Abstract
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.
Highlights
Heavy rainfall events are responsible for damaging floods across the world
Due to differences in storm development processes associated with long and short storm durations, homogeneous regions for the selected site based on the same method differ for short and long storm durations
The region for region of influence (ROI) differs from either canonical correlation analysis (CCA) or nonlinear CCA (NLCCA) as the latter methods take into account rainfall information in the construction of the canonical spaces, whereas ROI is based exclusively on standardized Euclidean distance in the space of the physiographic variables
Summary
Heavy rainfall events are responsible for damaging floods across the world. an appropriate characterization of rainfall extremes is important in the fields of water management, civil engineering, building design, and public safety, among many others. Producing reliable estimates of the frequency and magnitude of extreme rainfall events has long been a pressing and widely studied problem in science and engineering (e.g., El Adlouni et al 2007; Chu et al 2009; Matonse and Frei 2013; Langousis et al 2016). In many parts of the world, dense networks of short-duration rainfall observing sites with long records do not exist This raises the following question: how does one obtain IDF curves at partially gauged or ungauged sites? A fundamental assumption of RFA is that the region of interest is sufficiently homogenous, i.e., gauged sites should be selected so that the similarity with the ungauged target site is maximized
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