Disequilibrium is not Your Friend

You will probably recall from their “Pop” art heyday those “mobile” ceiling hanging art pieces in the style of Alexander Calder. These items get their charm from a delicate balance: they are constructed such that the slightest breeze reconfigures the angles among the pieces; an element of chance intervenes in how they are perceived at any moment. Here’s an actual Calder piece of the genre.

Whatever you may think of its artistic merit, consider such a piece, rather, as a scientist would. You are, let us suppose, trying to characterize the general behavior of the random variations of the piece. Its climate, so to speak.

It is not difficult to imagine, for example, that there might be a seasonal variation, as the museum’s heating or cooling systems kick on and off. Or perhaps some wooden pieces might absorb moisture under more humid conditions, altering the balance. You would be considering patterns that were periodically roughly stable over the course of a year.

Now suppose the beam on which the sculpture is mounted is suddenly damaged, but not broken. The mounting point abruptly moves by half an inch. What would you expect? Well, you’d expect wild swinging about of the piece. Oscillations might emerge that you had not seen before. Larger swings than usual are pretty much inevitable. And yet the average position of the sculpture has changed only slightly.

It’s a general principle of complex equilibria that the more they are disturbed, the more complex the processes involved in restoring their equilibrium. The mobile sculpture is not unusual in this regard.

(Even extremely simple linear dynamical systems sometimes show “ringing” in response to forcing. Think of your humming wine glass as an example. This means that as the glass responds to you rubbing the lip, it oscillates, as opposed to simply undergoing a small compression.)

What makes the sculpture less predictable under forcing? Both the size and duration of the impact matter. If you moved the piece ten yards very gently, its behavior might be nothing out of the ordinary, while if you moved it an inch suddenly, a lot of complexity would emerge. (If you moved the piece ten yards suddenly, you would expect permanent alterations, with a whole new set of modes created and many of the old ones destroyed. Let’s hope we do not take the analogous experiment that far.)

While this in no way constitutes a mathematical proof for any given system, the underlying behavior is common and intuitively understandable. If a complex system acts otherwise, it would be something extraordinary that deserves explanation. As applied to the climate system, consider it a plausibility argument: the more rapidly and extensively the system is disturbed, the more we would expect that unexpected behaviors will emerge, and the further from expectations they will be.

If this is the case, you cannot simply add “global warming” and “natural variability”. (Formally, arguments “from superposition” do not apply.) If a place is ten degrees above normal at a time of one degree of global warming, it does not make sense to say that one degree is due to climate change, and nine degrees “would have happened anyway”, even in a statistical sense. It implies that the dynamics of the system are the same under perturbation. Is that a realistic presumption in the absence of other evidence? I think it shows a weak understanding of general systems principles to make that case.

This complaint has been pretty strongly in my head, especially when Marty Hoerling says some of the things he says, or John Nielsen-Gammon does.

Fortunately, I don’t have to fend off this error alone. First, IPCC stepped up in their recent report on weather extremes, with this illustrative graphic


So, is this really what is happening? Just a few days ago I thought it was too early to tell, but I was wrong. Hansen, Sato and Reudy have a paper submitted to PNAS and published on Hansen’s website. Sure enough, looking at seasonal temperature anomalies we can see various curves like this:

Indeed, the distribution of regional anomalies isn’t just shifting to the warm side. It’s also getting broader.

It still seems to me surprising that anyone expected anything different. The presumption that global warming should be expected to be a benign and gradual process has no basis in anything but tradition. Any basis in general systems theory indicates the opposite. But this is why we can’t just shrug and say “only one degree out of the ten (or twenty)” is attributable to human forcing.

And this is no joke. Here are some typical examples of their maps of seasonal anomalies. It shows years early in the record with few three-sigma anomalies, and years late in the record with many warm ones and few cold ones.


scale is in standard deviations re: 1951-1980 climatology

note that only 0.53 C separates the years in global mean temperature anomaly (number at upper right

As someone who lived through last year’s bullseye, let me tell you that it isn’t pretty.

approaching Bastrop, Texas from Austin, Sept 5, 2011





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  3. Thank you for this exceptionally lucid article. For close to 20 years, when I reacted to each new climate change prediction by saying it was a drastic underestimate, my sister would ask how I knew. I could only talk vaguely about complex systems, and how no one was taking ALL the interrelated elements into account. This article presents a clear, elegant and accessible model for understanding the nature of the changes that are occurring.

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