By FRNash/PHX, AZ on Wednesday, November 21, 2007 - 03:51 pm: Edit Post
From General Discussions: ASK John: Lack of snow
Somehow that statement triggered a rusty old corner of my grey matter — something I have been intermittently ruminating on for several years, it just never gelled 'til now.
quote:By John Dee on Wednesday, November 21, 2007 - 10:25 am:
"… The weather is never the same from year to year or even decade to decade. I don't know if it is fair to say it runs in true cycles all the time …"
Maybe the ultimate explanation for that is that weather (and climate) are perhaps the most commonly encountered examples of chaotic systems, (see: Chaos theory) in that they are:
This realization in fact clearly demonstrates the problem of developing long-term weather forecasts, even with the most sophisticated computer models, running on the latest and greatest platforms.
quote:"… nonlinear dynamical systems that may exhibit dynamics that are highly sensitive to initial conditions — popularly referred to as the butterfly effect) — so called because of the title of a paper given by Edward Lorenz in 1972 to the American Association for the Advancement of Science in Washington, D.C. entitled Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas? (The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale phenomena. Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different.)"
Sensitivity to initial conditions, you say?
What — and when — were the "initial conditions" for the great "mother of all weather forecasting models"? Somewhere along the continuum from the initial "big bang" to relatively recent human history?
Not possible! So by definition the initial conditions used represent an approximation of some intermediate conditions rather far along along that continuum.
So there we are, right smack dab in the middle of the "butterfly effect" as in the work of Edward Lorenz, who in 1961 was using a numerical computer model to rerun a weather prediction, when, as a shortcut on a number in the sequence, he entered the decimal .506 instead of entering the full .506127 the computer would hold. The result was a completely different weather scenario!
Good luck nailing those "initial conditions", even for the "Maka daidai shōgi" (摩訶大大将棋) equivalent "big mother" computer model!
Not to mention that what we are attempting to model here is largely a stochastic process — the behavior of pressure in a gas.
Thoughts? Comments?
quote:"Even though (classically speaking) each molecule is moving in a deterministic path, the motion of a collection of them is computationally and practically unpredictable."
By John Dee on Wednesday, November 21, 2007 - 06:57 pm: Edit Post
I guess my main comment to this would be if Lorenz's point was to show the vast complexities involved with trying to model the atmosphere looks like he did it.
Only one problem. How are we to believe what he illustrated in his computations would in fact actually happen in real life?
Sort of a bit of a paradox.
All I know is that improvements are always being made. I doubt that all the mysteries will be solved in our lifetime, our childrens lifetime or perhaps even their childrens lifetime. But I also believe in pressing forward no matter how hard the challenges are.
Technology moves so fast I choose to never say never. What do you think the experts of the day would have said if you told them that the all computing power used in the NASA moon launches would be dwarfed by a childs toy in 2007?
-John
