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Hydrosystems engineers have been using the concept of the return period (or sometimes called recurrence interval) as a substitute for probability because it gives some physical interpretation to the probability. The return period for a given event is defined as the period of time on the long-term average at which a given event is equaled or exceeded. Hence, on average, an event with a 2-year return period will be equaled or exceeded once in 2 years. The relationship between the probability and return period is given by
in which xT is the value of the variate corresponding to a T-year return period. For example, if the probability that a flood will be equaled or exceeded in a single year is 0.1, that is, P (X > xT) = 0.1, the corresponding return period is 1/P (X > xT) = 1/0.1 = 10 years. Note that P (X > xT) must be the probability that the event is equaled or exceeded in any one year and is the same for each year regardless of the magnitudes that occurred in prior years. This is so because the events are independent, and the long-term probabilities are used without regard to the order in which they may occur. A common error or misconception is to assume, for example, that if the 100-year event occurs this year, it will not occur again for the next 100 years. In fact, it could occur again next year and then not be repeated for several hundred years. This misconception resulted in considerable public complaints when the Phoenix area experienced two 50-year and one 100-year floods in a span of 18 months in 1978-1979 and the Milwaukee area experienced 100-year floods in June 1997 and June 1998.
Hence it is more appropriate and less confusing to use the odds ratio; e. g., the 100-year event can be described as the value having 1-in-100 chance being exceeded in any one year (Stedinger et al., 1993). In the United States in recent years it has become common practice to refer to the 100-year flood as the 1 percent chance exceedance flood, and similar percent chance exceedance descriptions are used for other flood magnitudes (U. S. Army Corps of Engineers, 1996).
The most common time unit for return period is the year, although semiannual, monthly, or any other time period may be used. The time unit used to form the time series will be the unit assigned to the return period. Thus an annual series will have a return-period unit of years, and a monthly series will have return-period unit of months. However, one should be careful about compliance with the statistical independence assumption for the data series. Many geophysical data series exhibit serial correlation when the time interval is short, which can be dealt with properly only by time-series analysis procedures (Salas, 1993).
