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Rainfall

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Mefiante
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« Reply #15 on: 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.

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Rigil Kent
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« Reply #16 on: 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!  Cool Unfortunately the math as to why it should be so is beyond me. Lips Sealed

Rigil


« Last Edit: January 15, 2012, 20:29:40 PM by Rigil Kent » Logged
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« Reply #17 on: 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.
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Mefiante
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« Reply #18 on: 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.

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Rigil Kent
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« Reply #19 on: 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. Smiley

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« Reply #20 on: January 16, 2012, 01:30:50 AM »

I attended a lecture a few years back at my university by someone(cant remember who) from Weather SA. He pointed out that the 30% rain fall area they show on the news is not as random as most people think. That 30% means they have a 99% confidence based on the model that it would rain over 30% of the given area. But it is not random, because of the time window they give. He showed a simulation with a storm moving from right to left over the area. He said the models could predict that the storm would reach critical mass and start raining anytime in the next 10 hours. If it started to rain in the first hour or so the most right hand side of the given area would receive  rain whereas if it reached critical mass at 9 hours the most left hand side of the area would receive rain, based on the size and speed they know the storm would only last long enough to precipitate about 30% of the area.   
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