Define return period, frequency and risk

Return period

The return period (recurrence interval) $T$ is the average number of years within which an event of a given magnitude is equalled or exceeded once. It is the reciprocal of the exceedance probability, $T=1/P$. A 100-year flood has a 1% chance of being equalled or exceeded in any year; it does not mean it occurs exactly once in 100 years.

Frequency

The frequency of an event is the number of times it occurs (or the probability that it occurs) in a given period. In flood analysis it is expressed as the annual exceedance probability $P=1/T$ (e.g. P = 0.02 for a 50-year flood), or as the number of occurrences per unit time.

Risk

The hydrologic risk $\bar R$ is the probability that an event of return period $T$ will occur at least once during the n-year life of a structure:

$$\bar R=1-\left(1-\frac1T\right)^{n}$$

For example, a 100-year flood has a risk of $1-(0.99)^{50}=0.395$ (39.5%) in a 50-year project life. The reliability is $1-\bar R$.