Hello Mr. Yanez.

I am currently a AP Stats student at Cinco Ranch High School, and right now we’re studying probability. Given that statement and the subject of this e-mail you might be able to guess where this is headed.

Exactly what do rain percentages tell us? If there is a 40% chance of rain, does that mean that 40% of the viewing area will receive rain, or that there is a 40% chance that any given location will get rained on?

I asked my teacher if he had any issues with weather men and their probability of rain, and he said that he would like to call one up and ask them to clarify. I’m sort of taking the liberty for him.

Likewise, if there is a 20% chance of rain in the morning and a 20% chance of rain in the afternoon, does that mean the chance of rain the entire day (morning AND afternoon) would be 4%? (.2 x .2 = .04) Or am I over-complicating things?

Thanks for taking the time to read this, and keep up the good work!

~Scott

Hi Scott,

Honestly I hate using percentages in the forecast. If this were an exact science we wouldn’t need to, we would simply say it will rain here and be dry here. Of course we are still limited in what we know about the weather and forecasting so we use percentages to show how likely it is to rain where you live.

This is how I was taught to use probability of precipitation. If I give a 30% chance of rain for Houston I am saying there is a 3 in 10 chance you will get wet. The 30% does not express how much rain will fall or how strong the storms will be if you get them. I have to do that separately.

The impression sometimes is a 20% means it will be light rain or not rain at all and this is simply not true. A 20% chance means it much more likely to be dry but definitely not a guarantee. If there are higher rain chances north or south of Houston I will always make a separate map showing the differences. The National Weather Service in Georgia expressed the math like this:

**“The “Probability of Precipitation” (PoP) describes the chance of precipitation occurring at any point you select in the area. **

**PoP = C x A where “C” = the confidence that precipitation will occur somewhere in the forecast area, and where “A” = the percent of the area that will receive measurable precipitation, if it occurs at all. **

**So… if the forecaster knows precipitation is sure to occur ( confidence is 100% ), he/she is expressing how much of the area will receive measurable rain. ( PoP = “C” x “A” or “1” times “.4” which equals .4 or 40%.) **

**But, most of the time, the forecaster is expressing a combination of degree of confidence and areal coverage. If the forecaster is only 50% sure that precipitation will occur, and expects that, if it does occur, it will produce measurable rain over about 80 percent of the area, the PoP (chance of rain) is 40%. ( PoP = .5 x .8 which equals .4 or 40%. ) **

**In either event, the correct way to interpret the forecast is: there is a 40 percent chance that rain will occur at any given point in the area.”**

The last line is key. There is a four in ten chance you’ll get rain where you live.

I have heard other stations say 30% of the area, or there will be 30% coverage, of rain today. I think expressing the forecast like this is wrong. That forecast is basically stating 70% will be dry. What parts of the area will get rain and who will be dry? What happens if all of us get wet, doesn’t it make the forecast wrong? On a day when there is a 10% or 20% chance of rain and it doesn’t rain at all, it again makes the forecast wrong. Philosophically this explanation doesn’t work for me.

To answer your other question a 20% chance of rain in the morning and a 20% chance of rain at noon does not equal a 40% that day. For example, I make an hour by hour forecast that shows:

9am 20%

Noon 20%

5pm 20%

The chance of rain for the day is 20%.

But if I do this:

9am 20%

Noon 20%

5pm 60%

The chance of rain is 60% for the day, what I am saying is the chances to see early rain is very small but the evening looks like the time it would rain.

By the way, Frank Billingsley doesn’t like using percentages either. In fact, a few years back he got rid of using percentages past day three on the forecast. After hundreds of e-mails from people protesting, he put the percentages back on. People love seeing them even though not everyone knows what they mean.

I thought the first half of this was great. Very clear and helpful. But the second half…if there’s a 20% chance of rain for morning and another 20% for the rest of the day, the natural interpretation of that is two successive trials, each with a 20% probability of “success” (= rain). *IF* the two trials were statistically independent (unrealistic, but let’s go with that for now), the overall probability of at least one success in two trials would be 1 – (probability of no success) = 1 – (80%)*(80%) = 36%. So not exactly 40%, but Scott’s instincts were on the right track. If in fact the correct interpretation is 20% for the whole day, then I don’t know what 20% for the morning, or the afternoon, means.

Hi Kurt,

Good reasoning. When it comes to weather forecasting different times of the day are statistically independent. A normal summer is a good example of this. In the morning many days there will be light showers along the coast that almost never make it to the city. But I would say one or two out of ten days when there is rain on the coast there is also a brief shower in the city. So I’ll put a 20% chance of rain in Houston from 8-10am.

In the afternoon with a sea breeze pattern Houston will get rain 3 or 4 times in ten days. (Again this would be a “normal” sea breeze it can be more or less active.) So I’ll put a 30% or 40% chance of rain in the afternoon from 2pm to 7pm. I’m basically forecasting for two different weather patterns but they occur in the same day.

Good comment,

Anthony

Thanks for clarifying. So AM and PM *are* statistically independent. Surprising, but make sense now that I think about it more.

I see now I misread Scott’s original post. He was multiplying (.2 x .2 = .04). I thought he was adding (.2 + .2 = .4).

Thanks again. I learned quite a bit from this.

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