A Guide to Empirical Orthogonal Functions for Climate Data Analysis (eBook)

Antonio Navarra, Valeria Simoncini (Autoren)

eBook Download: PDF

2010 | 2010
VI, 151 Seiten
Springer Netherland (Verlag)
978-90-481-3702-2 (ISBN)

Infos

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

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 5.4.2010
• Zusatzinfo: VI, 151 p.
• Verlagsort: Dordrecht
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Naturwissenschaften ► Biologie ► Ökologie / Naturschutz
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Geologie
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Meteorologie / Klimatologie
• Themenwelt: Technik
• Schlagworte: climate change • Climate Diagnostics • Climate modeling • climatology • Data Analysis • descriptive statistics • linear regression • MATLAB • meteorology • Principal Component Analysis • Statistics
• ISBN-10: 90-481-3702-0 / 9048137020
• ISBN-13: 978-90-481-3702-2 / 9789048137022