Probability
There is approximately a 63.4% chance of one or more 100-year floods occurring in any 100-year period, not a 100 percent chance. The probability Pe that one or more of a certain-size flood occurring during any period will exceed the 100-yr flood threshold can be expressed as
where T is the return period of a given storm threshold (e.g. 100-yr, 50-yr, 25-yr, and so forth), and n is the number of years. The exceedance probability Pe is also described as the natural, inherent, or hydrologic risk of failure. However, the expected value of the number of 100-year floods occurring in any 100-year period is 1.
Ten-year floods have a 10% chance of occurring in any given year (Pe =0.10); 500-year have a 0.2% chance of occurring in any given year (Pe =0.002); etc. The percent chance of an X-year flood occurring in a single year can be calculated by dividing 100 by X.
The field of extreme value theory was created to model rare events such as 100-year floods for the purposes of civil engineering. This theory is most commonly applied to the maximum or minimum observed stream flows of a given river. In desert areas where there are only ephemeral washes, this method is applied to the maximum observed rainfall over a given period of time (24-hours, 6-hours, or 3-hours). The extreme value analysis only considers the most extreme event observed in a given year. So, between the large spring runoff and a heavy summer rain storm, whichever resulted in more runoff would be considered the extreme event, while the smaller event would be ignored in the analysis (even though both may have been capable of causing terrible flooding in their own right).
Read more about this topic: 100-year Flood
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