Research papersNon-stationary hydrologic frequency analysis using B-spline quantile regression

- We consider a framework for extreme frequency analysis based on B-spline quantile regression which allows to model data in the presence of non-stationarity and/or dependence on covariates which include linear and nonlinear dependence.
- A coeffcient of determination and BIC criterion for quantile regression are used to evaluate the estimate of the proposed model for each quantile level.
- The method is applied to annual maximum and minimum streamflow records in Ontario, Canada.
- To our knowledge, no studies have previously studied streamflow extremes using B-Spline quantile regression.

Hydrologic frequency analysis is commonly used by engineers and hydrologists to provide the basic information on planning, design and management of hydraulic and water resources systems under the assumption of stationarity. However, with increasing evidence of climate change, it is possible that the assumption of stationarity, which is prerequisite for traditional frequency analysis and hence, the results of conventional analysis would become questionable. In this study, we consider a framework for frequency analysis of extremes based on B-Spline quantile regression which allows to model data in the presence of non-stationarity and/or dependence on covariates with linear and non-linear dependence. A Markov Chain Monte Carlo (MCMC) algorithm was used to estimate quantiles and their posterior distributions. A coefficient of determination and Bayesian information criterion (BIC) for quantile regression are used in order to select the best model, i.e. for each quantile, we choose the degree and number of knots of the adequate B-spline quantile regression model. The method is applied to annual maximum and minimum streamflow records in Ontario, Canada. Climate indices are considered to describe the non-stationarity in the variable of interest and to estimate the quantiles in this case. The results show large differences between the non-stationary quantiles and their stationary equivalents for an annual maximum and minimum discharge with high annual non-exceedance probabilities.