Climate, Chaos, Confusion

Willard has been asking me for more science.

I was disappointed that the Los Angeles public TV stations KCET disappeared all the articles they paid me to write. Fortunately, somebody has stolen the best of the bunch from KCET and posted it (on an ostensibly Christian site). So here it is, for old times’ sake:

We climate scientists often hear the case made “If you can’t predict the weather next week, how could you predict the climate in a hundred years?” The answer to the question is hidden in the question. The weather and the climate are not exactly the same thing, and so what you can say about the one and what you can say about the other are also different.

Everyone knows what weather means. Sometimes we even speak of the weather as “it”. What will “it” be like tomorrow? “It” will probably rain in the afternoon. Clearly the weather must be important, since we call it “it”!

Suppose you ask me today, in mid-October, whether it will snow in your home town on Christmas Day. I have very little information to offer; that would be a ten week weather prediction. On the other hand, suppose you ask me whether the next Fourth of July will be warmer than the next Christmas. Here (assuming you live somewhere like the US mainland) I will have very little hesitation in making a prediction. The first prediction is a weather prediction, but the second is simply a climate fact: it is extremely unlikely for an early July day to be colder than a late December day.

That’s an easy one. There’s a closely related question which is much harder.

It’s asked by people who are somewhat interested in science. We hear “doesn’t chaos theory mean you can’t predict the climate”? Or “isn’t climate chaotic”? Here I have to get very careful with language, because a few things are getting confused. There is a way of thinking about these questions that makes sense, but not everybody who talks about them knows it.

Let’s start by thinking about what “chaotic dynamics” means.

The discovery of chaotic dynamics in any scientific application is often attributed to Ed Lorenz, one of the founders of the field of physical climatology. There’s a nice description of the discovery as well as some of the consequences at this link. It’s interesting that Lorenz was making an early effort at getting a computer to model weather when he ran into this phenomenon.

Chaos is a property of some (not all) nonlinear systems of evolution. Here the word “evolution” has nothing to do with biology, but simply the nature of the system we are modeling. These systems change gradually and in completely well-defined ways; their state at any given instant of time depends only on their previous state and the inputs. There is no randomness in this system, and so the behavior of the system is in principle predictable. What Lorenz discovered was an unanticipated behavior of the system that, among other things, greatly liimits the extent to which such a system can be predicted in practice. It turns out that this behavior is quite common in nonlinear systems of evolution. The best mathematical descriptions of fluids behave in just this way, and the atmosphere and the ocean are fluids.

If you’ve heard of this topic, you’ve probably also seen a diagram like this one.


Let’s review what this picture is showing us. What you see is the trail of the state of a mathematical model plotted on two axes. The vertical axis represents one physical quantity and the horizontal another. What we see is a system that has two separate behavior pattern, and can jump from one to the other. The locations of the jumps are systematic, but there are non-jumps very close, indeed as close as you specify, to jumps. So if you have the initial state of the system even very slightly wrong, if you want to predict the system into the future your model will eventually take the wrong branch.

You don’t know where on this surface the dot will be in the future, even though you know a great deal about how it behaves!

Is the climate of this system unpredictable?

What does the word “climate” even mean? Everyone knows it intuitively. Austin, Texas has a warmer climate than Madison, Wisconsin. This doesn’t mean that it is impossible that Madison is warmer than Austin on a given day, just that it is unlikely. Once we use the words “likely” or “unlikely” we have moved into the domain of statistics and must tread very carefully lest the statisticians mock us for our crude misuse of their delicate concepts. And indeed, we are sometimes a little bit sloppy when we define “climate” as “the statistics of weather”.

Whether that definition is adequate or whether it simply hides some difficulties under a rug depends on exactly what topic we are pursuing.

For the Lorenz case, though, it’s simple. The “weather” is the present position of the dot. The “climate” is the whole picture, both sets of loops, the tracks on which the dot moves. Those loops define the behaviors that the system is prone to. They are the climate of the system.

Is that climate predictable? Yes. It is more than predictable! It doesn’t change at all! In the long run, the moving dot will be somewhere on those loops, and not anywhere else!

The real climate of the world is a much more complicated system of evolution than Lorenz’s example, and there are lots of difficulties in getting it right. My point here is this: what I’d like you to appreciate is that chaotic weather is entirely consistent with totally predictable climate.

Let’s be careful. I haven’t proven that climate actually is predictable.

I have shown that the long term aggregate behavior of a system can be known (the shape of the two loops in the far future) even if the long term dynamic prediction (where on the loops the dot will be at some time in the far future) cannot.

In other words, I’ve shown that chaos in weather doesn’t demonstrate chaos in climate.

Which is practically the same thing as saying that I can’t tell you whether you’ll have a white Christmas, but I can still tell you whether you’ll have a hot July. It just took a lot longer to say, because a little knowledge is a dangerous thing.


  1. Just to stir the pot, I'm going to display my sloppy thinking and specific ignorance, though I would not agree that I am stupid, just to complicate that statement. Not enough discussion here lately.

    I haven't had time to read carefully and in any case would have trouble given my maths deficiency, but it seems to me the physics of climate change is fairly obvious and a little hard to ignore. So the sum over time would be inevitable, wouldn't it? Heat trapping and like that? Increased energy in the system?

    Now I really should write properly, given where I am, but I'm in the middle of complicated actions involved in a house closing, so am hoping I will provoke somebody better informed than I to react to this. One point I might make is that I have looked at global water vapor animations daily for many years now, and I do see a drift on average towards more extremes, clogged, weird, and other kinds of oddities in circulation. I find it odd that others do not note the obvious drift of weather on average in certain obvious directions. I get caught up, sometimes, in overinterpreting but I think the trends are fairly obvious to someone who looks at the whole over time. I love complexity, and weather is a stunner, but starting anywhere one is going to end up noticing that "something is going on."

    I am baffled that people think a set of isolated data points (even nearly a couple of decades worth) can run counter to the way things work, and it seems to me we've had a basic understanding of that for quite a long time now.

  2. The article simply refutes the idea that because you can't predict weather you necessarily can't predict climate.

    As I was careful to say "I haven’t proven that climate is predictable." I only said that the lack of predictability of weather gives no information about the predictability of climate. That is, I refuted a common talking point.

    But to discuss the extent to which climate is indeed predictable is a much more complicated matter.

    Unfortunately, there is a confusion in nomenclature that makes this discussion harder. Meteorologists think of something called "short term climate prediction" which really boiled down to prediction of the instantaneous state of the ocean. Oceanographers and whole system climatologists consider that to be a form of "weather". I saw a revealing disagreement between Gavin Schmidt and Kevin Trenberth on this once, so I'm on solid ground.

    I prefer the point of view that the ocean state is a kind of weather, i.e., I'm on Gavin's side, but ultimately this is a question of nomenclature and emphasis - they didn't have a theoretical disagreement.

    The extent to which climate is predictable depends first of all, then, on whether you consider the ocean to be part of the climate or a boundary condition for the climate. These are two separate questions.

    This distinction is important in considering the "hiatus", which appears almost certain to be at least partly a result of ocean circulation variations. If you insist that, the hiatus having been unpredicted, climate models must be considered refuted, you are taking the position that the bumps and wiggles in the global system trajectory are "climate events".

    The extent to which those are predictable in theory is interesting, but no one ever anticipated that they would be predictable in practice given the current knowledge of the actual state of the ocean - the data grid is underspecified and the models are too coarse in resolution. (There's no point in the huge expense of high resolution ocean models given the current data set.)

    In the tradition of Lorenz, though, and of GCMs, I consider "the climate system" to be the atmosphere, the ocean, and the sea ice. In this view, the bumps and wiggles (like the hiatus) are in all probability to be considered as noise, and we are certain that in the long run that greenhouse gases will warm the planet. In this view, the transient behavior is of secondary importance, and it's the equilibrium result that we are after. And we think the climate models can in practice give us a very good sense of that, and there's no real theoretical reason they shouldn't.

    In this view, the hiatus is the dot that is moving around a fringe of the multi-lobed structure in the illustration, and climate change is the structure of the lobes gradually (hopefully gradually!) shifting.

    Now, even this view breaks down once the great ice sheets get into motion. They too may be sensitive to initial conditions - the way they melt may depend sensitively on the fine details of their structure. And where and when they change adds an even longer time scale to the problem.

    In the end, I'd say the question of weather climate is chaotic is at best underspecified. My preferred way to look at it, though, is that chaos is a property of a model, not a property of a real physical system. The real world does what it does.

    Each model can track some aspects of the real world to a greater or lesser extent. In practice that is limited by process fidelity and data density.

    Time will tell how good our GCMs are at tracking the changes we are facing. But failure of the models, even failure to reproduce a slowdown, should offer no reassurance. Uncertainty is not our friend.

  3. This a nice series of video on chaos theory. Chapters 7 & 9 deal with the issues addressed Tobis' post.

    Chaos | Chapter 1 : Motion and determinism - Panta Rhei

    Chaos | Chapter 2 : Vector fields - The lego race

    Chaos | Chapter 3 : Mechanics - The apple and the Moon

    Chaos | Chapter 4 : Oscillations - The swing

    Chaos | Chapter 5 : Billiards - Duhem's bull

    Chaos | Chapter 6 : Chaos and the horseshoe - Smale in Copacabana

    Chaos | Chapter 7 : Strange Attractors - The butterfly effect

    Chaos | Chapter 8 : Statistics - Lorenz' mill

    Chaos | Chapter 9 : Chaotic or not - Research today

  4. Stirring the pot again, earth's circulation is again showing signs of

    Being a person who enjoys six impossible things before breakfast, I find it easy to look at these and know they are only snapshots, but also note trends and exceptional events. It will change, but right now there is a spectacular display of incursion that penetrates the North Pole, and we know that can't be good. Sadly US weather news carpetbombing has already forgotten Nuri and the western Pacific, and no doubt snarky commentary about how cold it is will come thick and fast.

    Meanwhile, perhaps this should go in a separate note on the open thread, but Dave Roberts has done a neat thing on epistemology and deception.

    A sample:
    "There are no signs or markers against which to steer. Epistemology becomes competing tantrums. Projection & reality blur."

    But it's all good, please take a look.

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