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墨西哥帽小波变换的影响域和计算方案新探讨
引用本文:谷德军,王东晓,纪忠萍,郑彬.墨西哥帽小波变换的影响域和计算方案新探讨[J].应用气象学报,2009,20(1):62-69.
作者姓名:谷德军  王东晓  纪忠萍  郑彬
作者单位:1.中国气象局广州热带海洋气象研究所热带季风重点开放实验室, 广州 510080
基金项目:国家自然科学基金,中国气象局实验室开放课题 
摘    要:该文分析了Torrence等人研究的墨西哥帽 (Mexican Hat) 小波变换的影响域和高频失真问题并探讨了解决方案。平移点b处、小波尺度为a的墨西哥帽小波函数的有效定义域为 b-2.12a, b+2.12a], 以墨西哥帽为母函数的小波变换的真正影响域是2.12a, 小波尺度a的最大值应为N/4.24(N为时间序列长度)。提出了充分利用小波函数速降性质和立方样条插值小波系数的新计算方案, 消除了该计算方案产生虚假的显著高频周期振荡问题。利用正弦函数型时间序列小波变换的解析式检验了文中提出的新计算方案的合理性。利用新计算方案对冬季Ni?o3.4指数进行分析, 冬季Ni?o3.4指数的平均整体小波功率谱表明, 存在约12年的年代际变化和准4年的年际变化, 不存在显著的准两年周期振荡。

关 键 词:小波变换    影响域    计算方案    Ni?o3.4指数
收稿时间:2007-07-23

New Research on Cone of Influence and Computing Scheme of Mexican Hat Wavelet Transform
Gu Dejun,Wang Dongxiao,Ji Zhongping and Zheng Bin.New Research on Cone of Influence and Computing Scheme of Mexican Hat Wavelet Transform[J].Quarterly Journal of Applied Meteorology,2009,20(1):62-69.
Authors:Gu Dejun  Wang Dongxiao  Ji Zhongping and Zheng Bin
Affiliation:1.Key Open Laboratory for Tropical Monsoon, Guangzhou Institute of Tropical and Marine Meteorology, CMA, Guangzhou 5100802.LED, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou 5103013.Guangzhou Central Meteorological Observatory, Guangzhou 510080
Abstract:Using the effective domain of wavelet function, the problems of cone of influence (COI) and high-frequency distortion of Mexican Hat wavelet transform in the paper of Torrence and Compo (1998) are analyzed and the solution are explored. The analytic expressions of wavelet coefficient and global wavelet power spectrum for time series of sinusoid and the relationship between period and wavelet scale are deduced. The effective domain of Mexican Hat wavelet transform is b-2.12a, b+2.12a] for localized time b and wavelet scale a. The authentic cone of influence for Mexican Hat wavelet transform is 2.12a. The maximum value of wavelet scale is N/4.24 (N is the length of time series). When wavelet scale approaches zero, wavelet function is singular. So the simple sum scheme replacing the integration for wavelet coefficient does not include the singularity of wavelet function, therefore the pseudo high-frequency oscillation is deduced. A new computing scheme for wavelet coefficient is designed. The major elements include improved-resolution and located time b in the new grids. The difference of effective domain of wavelet function for small different wavelet scales can be distinguished by the improved-resolution. Located time b has great contribution to its wavelet coefficient because the wavelet function is the biggest at the located point b. The pseudo significant high-frequency oscillation that is produced by the computing scheme proposed by Torrence and Compo (1998) can be eliminated by the new computing scheme of wavelet coefficient, well using sharply descending characteristics of wavelet function and cubic spline interpolation. The rationality of new computing scheme is tested by the analytic solution of wavelet transform of sinusoid time sequence. The global wavelet power spectrum from the new computing scheme indicates that the variability of winter Ni?o3.4 index exhibits interdecadal oscillation of about 12 years and interannual oscillation of quasi-four years, and no significant quasi-biennial oscillation. The questions of cone of influence and pseudo high-frequency oscillation have two adverse aftermaths. First is that the correct judgment of interdecadal variation can be affected and second is that pseudo quasi-biennial variation can be deduced. Therefore, the results about COI and the new computing scheme for wavelet coefficient make the conclusions induced from wavelet analysis more credible.
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