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This manual contains a fairly detailed discussion of two methods for analyzing the spatial and temporal variability of geophysical fields. They are the method of Empirical Orthogonal Functions (EOFs), also known as Principal Component Analysis (PCA), and the method of Singular Value Decomposition (SVD).
The description given here is by no means complete. Those who want a more detailed description should read some of the references. For the EOF/PCA method, the "big book" is Preisendorfer. It contains a wealth of information about the method, ranging from its history to detailed analyses of the method. For the SVD method the prime reference is the article by Bretherton et al., who compare several different methods for detecting coupled patterns between different components of the climate system. Another reference that everyone who is going to study climatic variability should be familiar with, is the text book edited by von Storch and Navarra. This book not only contains a review of methods for the analysis of patterns in geophysical fields, but has also examples of the application of those methods. The scope of the book is quite wide, and many methods not mentioned here are covered there thoroughly. Furthermore, the book contains an entertaining chapter on the misuse of statistical analysis in climate research. For readers with little experience in climatic data analyses, a very good introduction of the basic methods is given in the text book by Thiebaux.
All of the references mentioned above are fairly mathematical, and do not give detailed descriptions of how to perform the analyses. Thus these texts may be somewhat "unfriendly" for beginners. This manual is written for those who are beginning to use the EOF and SVD methods, and has the explicit aim of giving a step-by-step "How to do" recipe for the methods. For those wanting an intuitive understanding, we try to give hand-waving explanations of how the methods work. For beginners with mathematical inclinations we also include some mathematical results, but those should be easy for everyone familiar with matrix algebra. Those who do not care much for the mathematics can simply omit the sections that they feel are too mathematical.
As well as giving recipes for the methods, we also give Matlab scripts for them. Matlab is in many ways the ideal tool for matrix-based analysis methods. Matlab is a product of The MathWorks Company and is widely used among researchers in science and engineering. Matlab is not a free product, but there are several look-a-likes available for free over the Internet. Among these is Octave which is highly compatible with Matlab, and the French SciLab which is a comprehensive toolkit available for free from Institut National de Recherche en Informatique et en Automatique (INRIA). These packages are similar enough to Matlab so that the scripts given in the manual should be easily translated.