多变量EOF(MV-EOF)的多个fortran程序
多变量EOF(MV-EOF)由夏威夷大学气候学家王斌教授原创，属于最前沿的气候统计方法之一。气象家园亦有帖子寻找此类程序。现根据网页搜索的结果将多个有关程序提供于本帖。 来自夏威夷大学一研究者（已用MV-EOF发表论文）网页的程序未明确注明版权信息，作者应当是王斌教授指导的韩国女博士（Dr. June-Yi Lee (이준이) ）、合作者。王斌教授提出的另一方法——季节EOF(SEOF)暂未搜索到直接使用的程序。
MV-EOF 程序的应用价值是明显的，近几年国内外已有多篇方法应用类论文出现。
本人并未用过，只是介绍，有兴趣的网友可以进行一些对比性分析。
该程序的搜索过程并不容易，得来全需费功夫？
１.来源一 夏威夷大学June-Yi Lee女博士网页
从本帖所附的源程序中的下面一段语句“c PROGRAM OF GRID-CONVERTING FOR EQUAL-WEIGHTING WITH LATITUDE；c PROGRAMED BY **JUNE-YI LEE**； c LATEST REVISION : 12 MAY IN 2000”可以看出，June-Yi Lee博士即使不是全部，但至少参与了该程序的部分研制工作。
June-Yi Lee 博士的最近研究论文：***Lee, June-Yi and Bin Wang, 2012: Future change of global monsoon precipitation in the CMIP5\. Clim Dyn on-line first. Doi:10.1007/s00382-012-1564-0***
原页面标题：Multi-variate EOF analysis using daily OLR and U850 anomalies
Fortran code for EOF analysis（见于本文附件）
Fortran code for projection of model output (or observed data) onto the BSISO EOFs
Text file of Normalized Time Series for the BSISO1 and BSISO2 index
| PARA.STEP.H |
| S2.DAY.NORM.CTL |
| S2.DAY.NORM.GDAT |
| STEP1.f90 |
| STEP2.f90 |
| STEP3.f90 |
２.来源二 国内某网站网页（见于附件“EOF分析(据称，略作变换可做MV-EOF、SEOF).f”
３.来源三 网页对于方法的介绍名称为“Spatial structures of leading multivariate (combined) EOFs”，字面上也是“MV-EOF”，程序链接见于帖子内容中。
** Method for obtaining EOF structures**
We performed EOF analysis on the combined daily fields of equatorially-averaged (15°S to 15°N) OLR, 850hPa zonal wind, and 200 hPa zonal wind for the period of 1979 to 2001 (23 years). We did this on the covariance matrix with each field normalized by the square-root of its global mean variance first. This is necessary so that each field contributes the same amount of variance to the combined field. Before the EOF analysis, however, we also performed the following:
- Remove the long-term mean and climatological seasonal cycle (3 harmonics) from each field at each grid-point.
- Remove the variability associated with El Nino (that which is linearly related the ENSO SST1 index).
- Remove a 120-day mean of the most recent 120 days at each point..
All of these steps can be performed in real-time and are important for removing aspects of low frequency variability that can have spatial structures like that of the MJO.An ASCII file containing the EOF spatial structures and code for projecting model or observed data onto them is obtainable fromhere.
projectRMM1RMM2.f - Fortran code for computing the projection of model output (or observed data) onto the Wheeler-Hendon EOFs.
WH04_EOFstruc.txt- ASCII file containing the Wheeler-Hendon EOFs.
** The Index: RMM1 and RMM2**
Based on the first two Empirical Orthogonal Functions (EOFs) of the combined fields of near-equatorially-averaged 850 hPa zonal wind, 200 hPa zonal wind, and satellite-observed outgoing longwave radiation (OLR) data. Projection of the daily observed data onto such multiple-variable EOFs, with the annual cycle and components of interannual variability removed, yields principal component (PC) time series that vary mostly on the intraseasonal time scale of the MJO only. This projection thus serves as an effective filter for the MJO without the need for time filtering, making the PC time series an effective index for real time use. We call the two PC time series that form the index the Real-time Multivariate MJO series 1 (RMM1), and RMM2. For the observations, the OLR data is that measured by the NOAA polar-orbitting satellites, while for the winds we use the NCEP/NCAR Reanalyses and the NCEP Operational analyses. The index is usually available in near real time about 12 hours after the end of each Greenwich day (i.e. at about 1200 UTC). For more details, see Wheeler and Hendon (2004).
- Spatial structures of leading multivariate (combined) EOFs
- Code for projecting model/observed data onto RMM EOFs
４.来源四（无程序，仅有论文，见附件）
顺便指出，尽管多篇文献说明多变量EOF(MV-EOF)由夏威夷大学气候学家王斌教授1992年首先使用，但方法的名称可能并不是一致认可的。一篇名为《Multivariate Empirical Orthogonal Function analysis of the upper thermocline structure of the Mediterranean Sea from observations and model simulations》（Annales Geophysicae (2003) 21: 167–187 European Geosciences Union 2003）》的文献并未提到王斌教授1992年的论文，该文在方法介绍部分使用的是“Multivariate vertical EOF”，与王斌教授方法的具体差异我并不清楚。
附： 多变量EOF（MV-EOF）（转载）
EOF分析时，不仅会研究某一要素的时空特征，有时也会研究某现象的时空特征，而这些现象往往不能用单一的要素来表征，这时候就需要用到了多变量的EOF。
例如，研究海洋大陆的季风系统时空变化特征，很可能要考虑到850hPa风场、SST、和降水，此时只需要在EOF导入数据的时候将数组空间的维数扩大三倍就可以了，将数据按要素分别存入，运算完之后按照存入的顺序提取三个场，这三个场共用一个时间系数。当然这样做的时候一般也就只分析时间系数的特征了。很多人提到的风场的矢量EOF和王斌先生提出的季节EOF都是多变量EOF的特殊应用。
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