Accounting for high-dimensional predictors in RFA with MARS

Hydrological processes and phenomena are naturally complex and nonlinear. Many physiographical variables such as those dealing with drainage network characteristics may influence streamflow characteristics and should be considered in regional frequency analysis (RFA). These variables have hence a significant impact on the effectiveness of flood quantile estimation techniques. Although many statistical tools are considered to estimate flood quantiles at ungauged sites in the hydrological literature, little attention has been given to the nonlinearity and to the high-dimensionality of physio-meteorological variable space. In this study, the multivariate adaptive regression splines (MARS) approach is introduced in RFA. This model allows to account simultaneously for non-linearity and interactions between variables hidden in high-dimensional data. MARS is hereby applied on two datasets of 151 hydrometric stations located in the southern part of the province of Quebec (Canada): a standard dataset (STA) including commonly used variables and an extended dataset (EXTD) combining STA with additional variables dealing with drainage network characteristics. It is then compared to generalized additive models (GAM), a state-of-the-art method for regional estimation. Numerical results show that MARS outperforms GAM, especially with the extensive database EXTD. The study suggests that MARS may be a promising tool to take into account the complexity of the hydrological phenomena involved and the increasing number of variables used in RFA.