# Interpretation of Extended Empirical Orthogonal Function (EEOF) Analysis

Jeng-Ming Chen Department of Meteorology, Naval Postgraduate School, Monterey, California

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Patrick A. Harr Department of Meteorology, Naval Postgraduate School, Monterey, California

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## Abstract

Application of an empirical orthogonal function (EOF) analysis to a data matrix that contains two or more variable fields has been referred to as extended EOF (EEOF) analysis. Coherence between individual features contained within one EEOF has been implied to represent interrelationships between the fields (in the case of a combination of different variables) or propagating features (in the case of the same field at different times). However, caution must be exercised in the interpretation of interrelationships within one EEOF because the derivation of the EEOFs is based on the optimization of the variance of every EEOF as an entity and may not indicate correlations among substructures within one EEOF. These types of problems associated with interpretation of EEOF analyses are highlighted through an analytic example and application to a dataset with known statistical properties.

Although other multivariate analysis techniques such as singular value decomposition and canonical correlation analysis are being used with more frequency, it is important to highlight potential difficulties associated with the EEOF technique that has been an integral analysis tool in meteorological research.

## Abstract

Application of an empirical orthogonal function (EOF) analysis to a data matrix that contains two or more variable fields has been referred to as extended EOF (EEOF) analysis. Coherence between individual features contained within one EEOF has been implied to represent interrelationships between the fields (in the case of a combination of different variables) or propagating features (in the case of the same field at different times). However, caution must be exercised in the interpretation of interrelationships within one EEOF because the derivation of the EEOFs is based on the optimization of the variance of every EEOF as an entity and may not indicate correlations among substructures within one EEOF. These types of problems associated with interpretation of EEOF analyses are highlighted through an analytic example and application to a dataset with known statistical properties.

Although other multivariate analysis techniques such as singular value decomposition and canonical correlation analysis are being used with more frequency, it is important to highlight potential difficulties associated with the EEOF technique that has been an integral analysis tool in meteorological research.

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