Relationship between chaos theory indicators in monitoring of river flow at short-term time scales

This study was carried out to study and analyze the effect of time-scale changes on chaotic range of discharge of upstream and downstream stations of Zayandehrud Dam Reservoir, trend of changes in the correlation coefficient of flow and forecast horizon for 43 years (1971-2013). Also, the relationship between correlation dimension and forecast horizon is determined over time. For this purpose, discharge of hydrometric stations of Eskandari, Ghale Shahrokh, Pole Zamankhan and Pole Kaleh have been used in four daily, 3, 5, and 7-day time scales. As a first step, the time delay and embedding dimension of the system are calculated using the method of average mutual information and the nearest false neighbors. Then, fractal dimension of the system is estimated using the correlation dimension method. Then, using the Lyapunov's exponent, the prediction horizon is estimated in the chaotic series. Results revealed that flow rate at a 5-day scale has a random behavior at Pole Zamankhan station and at a 7-day scale at the Pole Zamankhan and Eskandari stations and is chaotic in other time scales. Eskandari, Ghale Shahrokh and Pole Zamankhan stations have low chaos at all chaotic scales. At Pole Kaleh station, the flow rate is low in chaos at daily scale and has average chaotic domain at 3, 5 and 7-day scales. According to the other results, by increasing the time scale, the correlation dimension increases and the forecast horizon decreases. On the other hand, according to the Lyapunov exponent, the upstream stations of Zayandehrud Dam Reservoir have more prediction horizon than downstream stations in all time scales.