Rainfall

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 Mefiante (January 15, 2012, 17:00:42 PM):
Take a simple shape like a square or a circle. If the chances of rain are, say, 30% then 30% of that area are shaded blue and the remainder red. Pick another simple shape to represent the blue area. Pin your drawing to a dartboard. Put on a blindfold and throw a dart at your drawing. Assuming your dart hits anywhere within the total area, what is the probability that you hit blue?

There is, of course, a small residual possibility that there is no rain anywhere within A during T, but if the Weather Bureau cites a chance of 20% or more, I wouldn’t put any money on it not raining anywhere over the relevant area and period. That is the nature of probabilities.

'Luthon64
 Rigil Kent (January 15, 2012, 19:53:24 PM):
I've checked this in a simulation - attached, hope it opens - and it turns out that if the probability of rain at each point in the forcast area is equal to P, then the percentage of points that experienced rain after the simulation is also jolly close to P! 8) Unfortunately the math as to why it should be so is beyond me. :-X

Rigil

 Tweefo (January 15, 2012, 20:06:15 PM):
This is short term forecast. My original stance was that this was supposed to a a El Nina year but as you can see on my graph this (here in M'burg at least) is definitely not the case.

I became very skeptical about the SA Weather when they forecast a 80% chance of heavy falls and there was not even a cloud in the sky on the day. I was still farming then and we needed the rain.
 Mefiante (January 15, 2012, 20:17:20 PM):
Good job Rigil (you star), but does it convince you that the two views are equivalent? More importantly, has it refined your understanding of what those rain probabilities mean?

The maths, as in most real-world problems, go back to calculus: Consider an area A and shrink it progressively so that it gets closer and closer to zero without ever quite getting there. The assumption is that a sub-area is representative of the whole. (Meanwhile, forget that the process is an idealisation!)

Tweefo, long-term weather prediction is, with today’s technology, a pipe-dream. Meteorological models are continuously being refined with advances in mathematics, computation and empirical understanding. It’s not an easy problem.

'Luthon64
 Rigil Kent (January 15, 2012, 20:25:41 PM):
.. does it convince you that the two views are equivalent? More importantly, has it refined your understanding of what those rain probabilities mean?
Yes and yes. :)

Rigil