In several problems and in climate science a challenging task is to find ways to redue the dimensionality of the system and find the most important patterns explaining the variations.The purpose of EOF is to reduce the large number of

variables of the original data to a few variables, but without compromising most of the explained variance. In the last several decades, scientists have put several  efforts for extracting patterns from measurements of atmospheric variables.

EOF analysis has been used in climate science to extract individual modes of variability (teleconnections) such as the AO. The physical interpretability of the obtained patterns is a matter of controversy because of thestrong constraints satisfied by EOF, namely orthogonality in both space and time. Physic

al modes such as normal modes are not in general orthogonal. Auto- and cross-correlation in time between grid points are, also, ignored in this technique. Exte

nded EOFs has been developed to attempt incorporating both the spatial and the

temporal correlation. The method has since become a useful tool to extract dynamical structure, trends and oscillations, and to filter data.

Read for a good review this article:

Empirical orthogonal functions and related techniques in

atmospheric science: A review

Int. J. Climatol. 27: 1119 – 1152 (2007)

Regards

In addition to the above information, I would also recommend the standard book by Wilks which covers this subject:

https://www.elsevier.com/books/statistical-methods-in-the-atmospheric-sciences/wilks/978-0-12-385022-5

See chapter 12 in particular

Best

Adam