Empirical Orthogonal Functions The Medium is the Message

• Published in: Journal of climate Vol. 22; no. 24; pp. 6501 - 6514
• Main Authors: Monahan, Adam H., Fyfe, John C., Ambaum, Maarten H. P., Stephenson, David B., North, Gerald R.
• Format: Journal Article
• Language: English
• Published: Boston, MA American Meteorological Society 15.12.2009
• Subjects: Atmospherics; Climate science; Compression; Data compression; Dictionaries; Earth, ocean, space; Eigenvalues; Eigenvectors; Empirical analysis; Empirical orthogonal functions; Exact sciences and technology; External geophysics; General circulation models; Kinematics; Linear algebra; Marine; Mathematical vectors; Meteorology; Modes; Oceanography; Orthogonal functions; Physical oceanography; REVIEW; Statistical mode; Statistical variance; Statistics; Time series; Variance analysis; Empirical orthogonal function; Variance; Review
• ISSN: 0894-8755; 1520-0442
• DOI: 10.1175/2009jcli3062.1

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.