UID:
kobvindex_GFZ1759344796
Format:
1 Online-Ressource (xxiv, 600 Seiten)
,
Illustrationen
ISBN:
9783030670733
,
978-3-030-67073-3
ISSN:
2194-5217
,
2194-5225
Series Statement:
Springer atmospheric sciences
Content:
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.
Note:
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
Language:
English
Keywords:
Electronic books
;
Lehrbuch
DOI:
10.1007/978-3-030-67073-3
URL:
Ebook (access only within the AWI network)