On the role of storm duration in the mapping of rainfall to flood return periods

While the correspondence of rainfall return period T(P) and flood return period T(Q) is at the heart of the design storm procedure, their relationship is still poorly understood. The purpose of this paper is to shed light on the controls on this relationship. To better understand the interplay of the controlling factors we assume a simplified world with block rainfall, constant runoff coefficient and linear catchment response. We use an analytical derived flood frequency approach in which, following design practise, T(P) is defined as the return period of the intensity-duration-frequency (IDF) curve given storm duration and depth. Results suggest that the main control on the mapping of rainfall to flood return periods is the ratio of storm duration and catchment response time, as would be expected. In the simple world assumed in this work, T(Q) is always smaller or equal than T(P) of the associated storm, i.e., T(Q)/T(P) <= 1. This is because of the difference in the selectiveness of the rectangular filters used to construct the IDF curves and the unit hydrograph (UH) together with the fact that different rectangular filters are used when evaluating the storm return periods. The critical storm duration that maximises T(Q)/T(P) is, in descending importance, a function of the catchment response time and the distribution of storm duration, while the maximum value of T(Q)/T(P) is mainly a function of the coefficient of variation of storm duration. The study provides the basis for future analyses, where more complex cases will be examined.