On the role of the runoff coefficient 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 examining in particular the effect of the variability of event runoff coefficients. A simplified world with block rainfall and linear catchment response is assumed and a derived flood frequency approach, both in analytical and Monte-Carlo modes, is used. The results indicate that T-Q can be much higher than T-P of the associated storm. The ratio T-Q/T-P depends on the average wetness of the system. In a dry system, T-Q can be of the order of hundreds of times of T-P. In contrast, in a wet system, the maximum flood return period is never more than a few times that of the corresponding storm. This is because a wet system cannot be much worse than it normally is. The presence of a threshold effect in runoff generation related to storm volume reduces the maximum ratio of T-Q/T-P since it decreases the randomness of the runoff coefficients and increases the probability to be in a wet situation. We also examine the relation between the return periods of the input and the output of the design storm procedure when using a pre-selected runoff coefficient and the question which runoff coefficients produce a flood return period equal to the rainfall return period. For the systems analysed here, this runoff coefficient is always larger than the median of the runoff coefficients that cause the maximum annual floods. It depends on the average wetness of the system and on the return period considered, and its variability is particularly high when a threshold effect in runoff generation is present.