Probabilistic model for the estimation of t-year flow duration curves

A flow duration curve (FDC) is the relationship between any given discharge value and the percentage of time that this discharge is exceeded. It represents the relationship between magnitude and frequency of streamflow discharges. In this paper, a new methodology for the evaluation of the flow duration curve with assigned return period T is proposed. The procedure is based on the use of distributions bounded by the interval 0 to 1 and exploits the properties of the beta and complementary beta (CB) distributions. The proposed model, called "EtaBeta," accounts for the interannual variability of the FDC using the distributions of annual minimum daily flow and total annual flow. The intra-annual variability is described by the CB distribution, which (like the beta distribution) has two parameters that characterize the shape of the distribution and in particular of its tails. The model is applied to basins of southern Italy characterized by strong seasonality and highly variable discharge. The results show good performance in terms of the model's ability to represent the analyzed flow duration curves of discharge data even in low-flow conditions. The EtaBeta model also offers interesting possibilities for use in regional analysis.