Timing of Floods a Matter of Percentages

The U. S. Army Corps of Engineers describes floods not in terms of their height but in terms of their statistically projected frequency.

A 10-year flood has a 10% chance of occurring every year. A 25-year flood has a 4% chance. A 50-year flood has a 2% chance. A 100-year flood has a 1% chance.

Ira Arzt, project manager for a study of the effects of a 100-year flood in the Los Angeles County Drainage Area, says the definition is frequently misunderstood.

For example, some think that the waters of a 100-year flood are twice as deep as a 50-year flood, or four times as deep as a 25-year flood. To predict depths of various floods, he said, the corps must use a sophisticated computer model of the area’s drainage patterns and historical rainfall and other climatological data.

The definition also does not mean that a 100-year flood has occurred in the past 100 years or will occur in the next 100.

“You can’t look at it in terms of a 100-year chunk,” said Carol Henderson, assistant project manager for the study. “In any given 100-year period, you might experience a 500-year flood. You can’t look at any particular 100-year period.

“People find just about every definition confusing. The corps has used several ways. You can say it has a .01 probability of happening.

Some, incorrectly, state that a 100-year flood is the worst flood that has a 100% chance of occurring in 100 years. Actually, the chance of a 100-year flood occurring in 100 years is not 100% or even close. It is 63%.

This result can be derived by using some simple probability theory. One starts by figuring out the probability of a 100-year flood not occurring in 100 years.

Since, by the corps’ definition, the probability that a 100-year flood will occur in any single year is .01, the probability that a 100-year flood will not occur in one year is .99.

The probability that a 100-year flood will not occur in two years is .99 x .99 = .9801. The probability for three years is .99 x .99 x .99 = .970299.

Continuing in this fashion, the probability of a 100-year storm not occurring in 100 years is .99 x .99 x . . . (100 times) . . . x .99 = .3660323.

So the probability of a 100-year flood occurring in 100 years is: 1 minus the probability of it not occurring, or 1 -- .366 = .633. Or 63%.

“The biggest question, the thing that I find is most often misunderstood,” said Henderson, “is that people think this is going to happen only once in 100 years, a logical-seeming conclusion. But it is not a specific date as to when a storm will occur. A 100-year flood could happen in any given flood season.

In fact, 100-year floods could hit two years running, but the chances are extremely small--one in 10,000.