Navarra / Simoncini A Guide to Empirical Orthogonal Functions for Climate Data Analysis

1. Auflage 2010
ISBN: 978-90-481-3702-2
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 151 Seiten

Climatology and meteorology have basically been a descriptive science until it became possible to use numerical models, but it is crucial to the success of the strategy that the model must be a good representation of the real climate system of the Earth. Models are required to reproduce not only the mean properties of climate, but also its variability and the strong spatial relations between climate variability in geographically diverse regions. Quantitative techniques were developed to explore the climate variability and its relations between different geographical locations. Methods were borrowed from descriptive statistics, where they were developed to analyze variance of related observations-variable pairs, or to identify unknown relations between variables. A Guide to Empirical Orthogonal Functions for Climate Data Analysis uses a different approach, trying to introduce the reader to a practical application of the methods, including data sets from climate simulations and MATLAB codes for the algorithms. All pictures and examples used in the book may be reproduced by using the data sets and the routines available in the book .Though the main thrust of the book is for climatological examples, the treatment is sufficiently general that the discussion is also useful for students and practitioners in other fields. Supplementary datasets are available via http://extra.springer.com

Autoren/Hrsg.

Navarra, Antonio

Simoncini, Valeria

Inhaltsverzeichnis

1;Contents;5
2;1 Introduction;7
3;2 Elements of Linear Algebra;10
3.1;2.1 Introduction;10
3.2;2.2 Elementary Vectors;10
3.3;2.3 Scalar Product;11
3.4;2.4 Linear Independence and Basis;15
3.5;2.5 Matrices;17
3.6;2.6 Rank, Singularity and Inverses;21
3.7;2.7 Decomposition of Matrices: Eigenvalues and Eigenvectors;22
3.8;2.8 The Singular Value Decomposition;24
3.9;2.9 Functions of Matrices ;26
4;3 Basic Statistical Concepts;29
4.1;3.1 Introduction;29
4.2;3.2 Climate Datasets;29
4.3;3.3 The Sample and the Population;30
4.4;3.4 Estimating the Mean State and Variance;31
4.5;3.5 Associations Between Time Series;33
4.6;3.6 Hypothesis Testing;36
4.7;3.7 Missing Data;40
5;4 Empirical Orthogonal Functions;42
5.1;4.1 Introduction;42
5.2;4.2 Empirical Orthogonal Functions;45
5.3;4.3 Computing the EOFs;46
5.3.1;4.3.1 EOF and Variance Explained;47
5.4;4.4 Sensitivity of EOF Calculation;52
5.4.1;4.4.1 Normalizing the Data;53
5.4.2;4.4.2 Domain of Definition of the EOF;54
5.4.3;4.4.3 Statistical Reliability;58
5.5;4.5 Reconstruction of the Data;61
5.5.1;4.5.1 The Singular Value Distribution and Noise;62
5.5.2;4.5.2 Stopping Criterion;65
5.6;4.6 A Note on the Interpretation of EOF;67
6;5 Generalizations: Rotated, Complex, Extended and Combined EOF;71
6.1;5.1 Introduction;71
6.2;5.2 Rotated EOF;72
6.3;5.3 Complex EOF;81
6.4;5.4 Extended EOF;89
6.5;5.5 Many Field Problems: Combined EOF;92
7;6 Cross-Covariance and the Singular Value Decomposition;99
7.1;6.1 The Cross-Covariance;99
7.2;6.2 Cross-Covariance Analysis Using the SVD;101
8;7 The Canonical Correlation Analysis;109
8.1;7.1 The Classical Canonical Correlation Analysis;109
8.2;7.2 The Modes;111
8.3;7.3 The Barnett–Preisendorfer Canonical Correlation Analysis;116
9;8 Multiple Linear Regression Methods;124
9.1;8.1 Introduction;124
9.1.1;8.1.1 A Slight Digression;126
9.2;8.2 A Practical PRO Method;127
9.2.1;8.2.1 A Different Scaling ;128
9.2.2;8.2.2 The Relation Between the PRO Methodand Other Methods;129
9.3;8.3 The Forced Manifold;130
9.3.1;8.3.1 Significance Analysis;137
9.4;8.4 The Coupled Manifold;142
10;References;148
11;Index;149