# Why a 50% chance of rain usually means a 100% chance of confusion.

It’s one of the most misunderstood terms in all of weather, the chance of rain. You hear it and see it in just about every weather forecast nowadays, but few people understand exactly what it means. Whenever people hear the chance of rain, I find that every person interprets it slightly differently. So when we say there’s a 40% chance of rain some people think that’s means 40% of the area will see rain. Some people think it means it will rain 40% of the time. Some people just think it’s the odds of seeing rain. The 3rd option is closest to the truth, but it’s not the whole story.

### What it is supposed to mean:

You have to start with the real terminology which is Probability Of Precipitation or POPS for short. That’s what us weather geeks call it. In the purest meaning of the term “chance of rain” used by most forecasters and The National Weather Service.  It is a mathematical calculation. It’s an equation using the forecasted coverage of the rain multiplied by the confidence in the forecast.

Its CHANCE OF RAIN = COVERAGE x CONFIDENCE

So I say tonight in Charlotte there is a 50% chance of rain. I am 100% confidence that 50% of our area will see measurable rain of 0.01” or more. The amount isn’t factored in, but I’ll get to that later. So the equation looks like this.

### 50% (Coverage) x 100% (Confidence) = 50%

What if I think that 50% of our area will have rain, but I’m only 50% confident in that forecast?

### 50% (Coverage) x 50% (Confidence) = 25%

You can see here even though I think the same area will be covered I’m not as confident in the forecast.

There are times I am 100% confident in my forecast, but just 20% of the coverage area is expected to see rain. So even in this case the chance of rain is 20%. So only when I am 100% confident in my forecast does the rain chance equal the coverage of rain.

### Increasing the odds & how we really use POPS:

(Note this does reduce the coverage weight, and this is how we use POPS on TV at WCNC)

Now that you know where the chance comes from I should also tell you how we use them on TV. For our area, I often say there is a 20% chance of rain and that means for any given point on the map. So if you stay in one spot all day your chance of rain remains 20%. The problem is people rarely stay in one spot on the map all day. So if you travel from home to work, school, the gym, the park, the grocery story or anywhere else you will be increased your chance of seeing rain. It’s like buying more raffle tickets each one you buy increases your chances of winning. For our purposes and as an example we will use a point on the map within 10 miles. So for every 10 miles you travel you will increase your odds of seeing rain by multiplying the chance of rain at each point.

Below you see a simple grid. If you travel from point A, to point B then to point C you will increase your rain chances. You multiply each locations chance. So for every point you cross you have increased your chance of rain by 4%

# 20% (Chance) X 20% (Chance) = 4%

After crossing 3 points, your total chance of rain now is 32%. Each point increases your chances by 4% that would be 12% added to the 20% for a total of 32%.

### Chance doesn’t equal intensity or amounts:

So can you have flooding if you only have a 20% chance of rain? Yes! The chance of rain is just that, the chance of seeing measurable rainfall which is 0.01” or more. There is nothing calculated into the chance of rain for how fast it falls or for how long. So yes if you are the 20% that get rain it most certainly could be a flash flood, especially in summer. Then again, the chance of rain can be 100% and it could just be a few hours of drizzle everywhere. Also just because it’s raining where you are, doesn’t mean that chance of rain should be 100%.

### So how do we use it on TV?

For the most part, we use the chance of rain as the odds of seeing rain during the forecasted times periods throughout the day at any given point on the map. For the most part, I use the chance of rain as my confidence in the possibility of rain. It is a safe bet to just use it as a scale. The higher the number, the better the chance is you will see rain on that day. Hope that helps clear it up the confusion to maybe about let’s say 40%. 🙂

### Update and Feedback:

Let me know how you interpret the chance of rain below in the comments. Maybe we can come sup with a unified way that works for everyone. Would a 1-10 rain factor scale work better? Not sure but I am open to the discussion.

• wxbrad

Clarified the “increasing the odds” section for who we use POPS primarily as a confidence tool on TV.

• fribster

Interesting. Thanks Brad. I had always interpreted it as the chance that anyone will see rain that day. Given the dual factors, maybe simply breaking out the two percentages would be beneficial for people trying to decide what to do on any given day. In other words, you could just say: I’m 50% confident that 50% of the viewing area will see rain today. Or, I’m 100% confident that at least 20% of the viewing area will see a storm between 5 and 8 tonight (which would seem to be the typical case in Charlotte in August). People have a really hard time interpreting probability, so maybe this wouldn’t help in the end, but I know I’d find it helpful.

• wxbrad

That is a good idea and sometimes verbally I do try to do that on TV. Maybe I can create a graphic to help show this better and show it daily.

• Jason Overcash

This is very helpful. I have interpreted percentages leaning more towards the coverage side. So, 20% always meant “isolated.” But, I see where the confidence factor is important, too, especially with large-scale events. Maybe your graphic could use the descriptions (isolated, scattered, etc…) with the confidence percentage. Sorta like what you do with the severe weather types (wind, hail, tornado)….

• wxbrad

This is close to what I would like to do. Maybe a 1-10 scale for sure, the only issue with isolated, scattered, widespread is that this too is interpreted completely different by different people.

• Brittney McNamara

I always assumed it meant probability. For example, if there was a 20% chance of rain the Charlotte area, then some part of the area had a 20% chance of rain. Appreciate the explanation, I had no idea what it actually meant.

• sos

“100% confidence in 50% coverage” and “50% confidence in 100% coverage” have the same numerical result in this scheme, but they are very different intents and different meanings, which get clouded by the resulting “50% chance” number.

• wxbrad

That is precisely why so many people don;t get what POPS really are and hence why we stick with the confidence chance only on TV.

• aCogent1

My 80 year old mother wants to know chance of rain and the time frame. That’s it.
Me, too.

The flooding is a new aspect of climate change which will require a separate index, Probability of flooding, based upon recent history, soil composition, etc. will be most important, and reported in a 1-10 scale.

As long as you use the same formula, people will learn what it means.
Some people will never learn. For weather generally, the single % and a general time frame is all that is necessary.

Most helpful is the extended radar projections showing the approaching extent and density of rain coverage.

More locally, the intensity of rain should be separated, as up to x max per hour if potentially dangerous, as you have done.

Historically, the Piedmont pattern resembles that of distant summers (i.e., 50’s 60’s) with summertime afternoon rains. The frequency and intensity are different.

If people are personally concerned, they should check the radar online.
If they can’t do that, then, as old timers, your warnings should be sufficient.

• aCogent1

Ok, ok, ok…If you must…Use a logarithmic scale which denotes volume of rain.
Think Richter.

• aCogent1

How about a bar graph for each town? One bar per town.
Different colors for each type of factor.

A different one for time of day.
Pretty simple after you convert your data.
Should I copyright the idea?

• Richard Clark

I like it when duration and intensity are included in the forecast as well because that often is a key factor in how any rain would affect me. For example, during the heat of summer in several areas of Florida that I’ve been to, it’s common for brief afternoon showers to occur. Some forecasts (particularly big name sites that I’d guess are using mostly automated forecasts), will show a good chance of rain every day during those conditions. That’s useless because what I really want to know is whether it will be “the usual” where I can just pop inside for an hour mid-afternoon to avoid it or if it will be an all-day rain that might ruin any outdoor plans. Good local forecasters will add a comment like “brief afternoon showers” to help the public understand what to expect, but all to often it’s just “50% chance of rain” which isn’t helpful when planning my day’s activities.

More locally, knowing the expected duration and intensity is also very important — often more so than knowing a percentage chance. I might decide to go ahead and spread lawn fertilizer if there is a 100% chance of an all-day light sprinkling, but will hold off if there is a 20% chance of a brief downpour that could wash it all away. So percentage chance by itself doesn’t tell the whole story.

• Ben

NOAA gives the expected rainfall and percent chance of rain on the hourly weather graph page. It helps a lot when planning a day.

• rkorm

It was actually explained to me in school that if there is a 20% chance of rain, it meant that 20 out of 100 days with similar conditions it would rain, 40% is 40 days out of 100 it would rain, and so on.

• rkorm

Also, I find the “confidence” factor to be a bit subjective to the forcaster.

• wxbrad

POPS have never been used by climatological determinations it’s always been based on a forecast driven basis. Using that technique would always be changing since every time those conditions occur again it would change the percentage. Confidence or lack thereof is always the prime factor is forecasting weather. Pretty much all forecaster use an uncertainty level that’s. Uncertainty is a major part of forecasting it’s ways important to express that uncertainly in your forecast.

• Harold Brooks

The NWS definition is that PoP is “the likelihood of occurrence (expressed as a percent) of a precipitation event at any given point in the forecast area.” (Precipitation event means >0.01 inches during the specified period). Schaefer and Livingston showed in a 1990 paper that this is mathematically equivalent to the expected areal coverage of precipitation in the forecast area. See http://bit.ly/157JmUN

• J Groton

Makes sense, but how do you explain the hourly PoP listed on websites like the Weather Channel. Often they’ll list a daily PoP of 40%, then list hourly PoPs of 40%. That doesn’t make sense. If we assumed that there was a 40% chance of rain occurring within a given hour for just four consecutive hours, the PoP for the day would be 87%: P(not observing rain within an hour =) 0.6). For four hours the probability of not observing rain is 0.6 x 0.6 x 0.6 x 0.6 = .1296, so the P(observing rain in a least one of those hours) = 1-.1296 = .8704 (87%).