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Below is the Dallas precipitation forecast I just got (requested from Google at 10am, Nov 29, 2019).

From this, what is the probability that a 10cm (diameter) cup placed in a Dallas park from 4:00pm will have some visible water in it at 4:10pm?

What about at 4:20pm?

I have never understood what the 61% in the chart really is forecasting and really want to know the probability of my getting hit by a liter of rain in a random 20 minute run...just asking two simpler questions here to work my way up.

Dallas Precipitation Forecast

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  • $\begingroup$ By the way, a different question is similar, but doesn't really help answer mine. earthscience.stackexchange.com/questions/4511/… $\endgroup$
    – bobuhito
    Nov 29 '19 at 16:42
  • $\begingroup$ Does this question help at all? earthscience.stackexchange.com/questions/17478/… $\endgroup$
    – Deditos
    Nov 29 '19 at 17:48
  • $\begingroup$ Yes, but that answer does not consider the time period. If I say 61% is the probability of my 10 cm cup getting at least a drop of rain in 10 minutes, my intuition tells me it should be at least a few percent higher in 20 minutes. Weather predictions must be assuming some integration time - I'd guess 60 minutes but can't find a reference on "weather.com" (the underlying forecast provider). By the way, this probability might go up slightly to 61.5% for a 20.3 cm cup (the official "rain gauge"), but I think that effect is ignorable. $\endgroup$
    – bobuhito
    Nov 29 '19 at 18:16
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    $\begingroup$ I am afraid is a case of using probability in ill defined / suggestive sense. I do have the same problem when reading "probability of a mechanical failure are...." and so on. It is rather a figure of confidence whatever determined. $\endgroup$
    – Alchimista
    Dec 5 '19 at 9:54
  • $\begingroup$ The forecast is for at least a 100 mile diameter area . So about 61% of the nearly 8000 sq miles will get some rain = roughly 3200 sq miles will not get rain. $\endgroup$
    – blacksmith37
    Dec 29 '19 at 18:34
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It is likely that the forecast is made using an ensemble of runs from a weather model. As weather is chaotic (deterministic, but heavily dependent on initial conditions), each run will show a different pattern of precipitation, and the probability is likely to be simply the proportion of model runs that exhibited precipitation in that location during that hour. Sometimes the pattern in each model will be very similar (e.g. a weather front going through) or they may be very different (AIUI convective rainfall, e.g. thunderstoms, are less predictable, so each run may have a broad pattern of isolated showers, but you will miss them in some runs but not in others).

Note that "location" will mean the grid box in the weather model (km^2?), it doesn't mean that it will rain everywhere in that grid box, and definitely not a cup. I used to play cricket quite regularly at a place with three cricket pitches all within sight of eachother. I can remember several occasions where it was raining on one pitch, but not another (play stopped on one pitch but carried on on the other).

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  • $\begingroup$ Very interest last paragraph. How far away were the three cricket pitches ? $\endgroup$
    – gansub
    Jan 2 '20 at 11:39
  • $\begingroup$ The edges two of the pitches were a 10m apart (but the middles of the pitches would have been about 100m apart, and that is where the umpires would have been who suspended play). The third was a little more distant. I suspect it was raining very slightly on one pitch and raining hard on the other. $\endgroup$
    – Dikran Marsupial
    Jan 2 '20 at 11:47
  • $\begingroup$ Could it be rain falling from two separate clouds on two different pitches ? $\endgroup$
    – gansub
    Jan 2 '20 at 12:28
  • $\begingroup$ Could be, IIRC it was a sharp shower rather than long lasting rain (possibly we just caught the edge of it?). $\endgroup$
    – Dikran Marsupial
    Jan 2 '20 at 12:33
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Given only this information and nothing else, there isn't really a definitively correct answer.

In reality, it depends on the nature of the precipitation. 61% could mean that there is a 61 percent chance of a thunderstorm between 4 and 5 PM, but since thunderstorms are short-lived, it might only be raining for 10 out of 60 minutes.

61% could also mean that an area of precipitation has a 61% chance of passing over Dallas. If that's the case, then it might be a 61% chance of rain for the entirety of the hour and a 39% chance of no rain at all.

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