基于Morlet小波的丹江口水库入库流量周期性分析

Morlet小波的波形与径流的形态相似,且其伸缩尺度与周期有直接的对应关系。Morlet小波是复数小波,比实型小波能更真实地反映时间序列的时频局部特征。本文采用一种新颖、快速、实用的非正交小波变换方法,并给出了该方法的推导过程。文中采用Morlet小波对丹江口水库入库流量进行分析,揭示了丹江口水库入库流量的多尺度震荡特性和周期性变化规律。分析结果表明,丹江口年平均入库流量具有两个周期(9年和24年)。根据小波系数的实部拟合出9年和24年的周期变化曲线,并与实际数据进行对比。在实际数据受到随机成分影响的情况下,比较结果仍然相当吻合。研究成果为汉江流域水资源开发利用和南水北调中线工程水资源优化配置提供技术支撑。

The Periodical Analysis of the Danjiangkou Reservoir Inflow Based on the Morlet Wavelet

The waveform of the Morlet wavelet is similar to the form of streamflow, and there is direct correlation be-tween the scale and the period. The Morlet wavelet is a complex wavelet, so it is able to reflect the time-frequency localiza-tion characteristics of the time sequence more realistically than the real wavelet. In this paper, a novel, rapid and practical method of non-orthogonal wavelet transform is used, and the derivation of the method is given. The Morlet wavelet is used to analyze the variation of the Danjiangkou Reservoir inflow, revealing the multi- scale fluctuation in and the law of periodi-cal variation. The result shows that the inflow series have two periods (9 years and 24 years). The periodical curves of 9 years and 24 years simulated according to the real part of the wavelet coefficients are in good agreement with the actual data affected by the random components. The research result provides a technical support for the water resources development in the Hanshui River and the South-to-North Water Diversion plan.