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气候变化研究中复Hermite 矩阵解的统计和物理意义
引用本文:彭茹,张小群.气候变化研究中复Hermite 矩阵解的统计和物理意义[J].气象科技,2008,36(4):385-388.
作者姓名:彭茹  张小群
作者单位:中国气象局培训中心远程部,北京,100081
摘    要:复经验正交分析在气象学和海洋学研究领域有着广泛的应用,其核心部分就是求解复Hermite矩阵的特征值、复特征向量和复主成分.但是,在以往的研究中,并没有讨论复Hermite矩阵解的统计和物理意义.研究证明,复Hermite矩阵的特征值反映了方差贡献、异常能量,复特征向量本身并没有明确的物理意义,而有明确的统计意义.但是复主成分有清晰的物理意义.并且其实部和虚部不是独立的.因此,在研究二维矢量场变化的优势模态时,只能使用一维线性回归分析方法.

关 键 词:复经验正交分析  复HerlTlite矩阵  气候变化
收稿时间:2007/4/13 0:00:00
修稿时间:6/6/2007 12:00:00 AM

Statistical and Physical Significances of Resolution of Complex Hermite Matrix in Climate Change Studies
Peng Ru and Zhang Xiaoqun.Statistical and Physical Significances of Resolution of Complex Hermite Matrix in Climate Change Studies[J].Meteorological Science and Technology,2008,36(4):385-388.
Authors:Peng Ru and Zhang Xiaoqun
Institution:CMA Training Center, Beijing 100081;CMA Training Center, Beijing 100081
Abstract:The complex Empirical Orthogonal Function (CEOF) analysis has been extensively used in the meteorological and oceanic fields, and the key part of this method is to extract eigenvalues, eigenvectors, and complex principal components from a Hermite matrix. In previous studies, however, no one explores statistical and physical significances of the resolution of a Hermite Matrix. It is demonstrated that the eigenvalues of a complex Hermite Matrix represent variance contribution or anomalous energy, and eigenvectors have clear statistical significances and no apparent physical significances. In contrast, a complex principal component has a clear physical significance, and their real and imaginary parts are related to each other. Thus, the dimensional linear regression method can be used to extract predominant modes of vector variability.
Keywords:complex empirical orthogonal function  complex Hermite matrix  climate change
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