Sunday, April 20, 2008

Chaos, weather, and climate

Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry.
- Richard Feynman

In the face of chaos, we might throw up our hands and abandon any attempt to understand climate at a deep level or make any predictions. After all, meteorologists don't try to predict weather beyond 10 days or two weeks. Such humility certainly beats the arrogance of the IPCC and "global warming" fanatics who wrongly believe that the climate problem is in the bag.

It isn't. Contained within it, as a subproblem, is the hardest question in physics, that of chaotic turbulence and turbulent heat convection - itself a problem that not only remains unsolved, but will probably never be solved in complete generality. Add to that the further severe difficulty of discontinuous water transformations (ice, liquid, vapor, and back), and you have a problem like nothing else in science. Soon we'll learn how the misguided idea that this problem is solved ever got started.

The search for the invariant structure of climate. Chaos means that climate can only be understood, crudely speaking, as a range, or climate regime. (Technically, the "range" is really a strange atttractor.) Besides, we're not talking about one thermodynamic variable (pressure, or temperature, say) at one point. We need a set of such variables at every point in space (multiple, spacetime-dependent fields) to specify what we mean by the state of atmosphere.

What's needed is some controlled simplification or approximation that captures this "range," without having to track every variable everywhere within the atmosphere, for all times. The Lorenz attractor, which is defined by only three variables (we need a continuous infinity of them), has an invariant set. "Invariant" means it doesn't change over time as the system does its chaotic thing. What's lacking is a "supershadow" of atmospheric turbulence, an invariant covering set for the whole atmosphere that would allow a simplification of the chaotic part.

On a somewhat different but related tack, it's better to avoid describing the atmosphere using local intensive variables like pressure or temperature. These are local averages and indicate the state of the atmosphere only at one point at a time. The right variables are extensive (meaning, they scale with the size of the system and are additive) and, for an open system, like our atmosphere, not fixed sums over static volumes, but flows. (That is, stop thinking about heat, for example, and start thinking about heat flow.) We already know what the basic flows are: dry air, water vapor and condensed droplets, heat. Their magnitude gives a much better sense of climate globally than beating the dead horse of meaningless temperature averages. (Besides, we need more than just temperature.) Even more compelling is the topology of these flows: their connectivity, regardless of where exactly they are in space or what exactly their magnitudes are.

If we're going to get a grip on "climate change," we'd better get a grip on "climate" and "climate state." Contrary to what everyone assumes, there's no good definition of either at this time, and thus no good definition of "climate change." The question, left unanswered and often unasked, is assumed away. In all branches of science, we get to meat of "what?" questions by looking for invariant or almost-invariant structure. This posting has pointed to some good candidates constituting a starting point for future definitions. And if more quantitative characteristics can also be nailed down, we can start ranking different aspects of atmospheric change in order of importance. At that point, we would have the beginnings of what is so far lacking in climate modeling, controlled approximations.

Why look for answers when you think you already know the answer or, worse, don't even know the question?

POSTSCRIPT: Certainly this past winter has been one of the longest and snowiest in a long time, reinforcing the trend that started in the late 90s. Wisconsin gets it here.

Meanwhile, here's an interesting article in the Wall Street Journal about the non-warming non-crisis in Greenland. It mentions the last warming period in Greenland in the 1950s, not to be confused with larger-scale warming trends mentioned in previous postings. And it makes an interesting and telling point: the warmest post-Ice Age period was the Hypsithermal (or Holocene) Climatic Optimum, about 8000 to 4000 years ago.* For example, Siberia had forests growing all the way up to Arctic Ocean, although the warmth was also worldwide. But the kicker is that Greenland's ice cover was not significantly smaller during the Hypsithermal. Evidently, it's pretty hardy, and there remain some big things that scientists don't understand about it.
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* In the northern hemisphere. In the southern, it was about 10,000 to 8000 years ago.

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