Misunderstandings
One lesson of blogging (and life) is that little imprecisions of language can lead to big misunderstandings. My earlier post on the so called "butterfly effect" links to some other blogs disputing the same points, especially Colorado State Professor Roger Pielke Sr's climate blog. Pielke says in one post:
After sleeping on it, I now think I see what he means (not that I accept the way he says it). Net momentum of the atmosphere with respect to the Earth is zero. We know that, because the atmosphere stays attached! Consequently, any local momentum of a parcel of air is matched by equal and opposite momentum other places. Turn off the Sun and the various momenta become well mixed, driving the local momentum to zero everywhere. Net momentum doesn't change, but any give parcel of air exchanges momentum with other parcels, which, on average are opposite in direction (because the net momentum is zero!) and the opposite vectors tend to cancel.
Turbulent energy is composed of momentum! Since turbulent energy dissipates into heat, so will momentum. Turn the Sun off, even in a climate model, and watch the momentum go to zero after a period of time.That's a big red flag to any physicist. Momentum conservation is just about as sacred a principle as you can find in physics.
After sleeping on it, I now think I see what he means (not that I accept the way he says it). Net momentum of the atmosphere with respect to the Earth is zero. We know that, because the atmosphere stays attached! Consequently, any local momentum of a parcel of air is matched by equal and opposite momentum other places. Turn off the Sun and the various momenta become well mixed, driving the local momentum to zero everywhere. Net momentum doesn't change, but any give parcel of air exchanges momentum with other parcels, which, on average are opposite in direction (because the net momentum is zero!) and the opposite vectors tend to cancel.
CIP,
ReplyDeletewhen viewed on the global scale in that way, the atmosphere clearly has non-zero angular momentum wrt the earth. And angular momentum is generally considered to be conserved too...
Of course if we switch off the Sun, then the momentum is eventually dissipated by friction at the planet's surface (more strictly, transferred to the Earth itself). But models have friction in too! So I don't see how that particular line of argument can be considered as supporting Roger Pielke's argument at all. Indeed, it is hard to see how his belief in the supposed non-chaotic nature of the real world can be considered falsifiable, even in principle. Since this belief seems to be axiomatic to him, the output from any chaotic model only serves to reinforce his opinion that the models are all wrong...
James - His argument looks faith based to me. There seems every reason to think that the kinds of sensitive dependence Belette recently blogged is real rather than an artifiact of the models. On the other hand, in principle at least, shouldn't there be perturbations that *only* excite modes with non-growing Lyupanov exponents - or am I just confused?
ReplyDeleteYes, in principle one could construct a perturbation which projects only onto the shrinking space (I did mention this somewhere buried in the middle of my first comment but I don't blame you for not wading through it that carefully :-)). However, such a lucky projection won't happen by chance, and has probability zero for any sort of random perturbation.
ReplyDelete