Streamflow Hydrograph Classification Using Functional Data Analysis

Abstract

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 ...

Stream Temperature Modeling Using Functional Regression Models

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Identification of Flood Reactivity Regions via the Functional Clustering of Hydrographs

“…In contrast to classical multivariate data, FD is continuously defined and does not depend on the choice of several hydrograph characteristics, such as peak discharge, hydrograph volume, duration, or a few parameters representing the shape of a hydrograph [Yue et al, 2002], but instead uses the whole information stored in the hydrograph [Chebana et al, 2012]. FD analysis is more general, flexible, and representative of the real hydrological phenomena than classical multidimensional analysis and avoids the subjective choice of a set of hydrograph characteristics [Ternynck et al, 2016]. FD are conceptually defined in a continuous framework.…”

“…All rights reserved. a range of temporal scales, such as yearly hydrographs [Merleau et al, 2007;Jamaludin, 2016], spring flood events (duration of six months) [Ternynck et al, 2016], and diurnal discharges (duration of one day) [Hannah et al, 2000].…”

A New Concept to Calibrate and Evaluate a Hydrological Model Based on Functional Data Analysis

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