南洞地下河月径流时间序列的混沌特征及预测

利用基于相空间重构技术、混沌识别与预测理论对1993-2013年南洞地下河月径流时间序列的非线性特征进行了分析，由所获得的延迟时间和最佳嵌入维数实现了月径流时间序列的相空间重构，运用饱和关联维数法和小数据量法计算出南洞地下河月径流时间序列的饱和关联维数和最大Lyapunov指数，并运用Volterra模型对南洞地下河月径流时间序列进行了多步预测研究。研究结果表明，南洞地下河月径流时间序列相空间重构的延迟时间和最佳嵌入维数分别为τ=5、m=8，饱和关联维数D和最大Lyapunov指数λ分别为4.63、0.748 9，从定性和定量的角度证明了南洞地下河月径流时间序列具有弱混沌特征。Volterra自适应滤波模型的预测结果能较好地表征南洞地下河月径流的变化趋势和规律，对18个月内的短期预测精度较高，模拟效果较好。 

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.