改进的奇异值分解方法及其效果验证
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公益性行业(气象)科研专项经费项目(GYHY200806009;GYHY201006017;GYHY201006020);国家科技支撑计划项目(2010CB951601)


Advanced singular value decomposition and its effect verification
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    摘要:

    改进的奇异值分解(advanced singular value decomposition,ASVD)方法,是对经过空间均匀化订正的格、站点网资料的奇异值分解(singular value decomposition,SVD)方法。根据奇异向量与经验正交函数(empirical orthogonal function,EOF)的关系,给出了格、站点网资料SVD方法中均匀化订正的方法,进而得到了改进的奇异值分解(ASVD)方法。将ASVD方法、SVD方法用于中国60 a(1951—2010年)160站冬季气温、降水同期相关系数矩阵C的分析,结果表明:ASVD方法的前4个主要模态的模方拟合率和累积模方拟合率均明显高于SVD方法;ASVD方法前两个奇异向量典型场图上高绝对值区与C模方图上高值区的关系明显较SVD方法合理。由此论证了SVD方法中资料均匀化订正的必要性,验证了实际分析中ASVD方法的效果。

    Abstract:

    The advanced singular value decomposition(ASVD) method is the singular value decomposition(SVD) method of homogeneity adjustment for the grid and station network data.Based on the relationship between SVD and EOF(empirical orthogonal function),it gives a homogeneity adjustment method of the grid and station network data in SVD method,in such a way that the advanced singular value decomposition(ASVD) method is achieved.Using the ASVD and SVD methods,this paper analyzes the correlation coefficient matrix C. between temperature and precipitation of 160 stations over China in winter during 1951—2010.Results show that both the squarefitting rate and the accumulated squarefitting rate of the preceding four principal modes by ASVD method are obviously higher than those by SVD method.Comparing with SVD method,the relationship between the high value area in C squarefitting figure and the high absolute value area in the preceding two typical singular vector fields by using the ASVD method is more reasonable.It is verified that the homogeneity adjustment is necessary by using the SVD method,and there is more reasonable effect in practical analysis by using the ASVD method.

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谢瑶瑶,王盘兴,李丽平,周国华,罗小莉,2013.改进的奇异值分解方法及其效果验证[J].大气科学学报,36(4):466-471.
XIE Yao-yao, WANG Pan-xing, LI Li-ping, ZHOU Guo-hua, LUO Xiao-li,2013. Advanced singular value decomposition and its effect verification[J]. Trans Atmos Sci,36(4):466-471.

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  • 收稿日期:2012-03-14
  • 最后修改日期:2012-10-15
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