Local Prediction in River Discharge Time Series

In this paper, chaotic behavior of the daily river discharge time series from the Karoon River, during January 1999-December 2004 is investigated. 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 minimum of the average mutual information (AMI) of the data. It is found that a delay time of 40 days and the sufficient embedding dimension is estimated using the false nearest neighbor algorithm which has a value of 8 for the river flow time series. Based on these embedding parameters we calculate the average divergence rate of nearby orbits given by the largest Lyapunov exponent. The largest Lyapunov exponent 0.0255 for is estimated. In this study the local prediction model has been applied to predict daily discharge time series. In this prediction model, the dynamics of the system are described step by step locally in the phase space, the results are quite satisfactory.