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What Makes Weather So Unpredictable? Why Is It So?
#1
The single most important factor in predictability of the weather is that the atmosphere is subject to nonlinear dynamics; it is technically a chaotic system, which means the outcome of the
forecast is very sensitive to the starting point. Imagine two people starting on a race that have very similar but not
exactly equal running ability - after a time, the faster one will have pulled away and left the other behind.

Weather systems never repeat exactly so even when the weather looks very similar to an event in the past, it will eventually
"run away" from what that past system did.

Mathematically, the atmosphere is
governed by a set of coupled nonlinear partial differential equations.
Tiny differences in the initial conditions can grow rapidly and cause two systems that look similar to follow paths that
eventually differ substantially.

Our knowledge of all the processes that contribute to the atmosphere is imperfectly expressed in the equations
as we currently know them, and our observations of the state of the atmosphere (and all the physical systems that affect the weather, like the oceans) are far from perfectly accurate and even
farther from being complete.

We have only limited observing capability over the oceans and many deserts. Some nations
are too poor to be able to support a system of weather observing.
Inaccuracies in our understanding of the initial state produce errors in the forecast that grow relatively rapidly,
eventually destroying any value the forecast might have.

Overall, we evaluate the "skill" of a forecasting system by its accuracy relative to some simple forecasting system - for example, we could forecast that today will be just exactly like yesterday.

We know that's wrong, of course, but it's not too bad short term at
times, and it's a standard of
comparison. Our current forecasts
exhibit skill over persistence (or
climatology) for roughly 7-10 days, at most. After that, we have no useful weather prediction skill.
When you see forecasts out to the range of 7-10 days, at the end of that range, the forecasts
have virtually no skill.

I hasten to add that weather forecasting is very different from climate forecasting, so please don't draw the conclusion
from what I've said that it's impossible to forecast climate change beyond 7-10 days.
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#2
hmmm... really educating.
It takes so long to learn simplicity.
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