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Orthogonality properties of rotated empirical modes
Author(s) -
MestasNuñez Alberto M.
Publication year - 2000
Publication title -
international journal of climatology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.58
H-Index - 166
eISSN - 1097-0088
pISSN - 0899-8418
DOI - 10.1002/1097-0088(200010)20:12<1509::aid-joc553>3.0.co;2-q
Subject(s) - orthogonality , empirical orthogonal functions , rotation (mathematics) , eigenvalues and eigenvectors , uncorrelated , normalization (sociology) , mathematics , mode (computer interface) , statistical physics , geometry , physics , statistics , computer science , quantum mechanics , sociology , anthropology , operating system
The properties (spatial orthogonality and temporal uncorrelatedness) of orthogonally rotated empirical modes depend on the normalization of the modes, prior to rotation. It is shown here that these properties also depend on how the empirical modes are formulated. The preferred convention is one that allows us to reconstruct the data from the unrotated or rotated modes. When the empirical modes are normalized so that the spatial eigenvectors are unit length (i.e. empirical orthogonal functions (EOFs)), the rotated modes preserve spatial orthogonality, but are no longer temporally uncorrelated. Relaxing the temporal orthogonality in this way does not prejudice conclusions that can be inferred regarding the temporal couplings of the rotated modes. Copyright © 2000 Royal Meteorological Society