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A Guide to Empirical Orthogonal Functions for Climate Data Analysis

DOI: 10.1007/978-90-481-3702-2

ISBN: 978-90-481-3701-5

Publisher: Springer Netherlands - Springer Journals

Nov 27, 2009

Available

Introduction

Navarra, Antonio; Simoncini, Valeria

Pages: 1 –3

[Climatology and meteorology has been basically a descriptive science without the means to perform quantitative experiments under controlled conditions. In fact, until the second half of the twentieth century, the border between climatology and geography was often blurred and the two disciplines...
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Elements of Linear Algebra

Navarra, Antonio; Simoncini, Valeria

Pages: 5 –23

[This book will use some basic concepts of linear algebra. In this chapter we will briefly recall the essential elements that will be necessary in the rest of the book to understand the various tools devoted to the analysis of variance. Readers that are interested in the more detailed treatment...
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Basic Statistical Concepts

Navarra, Antonio; Simoncini, Valeria

Pages: 25 –37

[A key scientific challenge is to better understand the functioning of the environment. Informed analysis of observations can make a strong contribution to this goal. The most insightful analysis requires knowledge of the relevant environmental processes and of statistical methodologies, that can...
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Empirical Orthogonal Functions

Navarra, Antonio; Simoncini, Valeria

Pages: 39 –67

[The atmospheric fields are three-dimensional fields by nature, the variation in longitude, latitude and altitude of winds, temperatures and the other quantities are normal. A major jump forward in the development of climate science was reached when it was realized that the analysis of...
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Generalizations: Rotated, Complex, Extended and Combined EOF

Navarra, Antonio; Simoncini, Valeria

Pages: 69 –96

[We have seen in the last section that the difficulty in identifying real physical patterns from EOF stems from their orthogonal nature. Orthogonality translates into the fact that typical patterns appear in secondary (higher order) EOF. Very often the first EOF has little structure, the second...
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Cross-Covariance and the Singular Value Decomposition

Navarra, Antonio; Simoncini, Valeria

Pages: 97 –106

[At the end of the previous chapter we have introduced the concept of the simultaneous analysis of different fields. We have introduced the Combined EOF that, after a suitable scaling, allow us to produce patterns of variability that reflect the covariance properties of different data types. This...
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The Canonical Correlation Analysis

Navarra, Antonio; Simoncini, Valeria

Pages: 107 –121

[The method based on the Singular Value Decomposition described in previous chapters was able to represent the largest amount of cross-covariance with fewest modes. The computed modes are designed so as to specifically explain most of the spatial variance. The spatial view point is a requirement...
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Multiple Linear Regression Methods

Navarra, Antonio; Simoncini, Valeria

Pages: 123 –146

[In the previous chapters we have introduced techniques to find relations between two or more different fields. In this chapter we describe a more general framework that may provide additional insight into previously analyzed methods. In general a relation between fields can be formulated...

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