Non-linear canonical correlation analysis in regional frequency analysis

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.