Return Period As "expected Frequency"
The theoretical return period is the inverse of the probability that the event will be exceeded in any one year (or more accurately the inverse of the expected number of occurrences in a year). For example, a 10 year flood has a or 10% chance of being exceeded in any one year and a 50 year flood has a 0.02 or 2% chance of being exceeded in any one year.
This does not mean that a 100 year flood will happen regularly every 100 years, despite the connotations of the name "return period". In any given 100 year period, a 100 year event may occur once, twice, more, or not at all, and each outcome has a probability that can be computed as below.
Note also that the estimated return period below is a statistic: it is computed from a set of data (the observations), as distinct from the theoretical value in an idealized distribution. One does not actually know that a certain or greater magnitude happens with 1% probability, only that it has been observed exactly once in 100 years.
This distinction is significant because there are few observations of rare events: for instance if observations go back 400 years, the most extreme event (a 400 year event by the statistical definition) may later be classed, on longer observation, as a 200 year event (if a comparable event immediately occurs) or a 500 year event (if no comparable event occurs for a further 100 years).
Further, one cannot determine the size of a 1000 year event based on such records alone, but instead must use a statistical model to predict the magnitude of such an (unobserved) event. Even if the historic return interval is a lot less than 1000 years, if there are a number of less severe events of a similar nature recorded, the use of such a model is likely to provide useful information to help estimate the future return interval.
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