水文序列噪声成分小波特性的揭示与描述

Description of the wavelet characters of noises in hydrologic series data

噪声成分对水文序列的真实变化特性产生了很大的干扰和影响,因此研究噪声对水文时间序列分析具有重要的意义.本文应用离散小波变换时常用的7个小波系共53个小波函数,对水文序列中噪声成分(包括正态分布、对数正态分布和P-Ⅲ型分布)的小波特性进行了系统的分析和研究.结果显示,依据小波系数幅值随时间尺度水平增大时的变化规律(近似相等、递减和递增),总体上可将小波函数分为3类.然后通过蒙特卡罗(Monte-Carlo)试验,对各类噪声序列对应不同时间尺度水平上小波系数均值、绝对值最大值和极值绝对值平均值的概率分布特性及变化规律进行了揭示和定量描述.最后通过对噪声小波特性进行分析和讨论,得到了关于水文序列小波阈值消噪的若干认识和建议,以提高水文序列小波分析结果的准确性和可靠性.

Noise is an inevitable part of natural existences and has great influence on the real characteristics of observed hydrologic series data,therefore research on noise is the substantial issue in hydrologic series data analysis,mainly to improve the analytic results and to provide reliable hydrologic guidance to various practical water activities.In the present paper,all the 53 wavelet basis functions（WBFs） in 7 wavelet series,which are used commonly in the process of discrete wavelet transform（DWT）,were used to reveal the wavelet characters of noises following the normal,lognormal and Pearson-III（P-III） probability distributions.Analytic results of various synthetic noise series indicate that the 53 WBFs can be divided into three types,by using which the varying rules of noises＇ wavelet coefficients are similar,increasing and decreasing with the increasing of decomposition levels respectively.Furthermore,the Monte-Carlo（MC） test was operated to identify and quantitatively describe the probability distributions and varying rules of three quantitative indexes of noises＇ wavelet coefficients,namely average value（AV）,absolute maximum value（AMV） and average absolute extreme value（AAEV） respectively.Finally,the results of MC test were discussed in detail and summarized,and a set of understanding and suggestions on the wavelet threshold de-noising were obtained;they include the issues of choice of wavelet basis function,reasonability of thresholding rules,estimation of thresholds,the relations of thresholds under different decomposition levels and the applicability of wavelet threshold de-noising method.In conclusion,the analytic process of hydrologic series data by wavelet analysis has reliable basis and the results can be improved based on these suggestions.