A probe into the chaotic nature of daily streamflow time series by correlation dimension and largest Lyapunov methods

Abstract

Two chaotic indicators namely the correlation dimension and the Lyapunov exponent methods are investigated for the daily river flow of Kizilirmak River. A delay time of 60 days used for the reconstruction is chosen after examining the first minimum of the average mutual information of the data. The sufficient embedding dimension is estimated using the false nearest neighbor algorithm, which has a value of 11. Based on these embedding parameters the correlation dimension of the resulting attractor is calculated, as well as the average divergence rate of nearby orbits given by the largest Lyapunov exponent. The presence of chaos in the examined river flow time series is evident with the low correlation dimension (2.4) and the positive value of the largest Lyapunov exponent (0.0061).