<p>Having read through pieces of this thread, I'm not sure if this has been mentioned or not.  This is my understanding and I welcome any corrections.  The probability is based upon the recurrence of a rain event in the weather model with at least 0.01 inches precipitation in the grid cell (assuming you are using a derivative of the US National Weather Service).  The probability is calculated using many simulations of the same time period, each scenario using different parameters, referred to as an &quot;ensemble&quot;.  So, for example, if 75% of the ensemble members predict at least 0.01 inches of rain, the prediction will show a 75% PoP. There are other corrections involved but essentially the probability is calculated as the number of ensemble members that predict rain.  Here are related National Weather Service sites: <a href="https://www.weather.gov/ilx/about_models#:%7E:text=The%20fundamental%20difference%20between%20the,the%20CMCE%20is%2020%20solutions." rel="nofollow noreferrer">How do we use models?</a> ; <a href="https://www.weather.gov/ffc/pop" rel="nofollow noreferrer">FAQ</a>.</p>

CC BY-SA 4.0
2024-07-27T00:54:38.020Z
IMHO this is only one part of the truth, an additional explanation is presented here: [What does the "Probability of Precipitation" mean?](https://repository.library.noaa.gov/view/noaa/33782). On top of that [Wikipedia](https://en.wikipedia.org/wiki/Probability_of_precipitation#U.S._National_Weather_Service): The hourly PoP is the probability that more than 0.01 inches (0.25 mm) of precipitation would occur **if conditions like those in the given hour continued for twelve hours**. Not to mention commercial weather services and the [wet bias](https://en.wikipedia.org/wiki/Wet_bias).
klanomath
CC BY-SA 4.0
2024-07-26T23:10:54.570Z
2024-07-26T23:10:54.570Z
f.thorpe
<p>How should I think about the maths (and actual probabilities of rain), with weather forecasting POP (probability of precipitation)?</p>
<p>Taking for example <a href="https://www.theweathernetwork.com/en/city/ca/british-columbia/vancouver/hourly" rel="nofollow noreferrer">Weather Network for Vancouver</a></p>
<p><strong>Mostly I am curious about we should reason over <em>groups of time periods</em> (i.e. more than 1 hour, or more than 1 day if we were looking at day by day weather forecasts with POPs).</strong></p>
<p>Looking out the door, in Vancouver on July 21st, pretty consistent cloud cover, bright clouds (i.e. not over thick).  At a guess, might rain, but probably not (despite living in Rain City it's still July) =&gt; possibly-but-likely-not.</p>
<p>p.s. what the forecaster would count as rain - i.e. <em>any</em> precipitation, <em>some minimum amount in mm</em> is not something this question is concerned about.</p>
<p><a href="https://i.sstatic.net/65P8vciB.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/65P8vciB.png" alt="enter image description here" /></a></p>
<ul>
<li>1 pm - 30%</li>
<li>2 pm - 30%</li>
<li>3 pm - 30%</li>
<li>4 pm - 20%</li>
<li>5 pm - 20%</li>
<li>6 pm - 10%</li>
</ul>
<p>Now, those familiar with the basics of <em>uncorrelated</em> flip-the-coin type of probabilities would think that counter-intuitively to my gut feeling of might-but-probably not, this would be a high risk of rain:  .7 * .7 * .7 * .8 * .8 * .9 =&gt; 19% of not raining (it doesn't rain only if each hour misses the rain).</p>
<p>But rain is <em>not</em> an uncorrelated event hour to hour.  <em>If</em> it starts to rain at any time, there's a higher chance it will rain for a while.  These are not coin flips.</p>
<p>Still - incorrectly - thinking about coin tosses, it seems that a single say <em>&quot;3pm POP 30%, surrounded by 0% POPs&quot;</em> would look less menacing, but that might be the wrong way to think to about it.</p>
<p>Should I instead think of those groupings as &quot;a window of probability for a cluster of hours that gradually moves up and down&quot;.</p>
<p>I.e. <em>&quot;Overall there's a 30% chance it will rain from 1 to 3, but if doesn't happen then it slips to 20%&quot;</em>?  Then <em>&quot;by 6pm, only 10% chance it will rain&quot;</em>  (<em>looking at it from the 1pm POV, because by 5 pm I will have another hourly prediction and that 10% might have gone up or down.</em>)</p>
<p>That would sit much better with possibly-but-likely-not.</p>
<p><strong>How do weather forecasters intend us to interpret those <s>precise</s> numerical values?</strong></p>
<p>p.s. FWIW I ended up leaving my raincoat at home on the day I took as an example.  But after setting out for a walk through a residential area with no cover, I quickly retreated back when we got a few fat drops - I've had several experiences here with sudden spring/summer rains dumping massive amounts of water very quickly over 10-15 minutes and soaking you if have no cover and the weather felt a bit like that.</p>

CC BY-SA 4.0
2024-07-26T20:51:11.873Z
[Weather Network](https://www.theweathernetwork.com/en/city/ca/british-columbia/vancouver/hourly?wx_auto_reload=).  That said, I object to the migration of a question intended for outdoors recreation considerations to a more scientific forum where it will not reach its intended audience.  I was interested in rough-and-ready ways to reasons about those numbers (bit like if I was asking what windchill numbers are based on) for recreational purposes.  Looking at the comments so far - including mine - about what those numbers mean and you can see few seem to have a clue.
Italian Philosopher
CC BY-SA 4.0
2024-07-26T20:54:07.773Z
I have thought about asking questions here, about climate change, but this Q is **not** one I would have chosen to ask here, because of its intended use: to better plan trips.  Nor would I have phrased it the way I did.  Great Outdoors has a *weather* tag in any case.
Italian Philosopher
CC BY-SA 4.0
2024-07-27T02:50:42.617Z
Fun fact: [Vancouver (Weather Network)](https://www.theweathernetwork.com/en/city/ca/british-columbia/vancouver/hourly) vs. [Vancouver (Government of Canada)](https://weather.gc.ca/forecast/hourly/bc-74_metric_e.html) no rain in 24h (starting Friday, 8pm using the flip-the-coin method: 2.3% vs 100.0% ;-)
klanomath
<meteorology>
What's the mathematical idea behind weather forecasting POP (probability of precipitation) by slices of time?
Italian Philosopher
# What's the mathematical idea behind weather forecasting POP (probability of precipitation) by slices of time?

(Asked by: username_0 on 2024-07-25)

How should I think about the maths (and actual probabilities of rain), with weather forecasting POP (probability of precipitation)?

Taking for example [Weather Network for Vancouver](https://www.theweathernetwork.com/en/city/ca/british-columbia/vancouver/hourly)

**Mostly I am curious about we should reason over *groups of time periods* (i.e. more than 1 hour, or more than 1 day if we were looking at day by day weather forecasts with POPs).**

Looking out the door, in Vancouver on July 21st, pretty consistent cloud cover, bright clouds (i.e. not over thick). At a guess, might rain, but probably not (despite living in Rain City it's still July) => possibly-but-likely-not.

p.s. what the forecaster would count as rain - i.e. *any* precipitation, *some minimum amount in mm* is not something this question is concerned about.

[![enter image description here](https://i.sstatic.net/65P8vciB.png)](https://i.sstatic.net/65P8vciB.png)

* 1 pm - 30%
* 2 pm - 30%
* 3 pm - 30%
* 4 pm - 20%
* 5 pm - 20%
* 6 pm - 10%

Now, those familiar with the basics of *uncorrelated* flip-the-coin type of probabilities would think that counter-intuitively to my gut feeling of might-but-probably not, this would be a high risk of rain: .7 \* .7 \* .7 \* .8 \* .8 \* .9 => 19% of not raining (it doesn't rain only if each hour misses the rain).

But rain is *not* an uncorrelated event hour to hour. *If* it starts to rain at any time, there's a higher chance it will rain for a while. These are not coin flips.

Still - incorrectly - thinking about coin tosses, it seems that a single say *"3pm POP 30%, surrounded by 0% POPs"* would look less menacing, but that might be the wrong way to think to about it.

Should I instead think of those groupings as "a window of probability for a cluster of hours that gradually moves up and down".

I.e. *"Overall there's a 30% chance it will rain from 1 to 3, but if doesn't happen then it slips to 20%"*? Then *"by 6pm, only 10% chance it will rain"* (*looking at it from the 1pm POV, because by 5 pm I will have another hourly prediction and that 10% might have gone up or down.*)

That would sit much better with possibly-but-likely-not.

**How do weather forecasters intend us to interpret those ~~precise~~ numerical values?**

p.s. FWIW I ended up leaving my raincoat at home on the day I took as an example. But after setting out for a walk through a residential area with no cover, I quickly retreated back when we got a few fat drops - I've had several experiences here with sudden spring/summer rains dumping massive amounts of water very quickly over 10-15 minutes and soaking you if have no cover and the weather felt a bit like that.

**Tags:** meteorology

> **Comments:**
> **username_0**: [Weather Network](https://www.theweathernetwork.com/en/city/ca/british-columbia/vancouver/hourly?wx_auto_reload=).  That said, I object to the migration of a question intended for outdoors recreation considerations to a more scientific forum where it will not reach its intended audience.  I was interested in rough-and-ready ways to reasons about those numbers (bit like if I was asking what windchill numbers are based on) for recreational purposes.  Looking at the comments so far - including mine - about what those numbers mean and you can see few seem to have a clue.  
> **username_0**: I have thought about asking questions here, about climate change, but this Q is **not** one I would have chosen to ask here, because of its intended use: to better plan trips.  Nor would I have phrased it the way I did.  Great Outdoors has a *weather* tag in any case.  
> **username_1**: Fun fact: [Vancouver (Weather Network)](https://www.theweathernetwork.com/en/city/ca/british-columbia/vancouver/hourly) vs. [Vancouver (Government of Canada)](https://weather.gc.ca/forecast/hourly/bc-74_metric_e.html) no rain in 24h (starting Friday, 8pm using the flip-the-coin method: 2.3% vs 100.0% ;-)  

---

## 1 answers

### Answer by username_2 on 2024-07-26. Score: 0

Having read through pieces of this thread, I'm not sure if this has been mentioned or not. This is my understanding and I welcome any corrections. The probability is based upon the recurrence of a rain event in the weather model with at least 0.01 inches precipitation in the grid cell (assuming you are using a derivative of the US National Weather Service). The probability is calculated using many simulations of the same time period, each scenario using different parameters, referred to as an "ensemble". So, for example, if 75% of the ensemble members predict at least 0.01 inches of rain, the prediction will show a 75% PoP. There are other corrections involved but essentially the probability is calculated as the number of ensemble members that predict rain. Here are related National Weather Service sites: [How do we use models?](https://www.weather.gov/ilx/about_models#:%7E:text=The%20fundamental%20difference%20between%20the,the%20CMCE%20is%2020%20solutions.) ; [FAQ](https://www.weather.gov/ffc/pop).

> **Comments:**
> **username_1**: IMHO this is only one part of the truth, an additional explanation is presented here: [What does the "Probability of Precipitation" mean?](https://repository.library.noaa.gov/view/noaa/33782). On top of that [Wikipedia](https://en.wikipedia.org/wiki/Probability_of_precipitation#U.S._National_Weather_Service): The hourly PoP is the probability that more than 0.01 inches (0.25 mm) of precipitation would occur **if conditions like those in the given hour continued for twelve hours**. Not to mention commercial weather services and the [wet bias](https://en.wikipedia.org/wiki/Wet_bias).  

---

