Probability of Rain in weather forecasts

[PhanthomJay]

TL;DR Summary

some say the percentage of probability of rain apply to a given point in the forecast area , while others say it applies to the percentage of the forecast area that will see rain. Are these two definitions actually the same from a mathematical perspective.?

I am trying to settle a debate over two definitions of the 'probability of rain' in a weather forecast area.

Definition 1 states that for example there is a 50% averaged probability of rain at some point in the forecast area over a given duration of time, that is, there is a 50-50 chance that I will get wet at my particular location in that area.

Definition 2 says that the 50% probability of rain implies that likely 50% of the forecast area will see some rain, and 50% of that area will not.

But here is my question: Others say that both definitions are the same. From a mathematical perspective , not a meteorological perspective, does the 50% probability of rain falling on my head, versus rain falling over 50% of the forecast area, mean the same thing?

Thanks.

 

[berkeman]

(Driving home with the family down I-5 in NorCal from our annual camping trip in Modoc National Forest in the late Spring / early Summer, I got pulled over for speeding by a CHP officer):

Officer: Do you know how fast you were going sir?

Me: Yes sir, sorry, I was doing more like the car speed limit instead of the trailer speed limit (I was pulling an enclosed trailer).

Officer: Well, I clocked you at 77mph, which is well over the car speed limit and way over the trailer speed limit.

Me: Yes sir, sorry about that. I just wanted to get the kids and dog home a little quicker, it's a 5-hour drive for us.

Officer: Where are you coming from?

Me: We were camping in Modoc National Forest for the past few days, heading home to the East Bay Area. The weather forecast was a 50% chance of rain, but it rained half of each day, so the family was done with it. They aren't used to camping in the rain.

Officer: Yeah, who knew that a 50% chance of rain meant it would rain 50% of the time? (he rolled his eyes...)

 

[PhanthomJay]

Great story! 50% chance of rain translates to 100% when you are on vacation..

 

[berkeman]

Yeah, I'm used to spending lots of time in the rain in Modoc (deer hunting, 4-wheeling, etc.), but those times were alone or with my buddies. The family was not into it when the weather rolled in.

You ask a good question though -- I wonder what the formal definition of % probability of rain is. Have you found anything in your Google searching? Links to the 2 definitions you've found?

 

[PhanthomJay]

Yeah, I'm used to spending lots of time in the rain in Modoc (deer hunting, 4-wheeling, etc.), but those times were alone or with my buddies. The family was not into it when the weather rolled in.

You ask a good question though -- I wonder what the formal definition of % probability of rain is. Have you found anything in your Google searching? Links to the 2 definitions you've found?

The formal definition is the first, but the argument is that the second, although worded differently, means the same thing. So the question is that say over a 100 square mile forecast area with a 50-50 chance of rain, is it the same thing saying there is a 50-50 chance (while not on vacation!) that I'll get wet, and saying that 50 sq miles will see rain and 50 sq miles won't?

 

[FactChecker]

You have stated the problem very carefully. Yes, the two probabilities are the same. They both are about the coverage of the area over the given time interval. Mathematically, the point-by-point probability is the same as the percent coverage area.

 

[PhanthomJay]

You have stated the problem very carefully. Yes, the two probabilities are the same. They both are about the coverage of the area over the given time interval. Mathematically, the point-by-point probability is the same as the percent coverage area.

Thank you, I was sort of leaning that way also, but the second definition sort of says to me that there is a 100 percent chance that 50% of the area will see rain, and it's that 100% chance that bothers me.

 

[FactChecker]

Thank you, I was sort of leaning that way also, but the second definition sort of says to me that there is a 100 percent chance that 50% of the area will see rain, and it's that 100% chance that bothers me.

No. As you said, "likely 50%". That is not 100% that it will be 50%.
But now that you have pointed that out, there never is any chance that EXACTLY 50% will get rain, there will always be some difference from 50%. To be very precise, there should be some confidence interval on how close the coverage will be to 50%. But that would be way too specific for the current accuracy of weather forecasting.

 

[PhanthomJay]

No. As you said, "likely 50%". That is not 100% that it will be 50%.
But now that you have pointed that out, there never is any chance that EXACTLY 50% will get rain, there will always be some difference from 50%. To be very precise, there should be some confidence interval on how close the coverage will be to 50%. But that would be way too specific for the current accuracy of weather forecasting.

I get your drift, thanks very much!

 

[256bits]

Thank you, I was sort of leaning that way also, but the second definition sort of says to me that there is a 100 percent chance that 50% of the area will see rain, and it's that 100% chance that bothers me.

Isn't that the same as at a point, the point has a 100% chance it will see 50% chance of rain?

 

[PhanthomJay]

Isn't that the same as at a point, the point has a 100% chance it will see 50% chance of rain?

Well let’s assume the 50% PoP forecast is for a county made up of 10 equally sized districts. Using the point definition, there is a 50% chance I will get wet whether I’m standing in district 1, or 2, or any other of the 10 districts. The area definition states that if one person is standing in each of the 10
districts, then 5 of them will get wet. In this latter scenario, I might be one of those 5, and I might not. So looks like the defs are the same, although there is a high likelihood that 5 persons will get wet, but a lower likelihood that I will be one of them. I leave it to the reader to interpret what this means.

 

[FactChecker]

I may have to correct my earlier answer.
Suppose that there is an area where rain completely covers the area 50% of the time and the other times there is no rain at all in that area. Then:
(Definition 1) The odds of a single person in that area getting wet are 50%
(Definition 2) There is never a case where 50% of the area gets rain.
So I would say that, mathematically, the definitions are not the same. I do not think that the weather forecasts fit this scenario, but the mathematics is different in the two definitions.

 

[jim mcnamara]

Authoritative link for the US:
https://www.weather.gov/media/pah/WeatherEducation/pop.pdf

 

[anorlunda]

There's a third interpretation. Every place in the area will get rained on 50% of the time.

Some people want to know if they should wash their car, and not get water spots on it. Others want to know if there will be enough rain to irrigate their grass. Others want to know if their 1 hour wedding ceremony should be planned for outdoors or indoors. All of them want to see an easy to understand weather forecast. So how would you make it simple for them?

In parts of Florida, the minimum probability of rain is about 10% for every day of the year. If you are out on the water and can see long distances, you see rain showers far away, but you may be dry. If you see it but don't get wet, would you say that is a rainy day?

In other words, it is a psychology problem, not a weather forecaster problem.

 

[hutchphd]

What is the definition of "rain"? One single drop will be difficult to predict this way...there must be some minimum. Also there is an implied time interval (I seem to remember that it is 6hrs but am too lazy today to track it down.

OOPS APOLOGY: I really am lazy . I see @jim mcnamara has already pointed in the correct diection.

 

[PhanthomJay]

What is the definition of "rain"? One single drop will be difficult to predict this way...there must be some minimum. Also there is an implied time interval (I seem to remember that it is 6hrs but am too lazy today to track it down.

The minimum is 0.01 inch. Like a drop. Yes, Interval is usually over a 6 hour period.

 

[PhanthomJay]

Authoritative link for the US:
https://www.weather.gov/media/pah/WeatherEducation/pop.pdf

Thanks. I found a peer reviewed journal publication (20 years old) that begs to differ. In the summary section 4, they list three definitions of the PoP: the 'true' definition, the 'however' definition, and the 'futhermore, also' definition. I don't know if they all more or less say the same or different things. Personally, I like your link.

 

[DaveC426913]

I have to 'splain to my wife frequently, when she sees that the forecast said 75% and it didn't rain, she thinks the forecast was poor.

I try to tell her it surely rained most of the places around us, just not on us, so it wasn't a poor forecast; it was just not very granular.

 

[anorlunda]

Authoritative link for the US:
https://www.weather.gov/media/pah/WeatherEducation/pop.pdf

There's the authoritative answer from the forecaster's point of view. I think the more interesting question is from the consumer's point of view. What words would make it more meaningful to the consumer?

The phrase, "scattered showers" seems to cover it, but in today's world, the forecast is reduced to numbers which appear on the weather dashboard of your app.

 

[DaveC426913]

I use TWN (The Weather Network) radar on my phone. I can see rain fronts sweeping in in real time, and what areas exactly they will hit.

Naturally, this only works over short time periods, but still.

I can say: "rain will start here in 10 minutes and end in about an hour", or "rain will pass 5 miles North of us".

This has transformed the way I imagine local weather.