Chaotic characters of the Yellow River Basin based on the sediment time series: An attempt to integrated research in geography

The sediment content of the Yellow River is resulted from the interactions of natural, economic, and social factors, so it includes some evolutive information of the Yellow River Basin system. Sediment contents from 1952 to 2007 on Toudaoguai, Tongguan, Huayuankou and Lijin sections along the river are chosen as the study time series, and correlation dimensions (D2), Kolmogorov entropies (K2), and Hurst indexes (H) of the time series were calculated. Correlation dimensions on Toudaoguai, Tongguan, Huayuankou, and Lijin sections are 3.24, 5.69, 6.57 and 7.34 respectively, and the Kolmogorov entropies are 0.13, 0.37, 0.40 and 0.38 respectively, which indicates that the systems controlled by different sections along the Yellow River are chaotic systems and the chaotic degrees increase gradually from the upper to lower section. The average predictable period of the sediment contents is 8 years on Toudaoguai section and 3 years on the other sections with the reciprocals of the Kolmogorov entropies. The more obvious the chaotic degree is, the shorter the average predictable period is. Hurst indexes on the sections are above 0.5, with the maximum of 0.86 on Tongguan section and the minimum of 0.68 on Toudaoguai section, which indicates that the time series have persistent trends in the average predictable period. Eight state variables and two control parameters are necessary to construct the dynamic model of the Yellow River Basin system.