I'm based in Boulder, and it's flooding. Luckily, we're all fine here.

Flooding is kind of a weird natural disaster. First: It doesn't feel very threatening: It's just raining outside... *a lot*. But it does post some serious risks and deserves to be taken seriously.

### 100 year floods (Should be called: **the 1% flood**)

When engineers discuss risk analysis, we like to rank things according to their return periods (i.e., how long is our design really relevant for). The common design parameter is the **100-year flood**, which has an unfortunate name because people assume the 100-year flood happens roughly every 100 years. This leads to statements like "The last 100 year flood was in 1894, so we're 19 years overdue for another one."

Really, a better name for the 100-year flood would be the 1% flood, in that each year there's a 1% chance of having the "100-year flood". Ranking the floods assumes that year to year is uncorrelated, so each year it's like rolling the dice and you have a 1/100 chance of getting a flood that big.

### Throwing Dice

If you have a 6 sided die, and you roll it 6 times, you're not guaranteed to get a 6 any of those times. In fact, you've only got a 66.5% chance of getting a 6 in those 6 rolls (1-(5/6)^6). These arn't bad odds... but it's not a "sure thing" either.

If you wanted a 90% chance of rolling at least one 6, you should roll the die 13 times. If to you a "sure thing" was a 99% chance: you'd have to roll the dice 26 times, and even then, you have a 1% chance of still not rolling a 6 in 26 rolls.

But, you still have a 1/6 chance to roll a 6. Every time. If you got 100 people in a room, and had them roll dice and count how many throws it took them to get a 6, your average would be 6 throws.

### Back to floods

So back to the floods. In any given 100-years, it's really only 63% (1-(99/100)^100) likely that you'll experience a 100-year flood. That said, it is also 0.01% possible to experience **two** 100-year floods in 100 years. This is why calling it "**The 100-year flood**" is a horrible idea.

It's been 119 years since the last "100-year flood" in Boulder. The chances of *not* having a "100-year" flood in a 120-year period are 30%, which isn't really that weird at all. And we are still under the assumption that next year, the chances of having a 100-year flood are 1/100. Next year doesn't know about the past 120 years.

### But wait: it gets worse...

See my next post about how to calculate the 100-year flood and some more problems with it's name. These include problems like small data sets and non-stationarity, but also different ways of calculating the 100 year flood yield different results.

Pingback: How to calculate the 100-year flood | Mike Soltys()