A Nonlinear Approach to Regional Flood Frequency Analysis Using Projection Pursuit Regression

Martin Durocher Eau Terre Environnement, Institut National de Recherche Scientifique, University of Québec, Québec, Canada

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Fateh Chebana Eau Terre Environnement, Institut National de Recherche Scientifique, University of Québec, Québec, Canada

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Taha B. M. J. Ouarda Institute Center for Water Advanced Technology and Environmental Research (iWater), Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates

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Abstract

This paper presents an approach for regional flood frequency analysis (RFFA) in the presence of nonlinearity and problematic stations, which require adapted methodologies. To this end, the projection pursuit regression (PPR) is proposed. The PPR is a family of regression models that applies smooth functions on intermediate predictors to fit complex patterns. The PPR approach can be seen as a hybrid method between the generalized additive model (GAM) and the artificial neural network (ANN), which combines the advantages of both methods. Indeed, the PPR approach has the structure of a GAM to describe nonlinear relations between hydrological variables and other basin characteristics. On the other hand, PPR can consider interactions between basin characteristics to improve the predictive capabilities in a similar way to ANN, but simpler. The methodology developed in the present study is applied to a case study represented by hydrometric stations from southern Québec, Canada. It is shown that flood quantiles are mostly associated with a dominant intermediate predictor, which provides a parsimonious representation of the nonlinearity in the flood-generating processes. The model performance is compared to eight other methods available in the literature for the same dataset, including GAM and ANN. When using the same basin characteristics, the results indicate that the simpler structure of PPR does not affect the global performance and that PPR is competitive with the best existing methods in RFFA. Particular attention is also given to the performance resulting from the choice of the basin characteristics and the presence of problematic stations.

Corresponding author address: Martin Durocher, INRS-ETE, University of Québec, 490 rue de la Couronne, Québec, QC G1K 9A9, Canada. E-mail: martin.durocher@ete.inrs.ca

Abstract

This paper presents an approach for regional flood frequency analysis (RFFA) in the presence of nonlinearity and problematic stations, which require adapted methodologies. To this end, the projection pursuit regression (PPR) is proposed. The PPR is a family of regression models that applies smooth functions on intermediate predictors to fit complex patterns. The PPR approach can be seen as a hybrid method between the generalized additive model (GAM) and the artificial neural network (ANN), which combines the advantages of both methods. Indeed, the PPR approach has the structure of a GAM to describe nonlinear relations between hydrological variables and other basin characteristics. On the other hand, PPR can consider interactions between basin characteristics to improve the predictive capabilities in a similar way to ANN, but simpler. The methodology developed in the present study is applied to a case study represented by hydrometric stations from southern Québec, Canada. It is shown that flood quantiles are mostly associated with a dominant intermediate predictor, which provides a parsimonious representation of the nonlinearity in the flood-generating processes. The model performance is compared to eight other methods available in the literature for the same dataset, including GAM and ANN. When using the same basin characteristics, the results indicate that the simpler structure of PPR does not affect the global performance and that PPR is competitive with the best existing methods in RFFA. Particular attention is also given to the performance resulting from the choice of the basin characteristics and the presence of problematic stations.

Corresponding author address: Martin Durocher, INRS-ETE, University of Québec, 490 rue de la Couronne, Québec, QC G1K 9A9, Canada. E-mail: martin.durocher@ete.inrs.ca
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