珠江流域日降水量时间序列的多重分形分析
Multifractal analyses of daily rainfall time series in Pearl River basin of China
摘要：
利用基于乘法级联模式和多重分形消除趋势波动分析（MF-DFA）的普适多重分形方法，研究了珠江流域45 a逐日降水量时间序列的多重分形特征。这两种多重分形分析的结果表明，该流域日降雨量时间序列在两个不同的时间尺度范围内具有多重分形行为。研究发现，日降雨量时间序列的经验多重分形矩函数$K(q)$可以用通用多重分形模型（UMM）进行很好的拟合。这些日降雨量数据的UMM的守恒参数$H$的估计值接近于零，表明它们对应于守恒场。在去除了降雨量的季节性趋势后，MF-DFA对指数$h(2)$的估计值表明珠江流域日降雨量时间序列不具有长期相关性。研究还发现，$K(2)$与海拔序列呈负相关。它显示了地形和降雨量变化之间的关系。
英文摘要：
The multifractal properties of daily rainfall time series at the stations in Pearl River basin of China over periods of up to 45 years are examined using the universal multifractal approach based on the multiplicative cascade model and the multifractal detrended fluctuation analysis (MF-DFA). The results from these two kinds of multifractal analyses show that the daily rainfall time series in this basin have multifractal behavior in two different time scale ranges. It is found that the empirical multifractal moment function $K(q)$ of the daily rainfall time series can be fitted very well by the universal mulitifractal model (UMM). The estimated values of the conservation parameter $H$ from UMM for these daily rainfall data are close to zero indicating that they correspond to conserved fields. After removing the seasonal trend in the rainfall data, the estimated values of the exponent $h(2)$ from MF-DFA indicate that the daily rainfall time series in Pearl River basin exhibit no long-term correlations. It is also found that $K(2)$ and elevation series are negatively correlated. It shows a relationship between topography and rainfall variability.
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