Local trend analysis method of hydrological time series based on piecewise linear representation and hypothesis test

Abstract

It is important to analyze the nonstationarity of hydrological time series under the influence of climate change and human activities. Compared with previous studies, this study focuses more on local trends rather than overall trend and mean value change, and presents a local trend analysis method, namely PLRHT method, for the nonstationary analysis of hydrological time series. In the PLRHT method, the fitted local trend lines determined by the piecewise linear representation algorithm and Akaike information criterion are used as the baseline component of hydrological time series. The difference between two adjacent fitted local trend lines includes the slope and intercept differences, which jointly determine the mean value difference of two corresponding subseries. In addition, based on the slope and intercept differences, three change points of the hydrological time series (inflection point, break point and bivariate point) are defined and their significance is tested by hypothesis test based on Monte Carlo experiments. Finally, the application effect of the PLRHT method is compared with five other representative methods of non-stationarity analysis (runs test, rank sum test, Brown-Forsythe test, T test and heuristic segmentation) by using artificial and observed hydrological time series as examples. The results show that, compared with the five nonstationarity analysis methods, the PLRHT method could not only detect more accurate change points of the artificial and observed hydrological time series, but also quantitatively analyze the contributions of trends and abrupt changes to mean value variations of these hydrological time series. Besides, the local trend analysis enables a deeper causality analysis for the nonstationarity of the observed hydrological time series. Therefore, local trend analysis could help understanding the variation characteristics and driving forces of hydrological processes in the changing environment, and the PLRHT method is a feasible local trend analysis method to reveal the relationship between local mean value changes and local trends.