Quantile Regression in Regional Frequency Analysis: A Better Exploitation of the Available Information

Abstract

lassical regression models are widely used in hydrological regional frequency analysis (RFA) in order to provide quantile estimates at ungauged sites given physio-meteorological information. Since classical regression-based methods only provide the conditional mean of the response variable, estimated at-site quantiles at gauged sites are commonly used to calibrate the regression models in RFA. Generally, only at-site quantiles estimated with long data records are retained for the calibration and the evaluation steps, whereas hydrological information from stations with few data is ignored. In addition, even if the at-site quantiles are estimated with long data series, they are always subject to model selection and parameter estimation. Hence, their use for the calibration of the RFA models may induce significant uncertainties in the modeled relationships. The aim of this paper is to propose a quantile regression (QR) model that gives directly the conditional quantile for RFA and avoids using at-site estimated quantiles in the calibration step. The proposed model presents another advantage where all the available hydrological information can be used in the calibration step including stations with very short data records. An evaluation criterion using observed data is also proposed in a cross-validation procedure. The proposed QR model is applied on a dataset representing 151 hydrometric stations from the province of Quebec and compared with a classical regression model. According to the proposed evaluation criterion, the QR is shown to be a viable model for regional estimations. Indeed, the proposed model proved to be robust and flexible, allowing for consideration of all the region?s sites, even those with extremely short flood records.