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Climate Forecast vs Weather Forecast
A weather forecast for the next several days is analogous to an individual
path through the matrix. Each horizontal line of pegs might represent a successive day.
If we know from which position (A, B, C, D, or E) the ball started (i.e., if
we know the initial conditions for the differential equations describing the atmospheric motions),
we will know reasonably well the first part of the trajectory through the matrix
but less and less as the ball moves downward. After the ball passes several pegs,
our predictability of the actual path is completely lost (the equations are nonlinear and dissipative and
include some approximations).
A climate forecast is analogous to the distribution of balls at the bottom of the matrix. If we know the positions of the pegs, the equations that describe (with some uncertainty at each bounce) the trajectory through the matrix, and the number of times each initial condition is used, we can estimate the distribution at the bottom. In this case, an individual trajectory through the matrix does not represent a forecast of day-by-day actual weather, but rather a plausible sequence of daily weather consistent with the known positions of all the pegs.