Analysis of River Parameters Using Chaos-Theory Based Indices (Case Study: Zayandehrud River Flow)

Analysis of hydrological parameters of rivers in short-term scales and during a long period of time plays a significant role in the study of production and storage of hydro-electrical energy as well as flood and drought control. In this research, by using chaotic indices, the dynamic status of flow time series and effect of time scale on Zayandehrud River flow behavior in 43 years (1971-2013) was evaluated. The data from Eskandari, Ghale Shahrokh, Pole Zamankhan and Pol Kalleh hydrometric stations in Zayandehrud River were investigated at two daily and 10-day time scales. The possibility of chaos in river flow rate was investigated using correlation dimension. Results showed that on a daily scale, the non-integer value of correlation dimension is 3.34, 3.60, 3.77 and 3.84, respectively, for Eskandari, Ghale Shahrokh, Pole Zmankhan and Pol Kalleh. This indicates the chaotic flow rate of these stations. By increasing the time scale to 10 days, the flow rate in all stations becomes random. Using the Lyapunov exponent test, sensitivity of the system to initial conditions was investigated as an attribute of chaotic systems and the forecast horizon was estimated. The largest Lyapunov exponents obtained at each of the four stations in two daily and 10-day time scales were positive. Hurst exponent was used to investigate the random process of data against its non-randomness. Considering the nonlinear dynamic indices, it seems that correlation dimension is more accurate for chaotic detection in nonlinear systems.