Umbrella Lottery

Flip a coin. There’s a 50% chance it will come up heads. Roll a six-sided die, and you have about a 33% chance of rolling a one or a two. Buy a lottery ticket and your odds of winning are astronomical, but at least it’s pretty straightforward. Check your weather forecast, and you may see something like this:

Mixed clouds and sun this morning. Scattered thunderstorms developing this afternoon. A few storms may be severe. High 93F. Winds W at 5 to 10 mph. Chance of rain 60%.

Does that mean you’re probably going to need an umbrella? Maybe not. Because if you stay roughly where you are all day long, the chance you’ll be rained on aren’t actually 60%. And that’s not your weatherman’s fault. While we tend to think meteorology is a fickle science, the real “problem” may just be how “chance of rain” is defined. It isn’t like flipping a coin.

The problem is that the weather forecast does not focus solely on the roughly four square foot area you’re standing in, but rather, a much larger area enclosing hundreds of square miles. And while it may rain in one part of that area, it does not necessarily rain throughout the whole area. So the formula for “chance of rain” — or, more accurately (and officially) “probability of precipitation” — has to account for this. So there’s a formula, as the National Weather Service explains: P = C x A.

P is, of course, the probability. C is the chance of rain anywhere in the area, and A is the percentage of area (within the forecast region) expected to get rain assuming that there’s rain in the region at all. So let’s say that there’s a storm coming up in the east, and the meteorologist determines that there’s an 80% chance that it’s going to hit his region. C would be .8. Let’s further assume that if the storm were to hit, it’d only hit the eastern half of the region — in that case, A would be .5. Multiply the two together, and last line of the forecast would read “chance of rain 40%.”

But that, in this case, isn’t really helpful. A resident on the far western reaches of the region would almost certainly not need an umbrella — the storm wouldn’t reach there. And if someone in the far eastern parts decided to roll the dice, so to speak, and leave the umbrella at home — 40% is less than half, after all! — well, he or she will likely be getting wet.

Forecast regions are designed to mitigate this but, as with most things, are by no means perfect. So if you have even a slight chance of rain, you may want to have an umbrella ready — just in case.

Bonus fact: NASA’s Vehicle Assembly Building, seen here, is a monstrous structure — one of the largest, by volume, in the world. (It has to be: that’s where they build spacecraft.) It’s so large that it when it gets humid outside, rain clouds form inside the building.

From the Archives: Watermelon Snow: Chance of it happening? Much less than 1%. But greater than zero!

Related: An ecosystem of your very own. Fits on your desk, too.