Largest Lyapunov Exponent of River Flow (Case Study: Karoon river)

In this paper, chaotic behavior of the daily river discharge time series from the Karoon river, during 1999-2004 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 first minimum of the Average Mutual Information (AMI) of the data. It is found that yield a delay time of 35 days for the daily river discharge time series. The sufficient embedding dimension is estimated using the false nearest neighbor algorithm which has a value of 9 .Based on these embedding parameters we calculate the average divergence rate of nearby orbits given by the largest Lyapunov exponent. The largest Lyapunov exponent 0.0344 is estimated.

Keywords:

Chaos theory , Karoon river , Lyapunov exponent , Time series