Technical NoteNote on a modified return period scale for upper-truncated unbounded flood distributions

- A new return period scale is proposed which includes a rightmost infinity tick-mark.
- Application is for right-unbounded unbounded distributions of flood maxima.
- Right-truncation avoids flood magnitudes tending to infinity in the limit.

Probability distributions unbounded to the right often give good fits to annual discharge maxima. However, all hydrological processes are in reality constrained by physical upper limits, though not necessarily well defined. A result of this contradiction is that for sufficiently small exceedance probabilities the unbounded distributions anticipate flood magnitudes which are impossibly large. This raises the question of whether displayed return period scales should, as is current practice, have some given number of years, such as 500 years, as the terminating rightmost tick-point. This carries the implication that the scale might be extended indefinitely to the right with a corresponding indefinite increase in flood magnitude. An alternative, suggested here, is to introduce a sufficiently high upper truncation point to the flood distribution and modify the return period scale accordingly. The rightmost tick-mark then becomes infinity, corresponding to the upper truncation point discharge. The truncation point is likely to be set as being above any physical upper bound and the return period scale will change only slightly over all practical return periods of operational interest. The rightmost infinity tick point is therefore proposed, not as an operational measure, but rather to signal in flood plots that the return period scale does not extend indefinitely to the right.