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“A Once in a hundred year Flood”

# “A Once in a hundred year Flood”

Oh. That’s what it means. In “Floods: Recurrence intervals and 100-year floods,” the United States Geologic Survey says:
Possibly you can remember when a really big rain, be it from a hurricane or a large frontal system, hit your town. If flood conditions occurred because of the rain then you might have heard the radio or TV weatherman say something like “This storm has resulted in a 100-year flood on Soandso River, which crested at a stage of 20 feet.” Obviously, this means that the river reached a peak stage (height) that happens only once every 100 years, right? A hydrologist would answer “Well, not exactly.” Hydrologists don’t like to hear a term like “100-year flood” because, scientifically, it is a misinterpretation of terminology that leads to a misconception of what a 100-year flood really is.

Instead of the term “100-year flood” a hydrologist would rather describe this extreme hydrologic event as a flood having a 100-year recurrence interval. What this means is described in detail below, but a short explanation is that, according to historical data about rainfall and stream stage, the probability of Soandso River reaching a stage of 20 feet is once in 100 years. In other words, a flood of that magnitude has a 1 percent chance of happening in any year.
I made some graphs and tables of this 1% idea, using a binomial distribution from statistics. I used the binomial because we have a two-possibility probability — either it floods badly or it doesn’t — and because each year, I think, would be pretty much independent of any other. Maybe the binomial oversimplifies the idea, or is a misunderstanding of it, but it helps understanding, anyway.

The tables and graphs I made using an online Binomial Distribution Calculator.

If we consider 10 years at a 1% occurrence, we get the following.

If we consider 100 years at a 1% occurrence, we get the following.

So we have a greater likelihood of having a big flood than we might think. We could also think about how often floods happen using power law distributions and distributions with heavy tails. Remember also the Birthday Problem: the probability of two people having the same birthday is high, about 70%, with a group as small as 30, and is near certain with a group as small as 50.