Or a clumsy oaf brushes into the fishtank and the waves move the fake coral around, changing the fish's preferential behavior.

I'm not being facetious here, analogies without a sense of proportion can get a much too alarmist reaction. The one you gave might better represent accidentally steering a large asteroid into a collision with the earth. Indeed, even the asteroid collision at the K/T boundary was probably more analogous with major sloshing in the tank than with tipping it over.

If I may, I'd like to introduce another aspect of the fishtank analogy, which is that the fish itself might tip over a piece of coral, changing the configuration, and ultimately its own preferred location pattern. If I were choosing a AGW analogy, it would be holding up a mirror, and maybe the fish will knock over a piece of coral while attacking its reflection.

AT least three interesting issues raised here, which I'd like to try to keep separate.

1) Art, your point that knocking over the tank is too strong and may be overinterpreted is fair.

I don't think anyone believes that we are facing a disruption in climate or environment as severe as that caused by the Chicxulub asteroid. Perhaps I should have spoken of dropping a bowling ball into the tank instead.

2) The distinction between forced vs intrinsic variation is an aspect of the model, and not of reality.

Is the asteroid part of the system or external to it? That is a strategic decision on the part of the model builder, depending on what purposes the modeler wishes to apply the model.

Arguments that climate is not predictable on any time scale based on chaotic dynamics neglect the importance of forcings. Some things about climate are predictable, given the forcings. When the next asteroid hits, we do know it will be messy, right? That has nothing to do with chaos in climate.

We don't know when that will be, arguably because of chaos in asteroid orbital dynamics, but that's not a statement about climate. A model has to be a simplification. If we model everything we end up knowing nothing. One of the issues my history of climate science series will address is what the boundaries between climate and not-climate are and should be.

3) When you you talk about fish attacking their reflection, though, you are changing the analogy pretty severely. The fish in that new analogy isn't just the weather, it is or at least it includes ourselves.

This raises the question of whether our own behavior should or shouldn't be part of the model.

Certainly we are part of the system, but we are the part that is potentially controllable by decision. If our own behavior is treated as chaotic, that amounts to a presumption that we are too lazy to take stock of the situation. I do not predict whether I will buy a new pair of shoes. I decide whether I will do so.

This line of reasoning leads to interesting issues about the appropriate role of economics in our long term decision making.

For my purposes here that is off topic, though. The point is not about the fish. It is about our capacity to model what happens to the fish. The distinction I am trying to make is between unforced and forced changes in a model. It makes no sense to focus exclusively on unforced changes in climate change, because on those time scales the forcings are large, so purely internal variation doesn't matter very much.

Actually, Michael, the analogy I was trying to make was of our activities to the "holding up the mirror", while the fish's behavior (knocking things over) could analogize to melting ice-caps or warming tundra (or melting methane hydrate clathrates). IOW, the actual effect of 2.5-4 Watts/square meter (average) forcing from doubled CO2 is predicted to be a 2-5C increased global averaged temperature (per Senior and Mitchel 1993), everything else, tipping points and so on, is primarily a result of what the weather does in response to that forcing. Isn't that right?

Of course, we could choose not to hold up the mirror, or to take it away before the fish gets too violent. So it still makes the point.

Ref
Senior and Mitchel (1993): Carbon Dioxide and Climate. The Impact of Cloud Parameterization
Journal of Climate Volume 6, Issue 3 (March 1993)pp. 393–418
http://ams.allenpress.com/perlserv/?request=get-abstract&doi=10.1175%2F1520-0442%281993%29006%3C0393%3ACDACTI%3E2.0.CO%3B2&ct=1

AK, while the knocking over may have seemed extreme, it was necessary for something to fall over so that Fudd's Law could be invoked, thus in turn providing an irresistible opportunity for me to both date myself and locate myself in what by now can only he called an obscure sub-culture. Thanks for the memory, MT!

Those numbers have firmed up a bit; per doubling or doubling equivalent (i.e., you have to account for other anthropogenic greenhouse gases) I think we're pretty confident of 4 W/m^2 and oh, 2.5 - 3.5 C equilibrium sensitivity.

Is everything else "primarily a result of what weather does"? To some extent that is a matter of definition. For instance, possible clathrate feedback is already hidden under that sensitivity.

Here's what I mean. Suppose we're right and the sensitivity to CO2 doubling is 3 C. Suppose we get our act together and limit human emission totals to where a doubling is the peak disturbance. Suppose, though, there's a clathrate feedback that we neglect in calculating our emissions. Then the final carbon content might say be quadruple background. So we'd be looking at a 6 C change. But that wouldn't change the sensitivity number, which would still be 3 C.

The cloud parameterization problem the article refers to is still open and in fact that is what my day job is about. However, there has been huge progress since 1991, when the work you link to was completed. That, for instance, was long before there was anything much like ocean dynamics in any climate model.

We are now planning for machines literally hundreds of thousands of times more powerful than Senior and Mitchell could have used. Does that mean the models are in any sense hundreds of thousands of times better now? Alas, no, there are some scaling issues to say the least.

Still, computational results that are almost twenty years old should be treated as a historical curiosity by now. The fact that the sensitivity is still in the same ballpark as the early estimates should indicate that there is some real science underpinning what we do, though.

I chose Senior and Mitchel because it's referenced in Marshak and Davis (2005) and could thus be considered authoritative. As an amateur I'd probably have trouble picking out which modern papers would do as well. And, as you say, the numbers haven't changed very much.

On page 10, Marshak and Davis (2005) have a bar graph (based on Senior and Mitchel) showing a cloud feedback range from below 2C to over 5C. Of course, they have an agenda, since it illustrates the importance of their book.

Anyway, supposing there's a clathrate feedback such as you mentioned. This would result from warmer weather (driven by the 3C sensitivity) causing release of methane. So, as you said, it's not part of the sensitivity to CO2 doubling. It's caused by a feedback relationship between the weather and something outside the weather (strictly speaking).

I really like the goldfish analogy, if we assume the goldfish's position to represent the current position of the weather in n-space. This allows things like coral sculpture, growing plants, human activity with food, mirrors, and bowling balls, etc. to be used for things linked with climate but not part of it, such as clathrates or tundra tree growth. It would probably even be possible to find something analogous to the effects of windborn pollen (and other spores) and mast years.

My primary interest is how much the whole thing can be analogized by a bunch of small coral sculptures sometimes being nosed around by the fish. That is, how often the weather pushes some external feedback process across a "tipping point" and settles into a new basin of attraction. My intuition, based on chaos theory rather than understanding of climate, would be that there are many similar basins depending on external feedbacks (e.g. vegetation, dust availability, pollen/spores, seasonal wildfires, sulfur compounds from algae), as well as forcings such as volcanoes, tectonic activity, and anthropogenic factors. Most of the changes (between basins) would be very small compared to variability of progress to/along the attractor, some would be of equivalent size, and a few, such as the major warming feedbacks everyone worries about, could be large. In addition, I would expect a change of attractors to represent more of a change in regional climates than overall.

N.B. I'm defining a "feedback" as something that helps influence the parameter(s) of the attractor while itself being influenced by the progress of the weather. Thus, dust availability can influence future cloud and rainfall patterns, but was influenced (via vegetation) by past rainfall and wind patterns.

Ref
Marshak and Davis (2005): 3D Radiative Transfer in Cloudy Atmospheres by Marshak, Alexander; Davis, Anthony (Eds.)
http://www.springer.com/west/home?SGWID=4-102-22-46979629-0

Could you elaborate on your statement that climate models are not chaotic? Certainly, the ocean and atmosphere are turbulent fluids, and hence chaotic. El-Nino has decadal variability which I would guess is chaotic, as does the thermohaline circulation. Further, I expect that the NAO is chaotic as well. It is hard to imagine there is not natural chaotic variability on century and longer timescales. To say that the climate is not chaotic is to say that one is averaging over long enough times that the statistics are stationary.

Even the transient response to increased CO2 should have chaotic features on century timescales due to ENSO, NAO, and thermohaline variability.

Jeff, you are exactly right:

"To say that the climate is not chaotic is to say that one is averaging over long enough times that the statistics are stationary." That is a good way to put it.

Chaos means that the phenomenon under study becomes, after a long enough time, increasingly hard to predict. If climate is increasingly easy to predict over a long enough time, then it isn't chaotic.

The phenomena you mention are indeed chaotic within the models that capture them, but that is "weatherlike" rather than "climatelike" in the dynamical systems view, and it is that latter view we must take when talking about "chaos". I hope that's clear.

Right now I am working on analyzing a set of 83 control realizations of ten years of atmosphere runs with a fixed ocean. Their climates are very similar. I also have a set of seven twenty year runs. Their climates are even more similar to each other. People have done comparable experiments with century scale runs. Same result.

There's no sign of chaos in these models. That doesn't mean some better climate model might be chaotic, particularly on very long time scales, but on those time scales you start to get significant changes in forcing, so it really is an "academic" question in the pejorative sense.

Michael,

You say, "Right now I am working on analyzing a set of 83 control realizations of ten years of atmosphere runs with a fixed ocean. "

I agree, with a fixed ocean, the atmosphere reaches statistical equilibrium quickly. But the climate system includes the ocean. Do you think that an ensemble of twenty-year coupled atmosphere-ocean models with realistic El-Nino would not show divergences among the ensemble members? I think they would, because twenty years is beyond the predictability time of ENSO, but too short to reach statistical equilibrium.

Jeff, yes, of course, you have to run instances of a coupled system, which has slower dynamics, longer in order for the climate to converge. The point is, though, that it does in practice converge.

It's hard, really, to say what a "chaotic" climate would mean, but the coupled models we have definitely aren't that by any formal definition of dynamic chaos I can imagine.

The longer we run the model, the less the initial conditions show up in the climate result.

What this tells us about reality is actually somewhat subtle. For myself, I can't really see how to get anything like deterministic chaos in the *statistics* of a model. I may be missing something subtle about "ergodicity" and such.

None of this matters. Climate change is mostly forced dynamics.

The one sentence explanation from Wikipedia:

Weather: The weather is the set of all extant phenomena in a given atmosphere at a given time.

Climate: Climate is the average and variations of weather in a region over long periods of time.

In the usual style of climate alarmists, you misrepresent the position of someone who dares to disagree with you, falsely accusing him of advocating pollution. Why do you do this?
You then falsely say that his comments are not relevant, when in fact they are precisely relevant to the question of chaos. Alexi is absolutely right, when he says that in the climate case, the
nonlinear chaotic interactions are between things like ice cover, ocean currents etc, evolving on longer timescales than weather events.
Your next false remark is that the question of whether the climate is
chaotic has no meaning. However big and complicated the climate system
is, it is still governed by physical processes and underlying
mathematical equations that may still be chaotic.
Your next false statement is that models are not chaotic. See
http://www.nonlin-processes-geophys.net/8/201/2001/npg-8-201-2001.html
for a simple climate model that has many positive Lyapunov exponents (ie chaotic in many different ways).
In one of the comments you say you have run your climate model for 10 or 20 years. How you hope to learn anything from this I don't know. To find out if a system is chaotic you need to run it for a long time, that is, many times the timescale over which the system fluctuates, so in the case of climate you would need to run it for several hundred years.
This sequence is marvellous:
"I don't want to duck the question altogether. So do I think climate is chaotic? I think that question has no meaning."

I will try this again.

Models related to climate may or may not be chaotic. Chaos is a property of a mathematical system.

In certain branches of physics, the models are so nearly complete that it makes some sense to talk about chaotic physics, but in fact it is really a matter of chaos in the model of the physics.

In climate, the models are of necessity incomplete.

Thank you for the very interesting reference.

Your referenced paper in fact refers to the "climate" of a very simple weather model of the sort that was in existence in the 1960s. It is specifically a case in point where the state evolution is chaotic but the manifold is stationary. So it is not likely to be inconsistent with what I am trying to say.

More to the point, I'd ask you to note specifically that the title refers to chaos "in models". The paper thus does not contradict my argument that chaos is a property of mathematical systems and not usefully defined for the real world.

My main point which you miss is this. Under some definitions of climate, some models may in fact be described as chaotic. However, under the usual definition of climate (statistics of weather) and the usual definition of climate model (dynamic general circulation model), the models are not in fact chaotic, and in fact can't be. Finally, what that tells us about the real world is rather limited and I think it's not a very fruitful direction either for investigation or criticism.

Regarding the ten year runs, these models are pure atmospheric models. (Ocean, land and sea are prescribed)

The atmosphere model physics has no processes with time constants comparable to ten years. This is why all of the runs produce almost exactly the same results in the statistical sense. (Of course, the final state of each system is different, but they all show the same climate.) In this case ten years is "long enough" for all the statistical behavior of the system to emerge. The 83 runs amount to a demonstration of that point.

Lest I be accused of wasting resources, the purpose of the 83 runs was not to prove anything about climate but to obtain a basis (in the mathematical sense of "basis") for dimensional reduction of the output of somewhat modified models.

We didn't do it to demonstrate that the model climate in such a model isn't chaotic. We already know that.