水文序列小波分析中小波函数选择方法

Wavelets selection method in hydrologic series wavelet analysis

将信号离散小波变换中常用的7个小波系共54个小波函数作为选择范围,应用蒙特卡罗方法,通过黄河利津站和浙江白溪流域的实测水文序列,探讨小波分析中影响小波函数选择的因素,进而建立合理选择小波函数的依据和方法。该方法应用每个小波函数对水文序列进行小波分解,并重构得到低频重构序列和高频重构序列两部分及相应的特征值,依据相应的小波函数选择判别标准分析特征值,从而得到合理的小波函数。研究结果表明,序列自身的变化特性是小波函数选择的重要影响因素;整体上序列变化特性越复杂时,适用的小波函数类型就越少。对两个流域资料分析结果验证了本文的小波函数选择方法的合理性。

The Monte-Carlo method is applied to simulate the hydrologic series obtained from the Lijin Station, Yellow River Basin and a station in Beixi River Basin, Zhejiang Province, to investigate the factors affecting the selection of wavelet function for hydrologic series wavelet analysis and establish the method for reasonable selecting the wavelet function. The wavelet functions to be considered include common used 54 functions of 7 wavelet series. Each wavelet is applied to the series with different hydrological characteristic to decompose and derive the low frequency series and high frequency series through reconstruction. The statistical evaluation values of every reconstructed series are calculated These values are analyzed based on certain criteria to obtain the suitable wavelets. The study result shows that the variation characteristic of series is the key factor affecting the selection of wavelet, the more complicated the series is, the less number of suitable wavelet will be. The validity of the proposed method for wavelet selection is verified by the analysis result of the hydrologic data in these two river basins.