Non-stationary hydrologic frequency analysis using B-spline quantile regression

Abstract

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.

A Climatic Perspective on the Impacts of Global Warming on Water Cycle of Cold Mountainous Catchments in the Tibetan Plateau: A Case Study in Yarlung Zangbo River Basin

“…The quantile regression analysis, introduced by Koenker and Hallock [55] as a location method to extend ordinary least square, was employed in this study to investigate the changes in the flow regimes in the YZRB. The method has been widely applied for investigating changes in different regimes of daily flow [15,16,27,[56][57][58][59]. For example, trend in 25% percentile flows is a least-square regression of the flow that is exceeded 25% daily flows in a given year.…”

Impact of Changing Climate and Land Cover on Flood Magnitudes in the Delaware River Basin, USA

“…Future flood hydrology will vary from historical patterns due to changes in climate and land cover (Merz et al 2010;Wagener et al 2010;Hirsch 2011;Nasri et al 2017), challenging conventional approaches to managing flood hazards based on assumptions of stationarity (Milly et al 2008(Milly et al , 2015. There is considerable debate about how best to estimate future flood magnitude and frequency (Galloway 2011), but understanding the key roles of changing climate and land cover is fundamental.…”

Non-stationary analysis for road drainage design under land-use and climate change scenarios

“…In this context, the implementation of statistical models that allow the adjustment of the parameters of the distribution functions through covariates that explain the trends in the hydrological series can improve the results of the flood frequency analysis and the estimation of the design flow (e.g., Agilan and Umamahesh, 2017;Nasri et al, 2017;Sraj et al, 2016). In the literature, various techniques have been developed to carry out non-stationary flood frequency analysis (Cannon, 2010;Villarini et al, 2010) and have mainly been applied to the design of hydraulic structures (e.g., Nasri et al, 2017;Mondal and Mujumdar, 2015).…”