北江流域径流时间序列的分形特征解析

Study on Fractal Characteristics of Runoff Time Series in the Beijiang River

径流时间序列具有非线性、复杂性和不确定性的特征,运用R/S分析法、多重分形方法对北江流域石角站1954-2006年的年平均径流量时间序列进行研究,解析其分形的特征。结果表明:北江流域石角站的Hurst指数远大于0.5,说明北江流域年平均径流时间序列具有明显的趋势性成分,即北江流域年平均径流量具有明显的持久性和长期记忆特性。结合V统计说明,北江流域的年平均径流量的持久性经过15～20年之后会消失。根据多重分形方法,通过对幂谱和统计矩函数的分析,得出北江流域石角站年平均径流量时间序列的无标度性,借助分配函数、广义分形维数和多重分形谱对年平均径流量的研究,表明北江流域石角站多年平均径流量具有多重分形的特征,为北江流域径流的预测工作的做了重要的铺垫。

The runoff time series is characterized by complexity and uncertainty. R/S analysis and multifractal method were used to analyze the data collected from 1954 to 2006 at Shijiao hydrology station of the Beijiang River in this paper. Results show that the Hurst index of Shijiao station is largely higher than 0. 5, indicating that the average annual runoff time series has obvious trend components, namely the average annual runoff of the Beijiang River shows obvious durability and long-term memory. According to the V statistical value, the average annual runoff persistence will disappear after 15 -20 years. Using the multifractal method, the power spectrum and statistical moment function were analyzed. The average annual runoff of the Beijiang River is of multi-fractal features. These results are important for the runoff forecasting.