Estimation of rainfall intensity–duration–frequency curves at ungauged locations using quantile regression methods

Intensity–duration–frequency (IDF) curves of extreme rainfall are used extensively in infrastructure design and water resources management. In this study, a novel regional framework based on quantile regression (QR) is used to estimate rainfall IDF curves at ungauged locations. Unlike standard regional approaches, such as index-storm and at-site ordinary least-squares regression, which are dependent on parametric distributional assumptions, the non-parametric QR approach directly estimates rainfall quantiles as a function of physiographic characteristics. Linear and nonlinear methods are evaluated for both the regional delineation and IDF curve estimation steps. Specifically, delineation by canonical correlation analysis (CCA) and nonlinear CCA (NLCCA) is combined, in turn, with linear QR and nonlinear QR estimation in a regional modelling framework. An exhaustive comparative study is conducted between standard regional methods and the proposed QR framework at sites across Canada. Overall, the fully nonlinear QR framework, which uses NLCCA for delineation and nonlinear QR for estimation of IDF curves at ungauged sites, leads to the best results.