Breakpoint detection in non-stationary runoff time series under uncertainty

Abstract

Most conventional hydrological time series models, used for forecasting or synthetic data generation, are based on the stationary hypothesis. Hydrologic variables such as surface runoff discharge exhibit non-stationary behavior due to the effects of climate change or human activities. In this paper, a new methodology is proposed to analyze the uncertainty of the number and location of breakpoints in runoff time series. The non-stationary runoff time series is simulated by segmenting the series into stationary pieces, which follow an Auto-Regressive Moving Average (ARMA) process, based on the minimum description length (MDL) principle. The length of each piece and the order of the piecewise ARMA model are optimized using the Genetic Algorithm (GA). Several runoff time series with variable lengths are generated based on the observed data and the probability distribution function(s) (PDFs) of breakpoint location(s) are constructed. An optimal set of breakpoint locations are found for each generated runoff time series by minimizing the objective function based on the MDL. Finally, the PDF(s) of breakpoint location(s) is (are) constructed using the results of the mentioned optimization model. To evaluate the proposed methodology, it is applied to the case study of Zayandehrud River in Iran. According to the obtained breakpoint PDF for the runoff time series, three breakpoints around years of 1987, 1996 and 2006 are identified. The results are analyzed by investigating the time series of agricultural lands derived using remote sensing data and studying the impacts of interbasin water transfer projects implemented in the study area. Overall, investigating human-induced changes in the study area confirms the obtained shape of the PDF of runoff breakpoint and shows the good performance of the developed method for finding the number and location of breakpoints in the runoff time series.