[wxqc] Rain Forecast

[Evan Bookbinder]

Victor,

In terms of the NWS, the zone forecasts imply the probability that 0.01" 
(measurable) precipitation will occur in a 12 hour time frame covering 
that period (today, tonight, etc...). That time frame is understood to 
be 12Z to 00Z and 00Z to 12Z.

With respect to the graphical forecasts used in the link below, those 
are 6 hourly pops covering time periods 00Z to 06Z, 06Z-12Z, 12Z-18Z, 
and 18Z-00Z. You'll notice the numbers remain constant in those 6 hour 
blocks. Again, the forecast is the chance that 0.01" (measurable) 
precipitation will be observed at that location in that 6 hour window.

With respect to your calculations below, this is incorrect. This is a 
matter of statistics equations (which I unfortunately don not have handy 
at the moment). You're assuming the events are cumulative, which they 
are not. Each 6 hour window is mutually exclusive from other events. In 
other words, the chance of rain in a 24 hour or 48 hour period is not 
the highest 6-hour number, not a sum of 6 hour numbers, nor an average 
of them. I wish I had my statistics book to reference the appropriate 
means to calculate what you're after, but I can say with 100% certainty 
that the approach below is not germane to the data provided.

Hope this helps,
Evan




Victor Engel wrote:
> I was having a conversation with someone recently about rain 
> forecasts. Something that people (myself included) seem to be confused 
> about is the probability of rain. What is the probability actually 
> supposed to be measuring?
>
> I did a lot of searching around the NOAA website, and it looks like 
> their numbers are not entered by computer, but are entered by people. 
> The numbers seem to be forecast probabilities for the covered time 
> periods. The time periods I looked at seemed to be three hours. This 
> seems to be confirmed by the chart given at the following URL (I 
> really like this chart, by the way):
>
> http://tinyurl.com/jvf7v
>
> I decided to take the data from this chart and compute 24 hour 
> probabilities as well as probabilities over longer periods, let's call 
> the periods UNTIL X, where X is some future time.
>
> If the data points represent probabilities that it will rain sometime 
> in the subsequent three hour period, then the probability that it will 
> rain in the subsequent 24 hour period is simple to derive.
>
> Let P3(i) be the probability of rain at sample i (a 3 hour period).
> P3(i+1) is the probability of rain for the following 3 hour period).
>
> P3 is a number from 0 to 1 where 0 is 0% chance of rain, and 1 is 100% 
> chance of rain.
>
> Then P24(i), the probability of rain for the 24 hour period, will be:
>
> 1 - (product of (1-P3(i)) for i from 1 to 8.
>
> For example, suppose the probabilities of rain for midnight, 3 am, 
> 6am, 9am, noon, 3pm, 6pm, 9pm are:
>
> 0.1, 0.1, 0.2, 0.2, 0.3, 0.1, 0.1, 0.1, then the probability that it 
> will rain sometime during the whole day is:
>
> 1 - (0.9 * 0.9 * 0.8 * 0.8 * 0.7 * 0.9 * 0.9 * 0.9) = 0.735 or about a 
> 74% chance of rain.
>
> Anyway, in the conversation I had, the person mentioned that it looks 
> like we'll be without rain until Monday. The link above, run early 
> this morning, gave probabilities of:
>
> Date/Time Probability
> 9/14 07:00 0.05
> 9/15 07:00 0.10
> 9/17 13:00 0.20
> 9/18 07:00 0.50
> 9/18 19:00 0.30
> 9/19 07:00 0.20
> 9/20 07:00 0.10
>
> Using the above calculations, I get the following probabilities for 
> the 24 hour periods following those same times:
>
> 9/14 07:00 0.34
> 9/15 07:00 0.57
> 9/17 13:00 0.93
> 9/18 07:00 0.98
> 9/18 19:00 0.90
> 9/19 07:00 0.83
> 9/20 07:00 ----
>
> The last line is blank because the projection does not go that far. 
> Now I show the probabilities that it will rain sometime BY the time 
> listed (these times are 3 hours later, because the times in the 
> numbers above are for subsequent periods).
>
> 9/14 10:00 0.05
> 9/15 10:00 0.40
> 9/17 13:00 0.92
> 9/18 07:00 0.99
> 9/18 19:00 1.00
> 9/19 07:00 1.00
> 9/20 07:00 1.00
>
> In other words, given the numbers on the site, it's a virtual 
> certainty that it will rain by 7PM on Monday.
>
> This analysis is very sensitive to error, especially at the low end. 
> Suppose, for example, I change all the 5% probabilities to 1% instead. 
> Then we get the following:
>
> 9/14 10:00 0.01
> 9/15 10:00 0.17
> 9/17 13:00 0.89
> 9/18 07:00 0.98
> 9/18 19:00 1.00
> 9/19 07:00 1.00
> 9/20 07:00 1.00
>
> Anyone see a problem in my analysis?
>
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