The thousand-year flood

A town is told its new defences will protect against a thousand-year flood. Two years later the town floods. The defences are called a failure and the engineers are blamed.

The phrase is the problem. A thousand-year flood does not mean a flood that happens once every thousand years. It means a flood with a one-in-a-thousand chance of occurring in any given year. Those are different statements, and only the second one is true.

The difference matters in two ways. First, a one-in-a-thousand event can happen twice in a decade without anything being wrong, in the same way that a coin can land heads twice in a row. Second, over a long period the chance accumulates. A house standing for seventy years faces roughly a seven per cent chance of seeing that flood at least once, which is low but is nothing like the impression the phrase gives.

There is a third difficulty that is more serious. The probability is estimated from past records, and in many places the past is no longer a good guide. If rainfall patterns are changing, a flood calculated as one-in-a-thousand from a hundred years of data may now be one-in-two-hundred, and the label on the defences will not have been updated.

Several agencies have begun replacing the phrase with a plain annual percentage, for a simple reason: a one-in-a-thousand chance per year is harder to misread than a thousand-year flood.