Regional Frequency Analysis at Ungauged Sites with the Generalized Additive Model

F. Chebana Eau Terre Environnement, Institut National de la Recherche Scientifique, Université du Québec, Québec, Québec, Canada

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C. Charron Institute Center for Water and Environment (iWater), Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates

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T. B. M. J. Ouarda Institute Center for Water and Environment (iWater), Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates, and Eau Terre Environnement, Institut National de la Recherche Scientifique, Université du Québec, Québec, Québec, Canada

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B. Martel Eau Terre Environnement, Institut National de la Recherche Scientifique, Université du Québec, Québec, Québec, Canada

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Abstract

The log-linear regression model is one of the most commonly used models to estimate flood quantiles at ungauged sites within the regional frequency analysis (RFA) framework. However, hydrological processes are naturally complex in several aspects including nonlinearity. The aim of the present paper is to take into account this nonlinearity by introducing the generalized additive model (GAM) in the estimation step of RFA. A neighborhood approach using canonical correlation analysis (CCA) is used to delineate homogenous regions. GAMs possess a number of advantages such as flexibility in shapes of the relationships as well as the distribution of the output variable. The regional model is applied on a dataset of 151 hydrometrical stations located in the province of Québec, Canada. A stepwise procedure is employed to select the appropriate physiometeorological variables. A comparison is performed based on different elements (regional model, variable selection, and delineation). Results indicate that models using GAM outperform models using the log-linear regression as well as other methods applied to this dataset. In addition, GAM is flexible and allows for the inclusion and presentation of nonlinear effects of explanatory variables, in particular, basin area effect (scale). Another finding is the reduced effect of CCA delineation when combined with GAM.

Corresponding author address: Fateh Chebana, INRS-ETE, Université du Québec, 490 rue de la Couronne, Québec, QC G1K 9A9, Canada. E-mail: fateh.chebana@ete.inrs.ca

Abstract

The log-linear regression model is one of the most commonly used models to estimate flood quantiles at ungauged sites within the regional frequency analysis (RFA) framework. However, hydrological processes are naturally complex in several aspects including nonlinearity. The aim of the present paper is to take into account this nonlinearity by introducing the generalized additive model (GAM) in the estimation step of RFA. A neighborhood approach using canonical correlation analysis (CCA) is used to delineate homogenous regions. GAMs possess a number of advantages such as flexibility in shapes of the relationships as well as the distribution of the output variable. The regional model is applied on a dataset of 151 hydrometrical stations located in the province of Québec, Canada. A stepwise procedure is employed to select the appropriate physiometeorological variables. A comparison is performed based on different elements (regional model, variable selection, and delineation). Results indicate that models using GAM outperform models using the log-linear regression as well as other methods applied to this dataset. In addition, GAM is flexible and allows for the inclusion and presentation of nonlinear effects of explanatory variables, in particular, basin area effect (scale). Another finding is the reduced effect of CCA delineation when combined with GAM.

Corresponding author address: Fateh Chebana, INRS-ETE, Université du Québec, 490 rue de la Couronne, Québec, QC G1K 9A9, Canada. E-mail: fateh.chebana@ete.inrs.ca
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