Exploratory functional flood frequency analysis and outlier detection

The prevention of flood risks and the effective planning and management of water resources require river flows to be continuously measured and analyzed at a number of stations. For a given station, a hydrograph can be obtained as a graphical representation of the temporal variation of flow over a period of time. The information provided by the hydrograph is essential to determine the severity of extreme events and their frequencies. A flood hydrograph is commonly characterized by its peak, volume, and duration. Traditional hydrological frequency analysis (FA) approaches focused separately on each of these features in a univariate context. Recent multivariate approaches considered these features jointly in order to take into account their dependence structure. However, all these approaches are based on the analysis of a number of characteristics and do not make use of the full information content of the hydrograph. The objective of the present work is to propose a new framework for FA using the hydrographs as curves: functional data. In this context, the whole hydrograph is considered as one infinite-dimensional observation. This context allows us to provide more effective and efficient estimates of the risk associated with extreme events. The proposed approach contributes to addressing the problem of lack of data commonly encountered in hydrology by fully employing all the information contained in the hydrographs. A number of functional data analysis tools are introduced and adapted to flood FA with a focus on exploratory analysis as a first stage toward a complete functional flood FA. These methods, including data visualization, location and scale measures, principal component analysis, and outlier detection, are illustrated in a real-world flood analysis case study from the province of Quebec, Canada.