Estimating the flood frequency distribution at seasonal and annual time scales

Abstract. We propose an original approach to infer the flood frequency distribution at seasonal and annual time scale. Our purpose is to estimate the peak flow that is expected for an assigned return period T, independently of the season in which it occurs (i.e. annual flood frequency regime), as well as in different selected sub-yearly periods (i.e. seasonal flood frequency regime). While a huge literature exists on annual flood frequency analysis, few studies have focused on the estimation of seasonal flood frequencies despite the relevance of the issue, for instance when scheduling along the months of the year the construction phases of river engineering works directly interacting with the active river bed, like for instance dams. An approximate method for joint frequency analysis is presented here that guarantees consistency between fitted annual and seasonal distributions, i.e. the annual cumulative distribution is the product of the seasonal cumulative distribution functions, under the assumption of independence among floods in different seasons. In our method the parameters of the seasonal frequency distributions are fitted by maximising an objective function that accounts for the likelihoods of both seasonal and annual peaks. In contrast to previous studies, our procedure is conceived to allow the users to introduce subjective weights to the components of the objective function in order to emphasize the fitting of specific seasons or of the annual peak flow distribution. An application to the time series of the Blue Nile daily flows at the Sudan–Ethiopia border is presented.