Return level ($z_T=F_{\mathrm{annual}}^{-1}(1-1/T)$)

A $T$-year return level has annual exceedance probability $1/T$ 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.