Comparison of reconstructed phase space and chaotic behavior of Nazloochay river flow at different temporal scales

The study of the behavior of river flow is the basic demand in water resources planning. The importance of identifying the river flow process at different temporal scales, by using chaos theory is to predict the river flow and select the proper model framework. River flow has dynamic and nonlinear nature. In dynamical systems, phase space is the space which includes all the possible conditions that are need to describe a system. Because of inaccessibility of exact mathematical equations of system, it is difficult to achieve the phase space. And all the available information is a scalar time series. Therefore, embedding method is used for reconstruction of phase space. In this study the daily, weekly and monthly measured discharges of Nazloochay river from 1990 to 2011 were used for reconstruction of phase space. Time delay was calculated by AMI method and it is 39 for daily, 18 for weekly and 9 for monthly scale. Embedding dimension as a minimum dimension for reconstruction of phase space for description of dynamical system was calculated by using FNN method for daily, weekly and monthly scale and that is 26, 8 and 4 respectively. Chaotic behavior of river flow for daily, weekly and monthly scale was evaluated by using correlation dimension and Hurst exponent methods. Correlation dimension is 2.8 for daily, 3.62 for weekly and 5.52 for monthly scale. Hurst exponent for daily, weekly and monthly scale is obtained 0.84, 0.77 and 0.76 respectively. The results imply that Nazluchay's river flow is chaotic.