Friday, October 14, 2005

More on the butterfly flap

(See here for previous.) Well, RP Snr's promised followup post consisted of an odd quotation from Richard Eykholt who works in the physics department of Colorado State University. His quotation contains the comment that
"The point of the [exponential growth of minuscule perturbations] effect is that it prevents us from making very detailed predictions at very small scales, but it does not have a significant effect at larger scales."
which RPSnr takes as vindication of his claim that small perturbations do not affect the real world, only models.

The quotation seemed a bit unclear, and RPSnr's position is clearly wrong, so I emailed Prof Eykholt to see what he really meant. He explained that he was referring to issues of practical prediction, in which case any additional perturbation of a similar size to the rounding error of a finite precision computer model cannot harm predictability over broad spatial scales, since the model already has lots of perturbations of equal size (not to mention more substantial errors) which limit predictability. Of course this is true (to the point of triviality), but it hardly seems relevant to RPSnr's claims. Further, Prof Eykholt explicitly agreed that a small random perturbation in a chaotic system will grow to a point at which the original and unperturbed systems are completely decorrelated.

Meanwhile, back in the comments section of his post, RPSnr seems so determined to defend his untenable position that he is now claiming that not only turbulent energy but even momentum itself will dissipate in the real world...

14 comments:

pielkesr said...

James-if you are going to refer to communications with Professor Ekyholt, it would be appropriate to post them. I also find it disappointing that you do not categorically state that a butterfly's flapping wings can have a significant effect on the weather thousands of kilometers away, if that is your conclusion. Quite frankly, it is amazing that you are focusing on a physically incomplete modelling perspective, rather than how the real world works.

EliRabett said...

A physicist and an engineer are in a hot-air balloon. They've been drifting for hours, and have no idea where they are. They see another person in a balloon, and call out to her: "Hey, where are we?" She replies, "You're in a balloon," and drifts off again. The engineer says to the physicist, "That person was obviously a mathematician." They physicist replies, "How do you know that?" "Because what she said was completely true, but utterly useless."

James Annan said...

I posted a reply to Roger Pielke here and also see this post. I'm pretty much gobsmacked that he is prepared to abandon such principles as the conservation of momentum in order to prop up some fundamentally unfalsifiable belief about how the real atmosphere actually is not sensitive to small perturbations, even though every sufficiently realistic model ever produced is.

I'm still not sure what Prof Eykholt really means, and judging from his last email, I'll never find out. Ho hum.

Alastair said...

I am gobsmacked that a scientist has never heard of friction.

James Annan said...

Alastair, the models already contain friction. Is your comment seriously intended as a defence of Roger Pielke's statement that "Any very small change to the momentum field (in the real world and not in the Lorenz equations or in an NWP model) will dissipate into heat"? The initial pertubation will spread upwards into the atmosphere as well as downnwards to a surface where it can be damped.

I'm still waiting for a description of the threshold below which perturbations are inevitably damped, and any suggestions as to how this idea can be tested, in the absence of any plausible alternative model...

crandles said...

Has Prof Pielke abandoned such principles as the conservation of momentum?

If body A splits into body B and body C the momentum of the whole system is conserved. However, if you only consider bodies A and C then there is a change in momentum. Read body B as a photon that has momentum and leaves the earth system (bodies A and C).

crandles said...

Forgot to mention that I don't think this makes Prof Pielke right, it just means a perturbation can spread to more locations faster (at speed of light instead of speed of molecules). I have expressed some views that I think it is the increase in the number of locations that matters more than the size of the perturbations on Prof Pielke blog.

Anonymous said...

James, both you and Crandles seem to be a bit confused about the Conservation of Momentum. It only applies during a collision, unlike the law of Conservation of Energy which is universal except during nuclear reactions.

Since the latest snooker championship has just been won by my fellow compatriot, I will use billiard balls of an example of what I am saying. When the balls collide there is a conservation of momentum, but this is lost to friction as the balls roll over the table and when they collide with the cushions.

Of course there is a third law; that of the Conservation of Mass which is also universal except in the case of nuclear reactions. The point here is that William ignored that law when he constructed his model. The atmospheric pressure on the Earth is set by the weight of the mass of air. In his experiment he reduced the pressure in one cell, thereby in effect changing the mass of air in that column and in his model. This is not a true simulation of the effect of a butterfly whose flaps would cause the pressure to decrease in one place but increase in another.

My argument is that W. should rerun his experiment altering the pressure in equal and opposite amounts in two adjacent cells. This would allow friction to dampen the effects he created. Friction cannot eliminate the effects of a change in mass!

I will atempt to perform the same experiment myself, not least because I am curious to know the result. The results of W.'s previous experiment were quite dramatic, and I am curious to know if this one will turn out to be a dampened squib!

Cheers, Alastair.

crandles said...

Alastair,

I am gobsmacked that you haven't considered whether there is a equal and opposite reaction to the friction and collision with the cushion that causes an equal change in momentum of the table, and if firmly fixed, the Earth).

James Annan said...

James, both you and Crandles seem to be a bit confused about the Conservation of Momentum. It only applies during a collision

Alastair, that is nonsense. CoM applies in the absence of an external force - which is what the friction is in your example. In the atmosphere, momentum is exchanged with the Earth's surface, but it is certainly not dissipated internally as Roger Pielke claims!

As for finding "cancelling pertubations" that genuinely decay, such beasties do exist, but are a measure zero subset of all pertubations, thus (with probability 1) any random perturbation will not have this property. But have fun looking for one!

Alastair B. McDonald said...

It is not nonsense. In the "real world" momentum is always being lost to friction. The conservation of momentum not a universal law like that of the conservation of mass. Momentum is mXv and mass (m) is conserved but velocity (v) is not conserved in the real world. You appear to be misreading Newton's First Law of Motion.

From what you wrote, it seems that Roger is confusing the molecular world of the atmosphere with the "real world". In the former momentum is not lost during the travel time. However, there will be a loss of momentum mainly with the surface of the Earth, but also in interactions with aerosols including clouds. Collisions with greenhouse gas molecules will also result in a loss of momentum. Both of those interactions will subsequently result in radiation of the change in energy to space. Thus it will be dissipated.

Cheers, Alastair.

James Annan said...

Alastair,

Stop it. You're being silly. A parcel of air can only lose momentum by passing it to a neighbouring parcel, not by "dissipating" it internally as Roger Pielke claims. There is no wriggle room here, he is simply wrong.

Arun said...

"I'm still waiting for a description of the threshold below which perturbations are inevitably damped, and any suggestions as to how this idea can be tested, in the absence of any plausible alternative model..."

That is easy. Chaos on the molecular scale has no practical effect, if it did, you would not be able to use the Navier-Stokes equation, equations of state, etc.. Molecular-level perturbations are irrelevant.

To come closer to weather models, I think despite the chaotic nature of the weather model, we nevertheless think that there is such a thing as climate; myriads of different weather histories correspond to the same climate. Whenever your model's variables are on the "climate" scale, it is insensitive to "weather". Continuum fluid mechanics is the "climate" where the molecular description is the "weather", i.e., the fluid mechanics time scale and length scale is such that it is very safe to simply average over the molecules.

In general, whenever a physical situation with a huge number of underlying degrees of freedom is successfully describable by a very small set of numbers compared to the number of degrees of freedom, it means the averaging procedure over the huge set of degrees of freedom makes sense, and that perturbations - small changes in initial conditions - at the underlying scale are mostly irrelevant.

Going by the arguments so far, butterfly wingflaps in Newark are indeed relevant to the weather in New Jersey. Nevertheless, climatology exists as a field because it makes sense to average over weather histories, where butterfly perturbations are irrelevant.

James Annan said...

Arun,

Chaos on the molecular scale has no practical effect, if it did, you would not be able to use the Navier-Stokes equation, equations of state, etc.. Molecular-level perturbations are irrelevant.

I don't think it is quite that easy, but am not 100% sure. Note that the question has never been about the "practical effect" but the actual effect. If the momentum is changed, then this change has no obvious way of being eliminated from the system, even if the perturbation is only one molecule. Chaos merely means that different initial states evolve in different directions. The big sourcce of RPSnr's error, I think, is that he treats the perturbation as a entity separable from the underlying state, that has to grow or shrink all on its own. In some ways this view can help, but it's a mistake to think of this simplification of the real world as a complete description of it. Consider a double pendulum system, and a perturbation of it - this perturbation has no real physical meaning in terms of the original system, it is merely the difference between two states, and it evolves according to the different trajectories of the two states, rather than according to its own intrinsic nature.