returnperiod

Return period, in hydrology and risk assessment, is the average interval between events of a given severity or greater. It is the reciprocal of the annual exceedance probability. If the probability that a given year experiences a flood of at least magnitude x is p = P(X > x), then the return period T = 1/p. Thus a flood with T = 100 years has a 1% chance of being exceeded in any given year. The phrase often yields a long-run average; it does not guarantee that such an event will occur once every T years, nor that it cannot occur in consecutive years.

To estimate T, analysts fit a statistical distribution to an annual series of extremes (annual maximum or annual flood peaks) and compute p(x) for the threshold of interest. Common approaches include parametric extreme value distributions, such as the Gumbel, or the Generalized Extreme Value family, and nonparametric methods. Once p is known, T = 1/p.

Limitations include sensitivity to model choice and the assumption of stationarity (unchanging climate). Under non-stationary conditions, such as climate change, return periods may evolve over time, and it may be more appropriate to use time-varying or nonstationary models. Also, the return period is a long-run average and should not be interpreted as a precise forecast for any specific year.

Applications: informing design criteria for dams and drainage systems, setting flood risk thresholds, and guiding insurance and land-use planning. Related concepts include recurrence interval and exceedance probability.