Open AccessA Nonlinear Approach to Regional Flood Frequency Analysis Using Projection Pursuit Regression
Author(s) -
Martin Durocher,
Fateh Chebana,
Taha B. M. J. Ouarda
Publication year - 2015
Publication title -
journal of hydrometeorology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.733
H-Index - 123
eISSN - 1525-755X
pISSN - 1525-7541
DOI - 10.1175/jhm-d-14-0227.1
Subject(s) - flood myth , projection pursuit , nonlinear system , computer science , regression , artificial neural network , projection (relational algebra) , structural basin , generalized additive model , quantile , representation (politics) , econometrics , artificial intelligence , mathematics , statistics , machine learning , geography , geology , algorithm , paleontology , physics , archaeology , quantum mechanics , politics , political science , law
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.