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Non-linear canonical correlation analysis in regional frequency analysis

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Abstract

Hydrological processes are complex non-linear phenomena. Canonical correlation analysis (CCA) is frequently used in regional frequency analysis (RFA) to delineate hydrological neighborhoods. Although non-linear CCA (NL-CCA) is widely used in several fields, it has not been used in hydrology, particularly in RFA. This paper presents an overview of techniques used to reproduce non-linear relationships between two sets of variables. The approaches considered in this work are based on NL-CCA using neural networks (CCA-NN), coupled to a log-linear regression model for flood quantile estimation. In order to demonstrate the usefulness of these approaches in RFA, a comparative study between the latter and linear CCA is performed using three different databases from North America. Results show that CCA-NN is more robust and can better reproduce the non-linear relationship structures between physiographical and hydrological variables. This reflects the high flexibility of this approach. Results indicate that for all three databases, it is more advantageous to proceed with the non-linear CCA approach.

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Abbreviations

DHR:

Delineation of homogeneous regions

RE:

Regional estimation

CCA & LR:

CCA associated to a log-linear regression

CCA-NN & LR:

Non-linear CCA based on Neural Network in DHR step associated to a log-linear regression in the RE step

CCA-NN & CLR:

Non-linear CCA based on Neural Network in DHR step associated to a log-linear regression in the canonical space in the RE step

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Acknowledgments

The authors thank M.A. Ben Alaya, for his valuable help and input into the present work. The authors wish also to express their appreciation to the reviewers, the Associate Editor and the Editor in Chief for their invaluable comments and suggestions. Financial support for the present study was provided by the National Sciences and Engineering Research Council of Canada (NSERC). To get access to the data used in this study, reader may refer to the report of A. Kouider (http://espace.inrs.ca/365/1/T000342.pdf).

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Authors and Affiliations

  1. Institut National de la Recherche Scientifique, Centre Eau Terre et Environnement, 490, rue de la Couronne, Quebec, QC, G1K 9A9, Canada

    D. Ouali, F. Chebana & T. B. M. J. Ouarda

  2. Institute Centre for Water Advanced Technology and Environmental Research, P.O. Box 54224, Abu Dhabi, UAE

    T. B. M. J. Ouarda

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  1. D. Ouali
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  2. F. Chebana
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  3. T. B. M. J. Ouarda
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Correspondence to D. Ouali.

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Ouali, D., Chebana, F. & Ouarda, T.B.M.J. Non-linear canonical correlation analysis in regional frequency analysis. Stoch Environ Res Risk Assess 30, 449–462 (2016). https://doi.org/10.1007/s00477-015-1092-7

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