不同时间尺度的径流时间序列混沌特性分析

Chaos analysis of runoff time series at different timescales

径流序列的动力行为是在复杂非线性和多尺度现象综合作用下的外在表现。基于混沌理论和相空间重构理论,以金沙江和美国Umpqua河统计的日径流序列为研究对象,对不同时间尺度(日、旬和月)的径流序列,首先利用0-1混沌测试算法计算其渐进增长率,探讨径流序列混沌特性随时间尺度的变化规律,然后重构以上径流序列的相空间,分别计算关联维数、最大Lyapunov指数和Kolmogorov熵。用这3个混沌判别指标分析不同时间尺度下径流序列的混沌特性及其随时间尺度的变化规律。研究结果表明,时间尺度和径流序列非线性特征之间的关系并不明显,渐进增长率随时间尺度的增加并无明显的变化规律,嵌入维数则随时间尺度的增大呈减小趋势,最大lyapunov指数和Kolmogorov熵随着时间尺度的增加逐渐增大。

Natural runoff dynamics is an outcome of complex nonlinear and multi-scale phenomena, integrat-ed together in some coherent manner. Based on chaos theory and the phase space reconstruction theory, dai-ly runoff series of the Jinsha River in China and the Umpqua River in America are used for this study at different timescales （one day, 1/3 month and one month）. In this paper, the asymptotic growth rate Ko is calculated by the 0-1 test algorithm and its variation with timescales are explored firstly. Then phase space reconstruction are adopted for the runoff series, and three discrimination indexes are used： correlation di-mension; Lyapuuov exponent; Kolmogorov entropy. An attempt has been made to identify the existence of chaos and the intensity of nonlinear behavior at three characteristic time scales. A comparison of results re-veals that the relationship between the timescales and the intensity of nonlinearity is not so obvious; there is no clear variation of the asymptotic growth rate along with the increase of timescale; and the embedded dimension decreases as the timescales increase. However, the largest Lyapunov exponent and Kolmogorov en-tropy increase gradually with the increase of the timescale.