‘hiatus’ will continue at least another decade
Climate models are too sensitive to external forcing
Hiatus persistence beyond 20 years would support a firm declaration of problems with the climate models
Incorrect accounting for natural internal variability implies: Biased attribution of 20th century warming [and] Climate models are not useful on decadal time scales

So, the Stadium Wave model goes a long way to explain recent surface temperature trends, and seriously calls into question the viability of climate models that show a strong human influence on global warming and that predict future catastrophic warming. For this reason, the Stadium Wave hypothesis brings up key questions, and if there is evidence either supporting it or falsifying it, that would be of utmost importance.

The paper under consideration here, “On Forced Temperature Changes, Internal Variability and the AMO” by Michael Mann, Byron Steinman, and Sonya Miller, addresses the Stadium Wave issue (and other matters). This is a very complicated study and if you really want to understand it I recommend getting at least a Masters Degree in Atmospheric Science then sitting down with it for a long time. The way I got through the paper was asking the lead author a bunch of questions. Here, I mainly want to address the Stadium Wave issue. The short version of the story is this: Curry’s Stadium Wave is an artifact of her methods. A second and probably more important finding is that the AMO, previously thought to have contributed to warming surface temperatures over the last ten years, is now thought, based on this new analysis, to have contributed to a relative flattening out of the warming, and thus may account for the so-called “hiatus” in part.

Previous work, including that done by Curry but also others, treated the AMO as a long term change in sea surface temperature that could be identified by removing other signals using some standard statistical techniques, most notably “detrending.” Detrending is where you have a known (or presumed) signal that imposes a certain pull on the system over time. This is then numerically removed from the signal as a linear adjustment. For example, if I want to know the average heart beat rate of a set of people, I could just hook them up to a monitor and collect data and get an average. But say I don’t want my signal to be messed up by certain factors, such as caffeine intake, aerobic exercise, or watching episodes of exciting TV shows. So, I estimate the effects of these other activities on heart rate using some independent information and come up with a linear fudge factor. Then, I record when my subjects are drinking their Latte, engaged in their Cardio-Kick class, or watching The Walking Dead. For those periods of time I adjust the heart rate data based my numerical model of those effects, and the result is the detrended heart rate.

A more straight forward use is found in climate studies. We know that there is long term global warming caused by the release of fossil Carbon (mainly as Carbon Dioxide) into the atmosphere. So if we want to observe something like the AMO all by itself, we take the long term temperature record of sea surface in the Atlantic, subtract a numerical value representing anthropogenic global warming over time, and what is left should be the AMO.

But there is a problem with that technique.

The relationship between different variables in a complicated system has to be known or assumed to do this kind of adjustment. For example, let’s say that drinking a latte before Cardio-Kick makes the effects of Cardio-Kick five times more intense on the heart rate. If you didn’t know that, than your detrending of heart rate would get messed up. If you knew about this non-linear relationship, you could adjust for it, but if you don’t know about it, or assume it to be not significant and thus ignore it, than your results will be wrong.

Here’s another analogy that may help. Let’s say you know how to drive a car. That includes how to steer the car through a turn. This involves turning the wheel in a certain direction a certain amount as the car goes through the curve, then straightening out the wheel to go straight after the curve. Now, lets say you get a job flying a high performance fighter jet. But, you slept through flight school. Now, you are flying the jet and you want to make a small turn, so you turn the “wheel” of the plane a bit, then straighten it out to continue in a straight line after the turn.

If you did that, you would actually tilt the plane with your first turn of the wheel, and it would stay tilted indefinitely thereafter, continuing with the turn. To properly turn the jet you have to tilt it, let it start flying in the new direction, then untilt it. In other words, if you fly a jet fighter like you drive a car, you will fly it wrong because you made incorrect assumptions about the relationships between the key variables leading to the final outcome (the direction you are going in). I recommend that you don’t do that with fighter planes or climate data.

Mann, Steinman and Miller, in this new paper, tried something interesting. They recreated a set of scenarios in which they could observe the AMO and other climate variables over time, but rather than having the AMO be a variable subject to emergence after other factors are accounted for, they introduced a known AMO. This way they could see the exact effects of the AMO on surface temperatures and other variables and explore the relationship between the variables. They call this the “differenced-AMO approach.” Knowing the true AMO signal they were able to produce a correct climate signal, and when the AMO signal was detrended in this scenario, the final result failed to match known internal variability. In other words, using the previously applied techniques, such as used by Curry, the modeling did not work. More importantly, the detrended AMO signal had an artificially increased amplitude, with lower lows and higher highs, and these peaks occurred at the wrong times.

Go back to the fly vs. drive analogy. Imagine you are now driving something … a car or a plane … with a blindfold. Your job is to drive or fly around for a while then later show your path on a map. You know how to drive a car. You drive around a bit at a regular speed, make four left turns, and when you are done you may be able to draw your path on a map with reasonable accuracy because you have an accurate expectation of what happens when you turn the wheel of a car. Now, do it with the high performance jet fighter but using your car-driving expectations. You think that first turn to the left made your path turn 90 degees to the left but it really sent you into an unending circle. Now you make two more left turns and you think you’d be back to the starting point like you would be in a car, but what you’ve really done is to send the jet into a tighter and tighter turn and while you think you flew in a big square, your actual path is more like something a kid might draw with a Sprograph(TM). That appears to be what Judith Curry did.

The Stadium Wave is alleged to happen when the AMO and other related climate factors peak and wane in sync, but this new paper shows that this is a statistical artifact. According to Mann, “Past studies arguing for a large AMO temperature signal with a substantial contribution to recent warming have assumed that the forced component of climate change (human factors such as greenhouse gases and sulphate aerosols, as well as natural factors such as volcanoes and solar output changes) is a simple straight line, a linear trend. That is the null hypothesis they assume. They subtract off that linear trend and interpret what is left over as an “oscillation”. But the significance of that oscillation rests upon the validity of the null hypothesis of a simple linear forced signal. That null hypothesis is just wrong.”

Driving a jet plane like a car.

“We estimate the forced signal (which includes a cooling component from 1950s–1970s due to human-generated sulphate aerosols) using a variety of climate model results, and show that the residual “internal variability” that results when you subtract off a more valid estimate of the forced climate trend is very different. The AMO signal turns out to be much smaller (and the estimated amplitude is consistent with findings from coupled model simulations that exhibit an AMO oscillation).”

So, the Stadium Wave hypothesis now looks more like this:

As I mention above, another important finding of this work is that the AMO probably accounts for part of the recent decade’s warming being less than previous years. According to Mann, “Rather than contributing to recent warming, the correctly-estimated AMO signal appears to have contributed cooling over the past decade, i.e. it offset some greenhouse warming.”

The previously used detrending also missed the contribution of other factors that probably make the AMO look like something it isn’t. There have been a number of other effects on surface temperatures that are left behind after anthropogenic warming is detrended out of the data, especially the effects of sulfate aerosols, which come from power plants and such. “These aerosols have cooled substantial regions of the Northern Hemisphere continents in recent decades, thus masking some of the warming we otherwise would have seen,” Mann told me. “But aerosols have tailed off in recent decades thanks to the Clean Air Acts, etc. That has allowed the hidden warming to emerge in recent decades. If you subtract off a straight line from the temperature trend, you will appear to have an “oscillation”, but that oscillation is just mostly due to the non-linear nature of the long-term forcing, with a substantial positive forcing (warming through 1950s, then slight warming or even cooling from the 1950s–1970s due to a large sulphate aerosol cooling contribution), followed by the accelerated warming in recent decades as aerosols have tailed off. We show in the paper that subtracting off a simple linear trend when you have this more complicated time history of human forcing of climate, gives rise to a spurious apparent “oscillation”.”

Go back, if you dare, to the abstract from Curry’s paper. Back when I used to teach multi-variate statistics for grad students (co-taught with a brilliant statistician, I quickly add) this is the kind of abstract we would look for to use in class. It demonstrates an all too common error, or at least potentially demonstrates it well enough to examine as an exemplar of what not to do. Climate systems are complex. There are a lot of known variables and accessible data sets, but those variables and data sets have often hidden relationships, or important factors are unknown, either entire variables or relationships between variables. If you take a set of possible causal variables and one or two ideal outcome variables, it is possible to mix and match among the candidate causal variables until you get a model that matches the outcome. Perhaps, in doing so, you’ve figured something out. Or, perhaps you just made up some stuff. One way to know if you’ve really explained a phenomenon is to have a sensible, even expected, physical process that links things together. In other words, you have a logical cause as well as a statistical link. The latter without the former is potentially wrong. A second way to evaluate your finding is to seek internal statistical or numerical relationships that result in apparent meaning but that are actually artifacts of your methods. In this case, Mann et al have done this; as demonstrated in this new paper, Curry’s stadium wave is one possible, but meaningless, outcome from the process of making statistical stone soup. Such is the way many theories of everything, large or small, seem to go.

Mann also told me that some of the other large scale oscillations that make up part of the standard descriptions of Earth climate systems could be subject to similar artifactual effects. It will be interesting to see if further work allows further refinement of our understanding of these systems over coming months or years. The models climate scientists use are pretty good, but this would make them more useful and accurate.

Mann, Michael, Byron Steinmann, and Sonya Miller. 2014. On Forced Temperature Changes, Internal Variability and the AMO. Geophysical Research Letters. DOI: 10.1002/2014GL059233

Special thanks to my facebook friends for helping me get the plane-car analogy right.

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