Investigating chaos in river stage and discharge time series

Abstract

The existence of chaotic behaviour in the river stage and discharge time series observed at the Sogutluhan hydrometric station, Turkey, is investigated. Five nonlinear dynamic methods are employed: (1) phase space reconstruction; (2) False Nearest Neighbour (FNN) algorithm; (3) correlation dimension method; (4) Lyapunov exponent method; and (5) local approximation method. These methods have their bases on data embedding, nearest neighbour search, dimensionality analysis, system divergence/convergence, and local approximation and have varying levels of sophistication in conceptualisation and implementation. They provide either direct identification of chaotic behaviour or at least facilitate identification through system reconstruction, complexity determination (especially in terms of dimensionality), and prediction (including predictability horizon). As the discharge data used in this study are produced by rating directly gauged stage time series, it becomes feasible to investigate any interference triggered by chaotic signals with the rating. The results indicate the existence of low-dimensional chaos in the two time series. They also suggest that the rating of the stage time series to obtain the discharge time series amplifies significantly the fluctuations in the latter in the presence of chaotic signals.