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Guide to Empirical Orthogonal Functions for Climate Data Analysis [Kõva köide]

  • Formaat: Hardback, 151 pages, kõrgus x laius: 235x155 mm, kaal: 890 g, VI, 151 p. With online files/update., 1 Hardback
  • Ilmumisaeg: 26-Feb-2010
  • Kirjastus: Springer
  • ISBN-10: 9048137012
  • ISBN-13: 9789048137015
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  • Formaat: Hardback, 151 pages, kõrgus x laius: 235x155 mm, kaal: 890 g, VI, 151 p. With online files/update., 1 Hardback
  • Ilmumisaeg: 26-Feb-2010
  • Kirjastus: Springer
  • ISBN-10: 9048137012
  • ISBN-13: 9789048137015
Teised raamatud teemal:

A Guide to Empirical Orthogonal Functions for Climate Data Analysis introduces the reader to a practical application of the methods used in the field, including data sets from climate simulations and MATLAB codes for the algorithms.



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

1 Introduction 1
2 Elements of Linear Algebra 5
2.1 Introduction
5
2.2 Elementary Vectors
5
2.3 Scalar Product
6
2.4 Linear Independence and Basis
10
2.5 Matrices
12
2.6 Rank, Singularity and Inverses
16
2.7 Decomposition of Matrices: Eigenvalues and Eigenvectors
17
2.8 The Singular Value Decomposition
19
2.9 Functions of Matrices
21
3 Basic Statistical Concepts 25
3.1 Introduction
25
3.2 Climate Datasets
25
3.3 The Sample and the Population
26
3.4 Estimating the Mean State and Variance
27
3.5 Associations Between Time Series
29
3.6 Hypothesis Testing
32
3.7 Missing Data
36
4 Empirical Orthogonal Functions 39
4.1 Introduction
39
4.2 Empirical Orthogonal Functions
42
4.3 Computing the EOFs
43
4.3.1 EOF and Variance Explained
44
4.4 Sensitivity of EOF Calculation
49
4.4.1 Normalizing the Data
50
4.4.2 Domain of Definition of the EOF
51
4.4.3 Statistical Reliability
55
4.5 Reconstruction of the Data
58
4.5.1 The Singular Value Distribution and Noise
59
4.5.2 Stopping Criterion
62
4.6 A Note on the Interpretation of EOF
64
5 Generalizations: Rotated, Complex, Extended and Combined EOF 69
5.1 Introduction
69
5.2 Rotated EOF
70
5.3 Complex EOF
79
5.4 Extended EOF
87
5.5 Many Field Problems: Combined EOF
90
6 Cross-Covariance and the Singular Value Decomposition 97
6.1 The Cross-Covariance
97
6.2 Cross-Covariance Analysis Using the SVD
99
7 The Canonical Correlation Analysis 107
7.1 The Classical Canonical Correlation Analysis
107
7.2 The Modes
109
7.3 The Barnett–Preisendorfer Canonical Correlation Analysis
114
8 Multiple Linear Regression Methods 123
8.1 Introduction
123
8.1.1 A Slight Digression
125
8.2 A Practical PRO Method
126
8.2.1 A Different Scaling
127
8.2.2 The Relation Between the PRO Method and Other Methods
128
8.3 The Forced Manifold
129
8.3.1 Significance Analysis
136
8.4 The Coupled Manifold
141
References 147
Index 149