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Umfang: 1 Online-Ressource (xxiv, 600 Seiten) , Illustrationen

ISBN: 9783030670733 , 978-3-030-67073-3

ISSN: 2194-5217 , 2194-5225

Serie: Springer atmospheric sciences

Inhalt: Advances in computer power and observing systems has led to the generation and accumulation of large scale weather & climate data begging for exploration and analysis. Pattern Identification and Data Mining in Weather and Climate presents, from different perspectives, most available, novel and conventional, approaches used to analyze multivariate time series in climate science to identify patterns of variability, teleconnections, and reduce dimensionality. The book discusses different methods to identify patterns of spatiotemporal fields. The book also presents machine learning with a particular focus on the main methods used in climate science. Applications to atmospheric and oceanographic data are also presented and discussed in most chapters. To help guide students and beginners in the field of weather & climate data analysis, basic Matlab skeleton codes are given is some chapters, complemented with a list of software links toward the end of the text. A number of technical appendices are also provided, making the text particularly suitable for didactic purposes. The topic of EOFs and associated pattern identification in space-time data sets has gone through an extraordinary fast development, both in terms of new insights and the breadth of applications. We welcome this text by Abdel Hannachi who not only has a deep insight in the field but has himself made several contributions to new developments in the last 15 years. - Huug van den Dool, Climate Prediction Center, NCEP, College Park, MD, U.S.A. Now that weather and climate science is producing ever larger and richer data sets, the topic of pattern extraction and interpretation has become an essential part. This book provides an up to date overview of the latest techniques and developments in this area. - Maarten Ambaum, Department of Meteorology, University of Reading, U.K. This nicely and expertly written book covers a lot of ground, ranging from classical linear pattern identification techniques to more modern machine learning, illustrated with examples from weather & climate science. It will be very valuable both as a tutorial for graduate and postgraduate students and as a reference text for researchers and practitioners in the field. - Frank Kwasniok, College of Engineering, University of Exeter, U.K.

Anmerkung: Contents 1 Introduction 1.1 Complexity of the Climate System 1.2 Data Exploration, Data Mining and Feature Extraction 1.3 Major Concern in Climate Data Analysis 1.3.1 Characteristics of High-Dimensional Space Geometry 1.3.2 Curse of Dimensionality and Empty Space Phenomena 1.3.3 Dimension Reduction and Latent Variable Models 1.3.4 Some Problems and Remedies in Dimension Reduction 1.4 Examples of the Most Familiar Techniques 2 General Setting and Basic Terminology 2.1 Introduction 2.2 Simple Visualisation Techniques 2.3 Data Processing and Smoothing 2.3.1 Preliminary Checking 2.3.2 Smoothing 2.3.3 Simple Descriptive Statistics 2.4 Data Set-Up 2.5 Basic Notation/Terminology 2.5.1 Centring 2.5.2 Covariance Matrix 2.5.3 Scaling 2.5.4 Sphering 2.5.5 Singular Value Decomposition 2.6 Stationary Time Series, Filtering and Spectra 2.6.1 Univariate Case 2.6.2 Multivariate Case 3 Empirical Orthogonal Functions 3.1 Introduction 3.2 Eigenvalue Problems in Meteorology: Historical Perspective 3.2.1 The Quest for Climate Patterns: Teleconnections 3.2.2 Eigenvalue Problems in Meteorology 3.3 Computing Principal Components 3.3.1 Basis of Principal Component Analysis 3.3.2 Karhunen–Loéve Expansion 3.3.3 Derivation of PCs/EOFs 3.3.4 Computing EOFs and PCs 3.4 Sampling, Properties and Interpretation of EOFs 3.4.1 Sampling Variability and Uncertainty 3.4.2 Independent and Effective Sample Sizes 3.4.3 Dimension Reduction 3.4.4 Properties and Interpretation 3.5 Covariance Versus Correlation 3.6 Scaling Problems in EOFs 3.7 EOFs for Multivariate Normal Data 3.8 Other Procedures for Obtaining EOFs 3.9 Other Related Methods 3.9.1 Teleconnectivity 3.9.2 Regression Matrix 3.9.3 Empirical Orthogonal Teleconnection 3.9.4 Climate Network-Based Methods 4 Rotated and Simplified EOFs 4.1 Introduction 4.2 Rotation of EOFs 4.2.1 Background on Rotation 4.2.2 Derivation of REOFs 4.2.3 Computing REOFs 4.3 Simplified EOFs: SCoTLASS 4.3.1 Background 4.3.2 LASSO-Based Simplified EOFs 4.3.3 Computing the Simplified EOFs 5 Complex/Hilbert EOFs 5.1 Background 5.2 Conventional Complex EOFs 5.2.1 Pairs of Scalar Fields 5.2.2 Single Field 5.3 Frequency Domain EOFs 5.3.1 Background 5.3.2 Derivation of FDEOFs 5.4 Complex Hilbert EOFs 5.4.1 Hilbert Transform: Continuous Signals 5.4.2 Hilbert Transform: Discrete Signals 5.4.3 Application to Time Series 5.4.4 Complex Hilbert EOFs 5.5 Rotation of HEOFs 6 Principal Oscillation Patterns and Their Extension 6.1 Introduction 6.2 POP Derivation and Estimation 6.2.1 Spatial Patterns 6.2.2 Time Coefficients 6.2.3 Example 6.3 Relation to Continuous POPs 6.3.1 Basic Relationships 6.3.2 Finite Time POPs 6.4 Cyclo-Stationary POPs 6.5 Other Extensions/Interpretations of POPs 6.5.1 POPs and Normal Modes 6.5.2 Complex POPs 6.5.3 Hilbert Oscillation Patterns 6.5.4 Dynamic Mode Decomposition 6.6 High-Order POPs 6.7 Principal Interaction Patterns 7 Extended EOFs and SSA 7.1 Introduction 7.2 Dynamical Reconstruction and SSA 7.2.1 Background 7.2.2 Dynamical Reconstruction and SSA 7.3 Examples 7.3.1 White Noise 7.3.2 Red Noise 7.4 SSA and Periodic Signals 7.5 Extended EOFs or Multivariate SSA 7.5.1 Background 7.5.2 Definition and Computation of EEOFs 7.5.3 Data Filtering and Oscillation Reconstruction 7.6 Potential Interpretation Pitfalls 7.7 Alternatives to SSA and EEOFs 7.7.1 Recurrence Networks 7.7.2 Data-Adaptive Harmonic Decomposition 8 Persistent, Predictive and Interpolated Patterns 8.1 Introduction 8.2 Background on Persistence and Prediction of Stationary Time Series 8.2.1 Decorrelation Time 8.2.2 The Prediction Problem and Kolmogorov Formula 8.3 Optimal Persistence and Average Predictability 8.3.1 Derivation of Optimally Persistent Patterns 8.3.2 Estimation from Finite Samples 8.3.3 Average Predictability Patterns 8.4 Predictive Patterns 8.4.1 Introduction 8.4.2 Optimally Predictable Patterns 8.4.3 Computational Aspects 8.5 Optimally Interpolated Patterns 8.5.1 Background 8.5.2 Interpolation and Pattern Derivation 8.5.3 Numerical Aspects 8.5.4 Application 8.6 Forecastable Component Analysis 9 Principal Coordinates or Multidimensional Scaling 9.1 Introduction 9.2 Dissimilarity Measures 9.3 Metric Multidimensional Scaling 9.3.1 The Problem of Classical Scaling 9.3.2 Principal Coordinate Analysis 9.3.3 Case of Non-Euclidean Dissimilarity Matrix 9.4 Non-metric Scaling 9.5 Further Extensions 9.5.1 Replicated and Weighted MDS 9.5.2 Nonlinear Structure 9.5.3 Application to the Asian Monsoon 9.5.4 Scaling and the Matrix Nearness Problem 10 Factor Analysis 10.1 Introduction 10.2 The Factor Model 10.2.1 Background 10.2.2 Model Definition and Terminology 10.2.3 Model Identification 10.2.4 Non-unicity of Loadings 10.3 Parameter Estimation 10.3.1 Maximum Likelihood Estimates 10.3.2 Expectation Maximisation Algorithm 10.4 Factor Rotation 10.4.1 Oblique and Orthogonal Rotations 10.4.2 Examples of Rotation Criteria 10.5 Exploratory FA and Application to SLP Anomalies 10.5.1 Factor Analysis as a Matrix Decomposition Problem 10.5.2 A Factor Rotation 10.6 Basic Difference Between EOF and Factor Analyses 10.6.1 Comparison Based on the Standard Factor Model 10.6.2 Comparison Based on the Exploratory Factor Analysis Model 11 Projection Pursuit 11.1 Introduction 11.2 Definition and Purpose of Projection Pursuit 11.2.1 What Is Projection Pursuit? 11.2.2 Why Projection Pursuit? 11.3 Entropy and Structure of Random Variables 11.3.1 Shannon Entropy 11.3.2 Differential Entropy 11.4 Types of Projection Indexes 11.4.1 Quality of a Projection Index 11.4.2 Various PP Indexes 11.4.3 Practical Implementation 11.5 PP Regression and Density Estimation 11.5.1 PP Regression 11.5.2 PP Density Estimation 11.6 Skewness Modes and Climate Application of PP 12 Independent Component Analysis 12.1 Introduction 12.2 Background and Definition 12.2.1 Blind Deconvolution 12.2.2 Blind Source Separation 12.2.3 Definition of ICA 12.3 Independence and Non-normality 12.3.1 Statistical Independence 12.3.2 Non-normality 12.4 Information-Theoretic Measures 12.4.1 Entropy 12.4.2 Kullback–Leibler Divergence 12.4.3 Mutual Information 12.4.4 Negentropy 12.4.5 Useful Approximations 12.5 Independent Component Estimation 12.5.1 Choice of Objective Function for ICA 12.5.2 Numerical Implementation 12.6 ICA via EOF Rotation and Weather and Climate Application 12.6.1 The Standard Two-Way Problem 12.6.2 Extension to the Three-Way Data 12.7 ICA Generalisation: Independent Subspace Analysis 13 Kernel EOFs 13.1 Background 13.2 Kernel EOFs 13.2.1 Formulation of Kernel EOFs 13.2.2 Practical Details of Kernel EOF Computation 13.2.3 Illustration with Concentric Clusters 13.3 Relation to Other Approaches 13.3.1 Spectral Clustering 13.3.2 Modularity Clustering 13.4 Pre-images in Kernel PCA 13.5 Application to An Atmospheric Model and Reanalyses 13.5.1 Application to a Simplified Atmospheric Model 13.5.2 Application to Reanalyses 13.6 Other Extensions of Kernel EOFs 13.6.1 Extended Kernel EOFs 13.6.2 Kernel POPs 14 Functional and Regularised EOFs 14.1 Functional EOFs 14.2 Functional PCs and Discrete Sampling 14.3 An Example of Functional PCs from Oceanography 14.4 Regularised EOFs 14.4.1 General Setting 14.4.2 Case of Spatial Fields 14.5 Numerical Solution of the Full Regularised EOF Problem 14.6 Application of Regularised EOFs to SLP Anomalies 15 Methods for Coupled Patterns 15.1 Introduction 15.2 Canonical Correlation Analysis 15.2.1 Background 15.2.2 Formulation of CCA 15.2.3 Computational Aspect 15.2.4 Regularised CCA 15.2.5 Use of Correlation Matrices 15.3 Canonical Covariance Analysis 15.4 Redundancy Analysis 15.4.1 Redundancy Index 15.4.2 Redundancy Analysis 15.5 Application: Optimal Lag Between Two Fields and Other Extensions 15.5.1 Application of CCA 15.5.2 Application of Redundancy 15.6 Principal Predictors 15.7 Extension: Functional Smooth CCA 15.7.1 Introduction 15.7.2 Functional Non-smooth CCA and Indeterminacy 15.7.3 Smooth CCA/MCA 15.7.4 Application of SMCA to Space–Time Fields 15.8 Some Points on Coupled Patterns and Multiva

Sprache: Englisch

Schlagwort(e): Electronic books ; Lehrbuch

DOI: 10.1007/978-3-030-67073-3

URL: Ebook (access only within the AWI network)