Predictability; Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas? This was the question proposed by Dr. Edward Lorenz at the 135th Meeting of the American Association for the Advancement of Science in 1972. Dr. Lorenz can be stated as one of the pioneers of modern day Meteorology, and laid the foundations for equations in weather prediction. He went on to research on whether the behavior of atmosphere is “unstable” with respect to small perturbations in amplitudes when it comes to long term weather predictions.
In his other seminal work, “On the Prevalence ofAperiodicity in Simple Systems”,
Lorenz states that weather predictions can be likened to a set of non-linear
differential equations, whose solutions are heavily governed by the initial
values. He states that periodic solutions would be naïve in weather
forecasting, since if there were indeed a periodicity, the statistical
prediction would be a trivial one.
It turns out that Lorenz started out with solving a set of
12 differential equations and stumbled upon the aperiodicity in the solutions
with minor changes to input conditions. He noticed that re-solving the
equations with small differences in the initial values resulted in vastly
different outputs over a period of time. To quote Lorenz, “These perturbations
were amplified quasi-exponentially, doubling in about four simulated days, so
that after two months the solutions were going their separate ways”. Meaning,
the instability in the solution was “due to the lack of its periodicity”. Lorenz’s
work on non-periodic equations for weather predictions has been the founding
blocks for Chaos Theory and the “Butterfly Effect”
.
To be cont'd.
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