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

Abstract. 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.