Chaos analysis and prediction of monthly runoff time series in the Nandong subterranean river

In order to provide scientific evidence for the development and utilization of water resources in the Nandong area，this study analyzes the nonlinear features of monthly runoff series of the subterranean river from 1990 to 2013. It is based on the phase space reconstruction theory and chaos theory. The optimal embedding dimension and time delay for the real monthly runoff series are determined using the improved false nearest neighbor method and mutual information method，respectively. And the saturation correlation dimension and the largest Lyapunov exponent for the series are calculated to distinguish its chaotic characteristics by using the Grassberger-Procaccia method and small data sets. According to Volterra series theory，a prediction model is established to describe the changes of monthly runoff series of the Nandong subterranean River in the future. The results show that the time delay and optimal embedding dimension τ=5 and m=8, respectively. The saturation correlation dimension of attractor of phase space is 4.63 and the maximum Lyapunov index is 0.748 9. The results also indicate that the monthly runoff series in the Nandong subterranean river has a weak chaotic characteristic in both quality and quantity. The model using the third-order Volterra adaptive filter is effective to predict hydrologic chaotic time series in the study area. It is accurate enough for monthly precipitation forecasting，especially for short-term precipitation forecasting within 18 months.