There is no expirimental data to support this. It's not clear that a butterfly flapping its wings provides enough impact to change anything, and the "Butterfly Effect" is just a poetic term to describe the huge impact on a weather simulation leaving off a few decimal points off a figure had,which represents way more than a butterfly.
Anyway, there are man-made events that almost certainly would effect weather, like huge fires or nuclear bombs, so there would still be no Katrina.
Taking your pachinko example, something would still have to have enough force to make a difference on the movement of the balls. A butterfly flapping it's wings is possibly too small an event to do anything at all.
Nope,
I'm sorry. The size of the initial divergence doesn't matter - its only effect is the amount of time it takes for the system to fly out of whack.
The important bit is from "The above discussion strongly suggests..." down, the last couple of paragraphs or so. It works out, in essence, that for the model there (
a pendulum) the length of time you can reasonably predict its activity is proportionate to the logarithm of the error - ie, if you can predict the pendulum's motion for one hour with a single digit of precision in your initial model, it takes two digits to predict it for two hours, 3 for three, and so on - to predict it for three days requires that you get your initial model to within 0.0000000000000000000000000000000000000000000000000000000000000000000000001 of its real value.
So, to your original comment: no, the effect of a butterfly's wings flapping is not "too small". There is
no such thing as a too-small input in a chaotic system. Sure, in
Lorenz's original model-rerun that started the whole thing he lost the fourth significant digit, which in a global model is a lot more than one butterfly. But it took less than a (simulated) month for him to realize the model was running differently than the first time; if we assume the butterfly could contribute 1*10^-100 of error, that gives us... a little over eight years before the model becomes as noticeably broken. I'll repeat what I said at the beginning - the size of the initial difference is irrelevant. The only difference the size makes is how long it takes for the system to diverge.