State-of-the-Art Statistical Approaches for Estimating Flood Events

Reliable quantile estimates of annual peak flow discharges (APFDs) are needed for the design and operation of major hydraulic infrastructures and for more general flood risk management and planning. In the present study, linear higher order-moments (LH-moments) and nonparametric kernel functions were applied to APFDs at 18 stream gauge stations in Punjab, Pakistan. The main purpose of this study was to evaluate the impacts of different quantile estimation methods towards water resources management and engineering applications by means of comparing the state-of-the-art approaches and their quantile estimates calculated from LH-moments and nonparametric kernel functions. The LH-moments (η = 0, 1, 2) were calculated for the three best-fitted distributions, namely, generalized logistic (GLO), generalized extreme value (GEV), and generalized Pareto (GPA), and the performances of these distributions for each level of LH-moments (η = 0, 1, 2) were compared in terms of Anderson–Darling, Kolmogorov–Smirnov, and Cramér–Von Mises tests and LH-moment ratio diagrams. The findings indicated that GPA and GEV distributions were best fitted for most stations, followed by GLO distribution. The quantile estimates derived from LH-moments (η = 0, 1, 2) had a lower relative absolute error, particularly for higher return periods. However, the Gaussian kernel function provided a close estimate among nonparametric kernel functions for small return periods when compared to LH-moments (η = 0, 1, 2), thus highlighting the importance of using LH-moments (η = 0, 1, 2) and nonparametric kernel functions in water resources management and engineering projects.