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About this book

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.

Table of Contents

Frontmatter

Chapter 1. Introduction

Abstract
This chapter describes the characteristic features of high dimensionality and introduces the problem of dimensionality reduction in high-dimensional systems with a particular focus on the importance of its application to the highly complex climate system.
Abdelwaheb Hannachi

Chapter 2. General Setting and Basic Terminology

Abstract
This chapter introduces some basic terminologies that are used in subsequent chapters. It also presents some basic summary statistics of data sets and reviews basic methods of data filtering and smoothing.
Abdelwaheb Hannachi

Chapter 3. Empirical Orthogonal Functions

Abstract
This chapter describes the idea behind, and develops the theory of empirical orthogonal functions (EOFs) along with a historical perspective. It also shows different ways to obtain EOFs and provides examples from climate and discusses their physical interpretation. Strength and weaknesses of EOFs are also mentioned.
Abdelwaheb Hannachi

Chapter 4. Rotated and Simplified EOFs

Abstract
This chapter describes further the drawbacks of EOFs mentioned in Chap. 3. It also provides different ways to overcome those drawbacks, including EOF rotation and simplified EOFs. A number of applications to climate data are also provided.
Abdelwaheb Hannachi

Chapter 5. Complex/Hilbert EOFs

Abstract
Weather and Climate data contain a myriad of processes including oscillating and propagating features. In general EOF method is not suited to identify propagating patterns. In this chapter describes a spectral method based on Hilbert transform to identify propagating features, with application to the stratospheric quasi-biennial oscillation.
Abdelwaheb Hannachi

Chapter 6. Principal Oscillation Patterns and Their Extension

Abstract
EOF method is essentially an exploratory method to analyse the modes of variability of multivariate weather and climate data, with no model is involved. This chapter describes a different method, Principal Oscillation Pattern (POP) analysis, that seeks the simplest dynamical system that can explain the main features of the space–time data. The chapter also provides further extension of POPs by including nonlinearity. Examples from climate data are also given.
Abdelwaheb Hannachi

Chapter 7. Extended EOFs and SSA

Abstract
Hilbert EOFs presented in Chap. 5 are based on a spectral method to identify propagating or oscillating features. This chapter describes a time domain method, the extended EOFs, to identify propagating patterns from spatio-temporal data sets. The method is similar to the EOF method except that the spatial dimension is extended to include lagged information. Examples from the Madden–Julian oscillation are also provided.
Abdelwaheb Hannachi

Chapter 8. Persistent, Predictive and Interpolated Patterns

Abstract
Previous chapters discuss methods with no particular predictive power. This chapter describes further advanced linear methods that are more related to prediction. Three related methods, involving extrapolation (or prediction) and interpolation, with climate applications are discussed in this chapter.
Abdelwaheb Hannachi

Chapter 9. Principal Coordinates or Multidimensional Scaling

Abstract
This chapter describes patterns obtained based on proximity or similarity measures, i.e. multidimensional scaling (MDS). Conventional EOFs correspond to the case of quadratic distance. In this chapter other forms of similarities are discussed, with climate application, and which can yield structures that cannot be revealed by classical MDS.
Abdelwaheb Hannachi

Chapter 10. Factor Analysis

Abstract
This chapter describes a model-based method that attempts to explain the variability and correlation structure in the data, and reducing its dimension, using hidden factors. Various algorithms to identify the factor model are discussed, along with various factor rotations in addition to the link to conventional EOFs. An application to climate data is also provided.
Abdelwaheb Hannachi

Chapter 11. Projection Pursuit

Abstract
This chapter describes a method that attempts to identify, sequentially, ‘interesting’ patterns by seeking directions in the data state space that optimises a specific projection index. A number of projection indexes, including indexes measuring non-normality such as skewness, are discussed and application to climate data presented.
Abdelwaheb Hannachi

Chapter 12. Independent Component Analysis

Abstract
Conventional EOFs yield orthogonal spatial patterns and uncorrelated time series. Non-correlation does not necessarily yield independence, which is a strong constraint compared to non-correlation. This chapter discusses the concept of independence, and its relation to non-normality and describes different ways to obtain independent components. The chapter also discusses the application to climate data.
Abdelwaheb Hannachi

Chapter 13. Kernel EOFs

Abstract
This chapter describes a different way to obtain nonlinear EOFs via kernel EOFs based on kernel methods. The kernel EOF method is based on mapping the data onto a feature space and helps delineate complex structures. The chapter discusses various types of transformations to obtain kernel EOFs, with particular focus on the Gaussian kernel and its application to data from models and reanalyses.
Abdelwaheb Hannachi

Chapter 14. Functional and Regularised EOFs

Abstract
Weather and climate data are in general discrete and result from sampling a continuous system. This chapter attempts to take this into account when computing EOFs. The first part of the chapter describes methods to construct EOFs/PCs of profiles with application to oceanography. The second part of the chapter describes regularised EOFs with application to reanalysis data.
Abdelwaheb Hannachi

Chapter 15. Methods for Coupled Patterns

Abstract
Previous chapters focussed mostly on single fields, such as EOFs of seal level pressure. This chapter is an extension of previous methods. It describes different methods that mostly deal with two fields to identify coupled patterns that covary coherently. The chapter discusses both the conventional and regularised problems. It also explores the predictive power of coupled pattern analysis.
Abdelwaheb Hannachi

Chapter 16. Further Topics

Abstract
This chapter describes a number of further methods that have been developed and applied to weather and climate. They include random projection, which deals with very large data size; trend EOFs, which finds trend patterns in gridded data; common EOFs, which identifies common patterns between several fields; and archetypal analysis, which finds extremes in gridded data. The chapter also discusses other methods that deal with nonlinearity.
Abdelwaheb Hannachi

Chapter 17. Machine Learning

Abstract
This last chapter discusses a relatively new method applied in atmospheric and climate science: machine learning. Put simply, machine learning refers to the use of algorithms allowing the computer to learn from the data and use this learning to identify patterns or draw inferences from the data. The chapter describes briefly the flavour of machine learning and discusses three main methods used in weather and climate, namely neural networks, self-organising maps and random forests. These algorithms can be used for various purposes, including finding structures in the data and making prediction.
Abdelwaheb Hannachi

Backmatter

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