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From General Discussions: ASK John: Lack of snow<blockquote><hr size=0><!-quote-!><font size=1>quote:</font>
By <u>John Dee</u> 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 "<!-/quote-!><hr size=0></blockquote>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.
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: <blockquote><hr size=0><!-quote-!><font size=1>quote:</font>
" 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.)"<!-/quote-!><hr size=0></blockquote>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.
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.<blockquote><hr size=0><!-quote-!><font size=1>quote:</font>
"Even though (classically speaking) each molecule is moving in a deterministic path, the motion of a collection of them is computationally and practically unpredictable."<!-/quote-!><hr size=0></blockquote>Thoughts? Comments?
By <u>John Dee</u> 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 "<!-/quote-!><hr size=0></blockquote>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.
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: <blockquote><hr size=0><!-quote-!><font size=1>quote:</font>
" 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.)"<!-/quote-!><hr size=0></blockquote>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.
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.<blockquote><hr size=0><!-quote-!><font size=1>quote:</font>
"Even though (classically speaking) each molecule is moving in a deterministic path, the motion of a collection of them is computationally and practically unpredictable."<!-/quote-!><hr size=0></blockquote>Thoughts? Comments?