Chaotic analysis of time series in the sediment transport phenomenon

In this paper, nonlinear time series modeling techniques are applied to analyze suspended sediment data. The data are collected from the Yellow River basin at Tongguan, Shanxi, China during January 1980-December 2002. The phase space, which describes the evolution of the behavior of a nonlinear system, is reconstructed using the delay embedding theorem suggested by TAKENS. The delay time used for the reconstruction is chosen after examining the first zero-crossing of the autocorrelation function and the first minimum of the average mutual information (AMI) of the data. It is found that both methods yield a delay time of 7 days and 9 days, respectively, for the suspended sediment time series. The sufficient embedding dimension is estimated using the false nearest neighbor algorithm which has a value of 12. Based on these embedding parameters we calculate the correlation dimension of the resulting attractor, as well as the average divergence rate of nearby orbits given by the largest Lyapunov exponent. The correlation dimension 6.6 and largest Lyapunov exponent 0.065 are estimated. Finally, the phase space embedding based weight predictor algorithm (PSEWPA) is employed to make a short-term prediction of the chaotic time series for which the governing equations of the system may be unknown. The predicted values are, in general, in good agreement with the observed ones within 15 days, but they appear much less accurate beyond the limits of 20 days. These results indicate that chaotic characteristics obviously exist in the sediment transport phenomenon; techniques based on phase space dynamics can be used to analyze and predict the suspended sediment concentration.