.[1] 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.

Classification of streamflow hydrographs plays an important role in a large number of hydrological and hydraulic studies. For instance, it allows to make decisions regarding the implementation of hydraulic structures and to characterize different flood types leading to a better understanding of extreme flow behavior. The employed hydrograph classification methods are generally based on a finite number of hydrograph characteristics, and do not include all the available information contained in a discharge time series. In this paper, we adapt and apply two statistical techniques from the theory of functional data classification for the analysis of flood hydrographs. Functional classification directly employs all data of a discharge time series and thus contains all available information on shape, peak and timing. This potentially allows a better understanding and treatment of floods as well as other hydrological phenomena. The considered functional methodology is applied to streamflow datasets from the province of Quebec, Canada. We show that classes obtained using functional approaches have merit and can lead to better representation than those obtained using a multidimensional hierarchical classification method. The considered methodology has the advantage of using the entire information contained in the hydrograph, reducing hence the subjectivity that is inherent in multidimensional analysis on the type and number of characteristics to be used, and diminishing consequently the associated uncertainty. 12 13 14 15 16 17 18 19 20 Hierarchical classification. 33 ables (shape mean and shape variance) to classify flood hydrographs. This approach, although 55 simplistic, was useful for the classification of hydrographs for practical purposes in the Province 56 of Quebec, Canada. The hydrological community needs hydrograph classification methods that 57 can provide a full representation of the hydrograph and a full use of all the information contained 58 in it. 59 In terms of methods, hierarchical classification (HC) is the most commonly used technique 60 for hydrograph classification. Hannah et al. (2000) proposed a multidimensional technique to 61 classify diurnal discharge hydrographs from glacier basins separately according to their shape and 62 magnitude. Their procedure involves two separate classifications of the hydrographs that have 63 been combined. The aim of the first classification is to derive a set of distinct diurnal hydrograph 64 shape classes using the HC approach based on principal component analysis (PCA). The second 65 classification is based on four magnitude indices: the mean, minimum, maximum and variance 66 of monthly observations. This method was adapted by Harris et al. (2000) to riparian systems on 67 four British rivers, where flow regimes are defined by monthly mean flow series. Bower et al. 68 (2004) used this same method to develop a regime classification to identify spatial and temporal 69 patterns in intra-annual hydro-climatological response as well as an index to assess river flow 70 ...

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Streamflow, as a natural phenomenon, is continuous in time and so are the meteorological variables which influence its variability. In practice, it can be of interest to forecast the whole flow curve instead of points (daily or hourly). To this end, this paper introduces the functional linear models and adapts it to hydrological forecasting. More precisely, functional linear models are regression models based on curves instead of single values. They allow to consider the whole process instead of a limited number of time points or features. We apply these models to analyse the flow volume and the whole streamflow curve during a given period by using precipitations curves. The functional model is shown to lead to encouraging results. The potential of functional linear models to detect special features that would have been hard to see otherwise is pointed out. The functional model is also compared to the artificial neural network approach and the advantages and disadvantages of both models are discussed. Finally, future research directions involving the functional model in hydrology are presented.Comment: 30 pages, 12 figure