Analysis of the relationships between flood peaks and flood volumes based on crossing properties of river flow processes

Abstract

A stochastic approach is developed for the determination of the reduction ratio between the annual maximum flow averaged over a consecutive D hour period and the annual maximum of peak instantaneous flow with the same frequency of occurrence. Initially, crossing properties of the integrated flow process are related to those of the instantaneous flows, using a Gaussian hypothesis. The scale of fluctuation of the river flow process is the key parameter which governs the theoretical reduction function. Application is made to numerous historical series from Italy. To facilitate the applicability of the model, a method of calibration based on currently available hydrometric information is proposed. Quantiles of flood volumes are obtained from the theoretical reduction function. It is verified that the reduction ratio is independent of the return period and appears to be insensitive to the underlying distributions of the component processes. The non‐Gaussian case and scaling properties are discussed.