Monthly flow analysis of Sefidrood River using Chaos theory

Measuring complexity and ways to reduce it in organizations and decision-making processes has become one of the topics of the day. The chaos theory was proposed in the 1960s, and the most effective and most successful effort was made by Edward Lorenz. Towards this, the flow rate of Sefidrood River as the most important river in Guilan Province and the second-longest river in Iran was studied using Chaos theory.

The study area in this research is a sub-basin of the Sefidrood River Basin. After collecting the monthly and annual discharge data of Sefidrood River, the following items were investigated:1- chaotic dynamic systems, 2- phase space reconstruction, 3- determining the time delay, 4- determining the embedding dimension, 5- determining the correlation dimension, and 6- determining the Lyapunov and Hurst exponents.

In determining the delay time using the autocorrelation function (ACF( curve, the appropriate lag is where the graph reaches a value close to zero or about 0.1 to 0.2. An appropriate embedding dimension is an embedded dimension in which the number of false neighbors has reached to about zero. For a lag of 1-month, the delay vectors are concentrated around the diagonal axis of space. Therefore, X(t) and X(t +1) are very close and continuous. Therefore, they will cause the characteristics of the adsorbent structure to be lost. Also in the state (phase) space for the delay time of 100 months, the density of lag vectors is close to the horizontal and vertical axes of the graph and indicates the incoherence and complexity of successive components in the lag vectors and its inadequacy to achieve system dynamics. However, due to the 5 months delay state space obtained from the average actual information (AMI) method, the delay vectors have a better distribution and the state space is well filled with points. The correlation dimension of the monthly time series is 3.37.

The presence of stochastic behavior in the river flow was determined using the correlation dimension test and Hurst exponent. The correlation exponent was saturated after increasing the embedded dimension in an incorrect value equal to 3.37. In addition, the closest correct value to the correlation dimension indicates the minimum variables required to describe the system, which is a value of 4. The obtained Hurst exponent is opposite to 0.5 and according to Hurst studies, it indicates the non-randomness and the presence of chaos in the river. The Hurst exponent obtained in daily scales is between 0.5 and 1 and indicates the existence of long-term memory in this series.