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With the impending landfall of Cyclone Yasi, we were pondering how much water would be dropped by storm after hearing them say there would be about a metre of rain falling.

Assuming that this is the amount of rain falling on one square metre, and is constant across the main storm, and that the storm is a regular circle of 500 kilometres diameter, we arrived at:

3.1415 * 250 000 * 250 000 = 196 343 750 000     cubic meters
                           = 196 343 750 000 000 litres
                           = 196 344             gigalitres

By comparison - we have a reservoir which holds about 20 gigalitres.

Even if we assumed a constant falloff from the centre to the edge - we would still get 49 086 gigalitres.

We then figured out how much water was dropped in QLD in December (209 mm average over the month) which caused the severe floods. Queensland covers 1 852 642 square kilometres:

0.209 * 1 852 642 000 000 = 387 202 178 000     cubic meters
                          = 387 202 178 000 000 litres
                          = 387 202             gigalitres

Which means that this storm will dump a significant amount of water on a very small area...

Is there anything wrong with our assumptions - are these calculations right?

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This is not a question about physics – gigacyan Feb 2 '11 at 7:27
I have to a gree that this is not a question about physics, not even about meteorology in a broader sense, therefore I'm voting to close. – Tim van Beek Feb 2 '11 at 7:46
This is maybe not perfectly formulated, but this is a perfectly valid environmental physics. – mbq♦ Feb 2 '11 at 10:18
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I couldn't find an SE site for weather - and I'm asking if my assumptions are good, the maths is there to show where those assumptions come in... – HorusKol Feb 2 '11 at 10:39
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@gigacyan Read again -- the problem is not how to multiply few numbers, but if the result obtained with trivial approximation makes sense. – mbq♦ Feb 2 '11 at 10:42
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1 Answer

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I don't think there is anything wrong, but depending on the application you should consider studying a more complex dynamics. Consider how much water enters your system (per unit of time) and how much is drained.

You see that 1 meter of water in 1 square meter sounds a lot! but if it's in a period of one week then the water will probably drain or evaporate at almost the same rate. No flood in this case.

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I see - although, with that 200 mm over a month in December there was extensive flooding. I think this storm will be dropping most of that 1000 mm in only a few hours... – HorusKol Feb 2 '11 at 6:05
1 meter is a lot! Even when averaged for a week. Here in central Europe we would name some cm within a day a catastropy. – Georg Feb 2 '11 at 10:30

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