Empirical Orthogonal Function (EOF) analysis of spatial random fields: Theory, accuracy of the numerical approximations and sampling effects

1993 ◽  
Vol 7 (2) ◽  
pp. 146-160 ◽  
Author(s):  
I. Braud ◽  
Ch. Obled ◽  
A. Phamdinhtuan
Keyword(s):  
Empirical Orthogonal Function ◽  
Random Fields ◽  
Eof Analysis ◽  
Numerical Approximations ◽  
Orthogonal Function

scholarly journals Statistical characteristics of the total ion density in the topside ionosphere during the period 1996-2004 using empirical orthogonal function (EOF) analysis

2005 ◽  
Vol 23 (12) ◽  
pp. 3615-3631 ◽  
Author(s):  
B. Zhao ◽  
W. Wan ◽  
L. Liu ◽  
X. Yue ◽  
S. Venkatraman
Keyword(s):  
Empirical Orthogonal Function ◽  
Original Data ◽  
Statistical Characteristics ◽  
Topside Ionosphere ◽  
Eof Analysis ◽  
Data Set ◽  
Ion Density ◽  
Orthogonal Function ◽  
Solar Declination ◽  
Close Relationship

Abstract. We have applied the empirical orthogonal function (EOF) analysis to examine the climatology of the total ion density Ni at 840 km during the period 1996-2004, obtained from the Defense Meteorological Satellite Program (DMSP) spacecraft. The data set for each of the local time (09:30 LT and 21:30 LT) is decomposed into a time mean plus the sum of EOF bases Ei of space, multiplied by time-varying EOF coefficients Ai. Physical explanations are made on the first three EOFs, which together can capture more than 95% of the total variance of the original data set. Results show that the dominant mode that controls the Ni variability is the solar EUV flux, which is consistent with the results of Rich et al. (2003). The second EOF, associated with the solar declination, presents an annual (summer to winter) asymmetry that is caused by the transequatorial winds. The semiannual variation that appears in the third EOF for the evening sector is interpreted as both the effects of the equatorial electric fields and the wind patterns. Both the annual and semiannual variations are modulated by the solar flux, which has a close relationship with the O+ composition. The quick convergence of the EOF expansion makes it very convenient to construct an empirical model for the original data set. The modeled results show that the accuracy of the prediction depends mainly on the first principal component which has a close relationship with the solar EUV flux.

Significance test for empirical orthogonal function (EOF) analysis of meteorological and oceanic data

2000 ◽  
Vol 18 (1) ◽  
pp. 10-17 ◽  
Author(s):  
Li Xiao-feng ◽  
L. Pietrafesa ◽  
Lan Shu-fang ◽  
Xie Li-an
Keyword(s):  
Empirical Orthogonal Function ◽  
Significance Test ◽  
Eof Analysis ◽  
Orthogonal Function

Empirical Orthogonal Functions: The Medium is the Message

2009 ◽  
Vol 22 (24) ◽  
pp. 6501-6514 ◽  
Author(s):  
Adam H. Monahan ◽  
John C. Fyfe ◽  
Maarten H. P. Ambaum ◽  
David B. Stephenson ◽  
Gerald R. North
Keyword(s):  
Dimensionality Reduction ◽  
Data Compression ◽  
Empirical Orthogonal Function ◽  
Degrees Of Freedom ◽  
Empirical Orthogonal Functions ◽  
Eof Analysis ◽  
Orthogonal Functions ◽  
Entire Domain ◽  
Orthogonal Function

Abstract Empirical orthogonal function (EOF) analysis is a powerful tool for data compression and dimensionality reduction used broadly in meteorology and oceanography. Often in the literature, EOF modes are interpreted individually, independent of other modes. In fact, it can be shown that no such attribution can generally be made. This review demonstrates that in general individual EOF modes (i) will not correspond to individual dynamical modes, (ii) will not correspond to individual kinematic degrees of freedom, (iii) will not be statistically independent of other EOF modes, and (iv) will be strongly influenced by the nonlocal requirement that modes maximize variance over the entire domain. The goal of this review is not to argue against the use of EOF analysis in meteorology and oceanography; rather, it is to demonstrate the care that must be taken in the interpretation of individual modes in order to distinguish the medium from the message.

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