For independent repeated time blocks, an event with exceedance probability has mean waiting time blocks by the geometric distribution. The return period is a long-run average waiting time, not a deterministic recurrence interval. For annual exceedance events, it is measured in years.
A -year return level has annual exceedance probability under the assumed stationary model. It is the corresponding quantile of annual maxima. Daily exceedance probabilities must be converted to annual event probabilities before using the annual return period definition.
A return level plot shows estimated return levels against their return periods, often on a logarithmic horizontal axis. Confidence curves describe uncertainty in estimated return levels. They are not prediction bands for individual extreme observations, and uncertainty typically increases when extrapolating far beyond the observation window.
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The return period, also known as the recurrence interval, is a statistical measure used to describe the frequency at which an event of a certain magnitude is expected to occur within a specific time frame. It is commonly used in fields such as hydrology, meteorology, and risk assessment, particularly for events like floods, storms, earthquakes, and other natural phenomena. The return period is typically expressed in years and calculated using historical data.