Statistical Methods in the Atmospheric Sciences, Volume 100

I Preliminaries
Chapter 1 Introduction
1.1 What Is Statistics?
1.2 Descriptive and Inferential Statistics
1.3 Uncertainty about the Atmosphere

Chapter 2 Review of Probability
2.1 Background
2.2 The Elements of Probability
2.3 The Meaning of Probability
2.4 Some Properties of Probability
2.5 Exercises

II Univariate Statistics
Chapter 3 Empirical Distributions and Exploratory Data Analysis
3.1 Background
3.2 Numerical Summary Measures
3.3 Graphical Summary Devices
3.4 Reexpression
3.5 Exploratory Techniques for Paired Data
3.6 Exploratory Techniques for Higher-Dimensional Data
3.7 Exercises

Chapter 4 Parametric Probability Distributions
4.1 Background
4.2 Discrete Distributions
4.3 Statistical Expectations
4.4 Continuous Distributions
4.5 Qualitative Assessments of the Goodness of Fit
4.6 Parameter Fitting Using Maximum Likelihood
4.7 Statistical Simulation
4.8 Exercises

Chapter 5 Frequentist Statistical Inference
5.1. Background
5.2 Some Commonly Encountered Parametric Tests
5.3 Nonparametric Tests
5.4 Multiplicity and "Field Significance"
5.5. Exercises

Chapter 6 Bayesian Inference
6.1 Background
6.2 The Structure of Bayesian Inference
6.3 Conjugate Distributions
6.4 Dealing With Difficult Integrals
6.5 Exercises

Chapter 7 Statistical Forecasting
7.1 Background
7.2 Linear Regression
7.3 Nonlinear Regression
7.4 Predictor Selection
7.5 Objective Forecasts Using Traditional Statistical Methods
7.6 Ensemble Forecasting
7.7 Ensemble MOS
7.8 Subjective Probability Forecasts
7.9 Exercises

Chapter 8 Forecast Verification
8.1 Background
8.2 Nonprobabilistic Forecasts for Discrete Predictands
8.3 Nonprobabilistic Forecasts for Continuous Predictands
8.4 Probability Forecasts for Discrete Predictands
8.5 Probability Forecasts for Continuous Predictands
8.6 Nonprobabilistic Forecasts for Fields
8.7 Verification of Ensemble Forecasts
8.8 Verification Based on Economic Value
8.9 Verification When the Observation is Uncertain
8.10 Sampling and Inference for Verification Statistics
8.11 Exercises

Chapter 9 Time Series
9.1 Background
9.2 Time Domain—I. Discrete Data
9.3 Time Domain—II. Continuous Data
9.4 Frequency Domain—I. Harmonic Analysis
9.5 Frequency Domain—II. Spectral Analysis
9.6 Exercises

III Multivariate Statistics
Chapter 10 Matrix Algebra and Random Matrices
10.1 Background to Multivariate Statistics
10.2 Multivariate Distance
10.3 Matrix Algebra Review
10.4 Random Vectors and Matrices
10.5 Exercises

Chapter 11 The Multivariate Normal (MVN) Distribution
11.1 Definition of the MVN
11.2 Four Handy Properties of the MVN
11.3 Assessing Multinormality
11.4 Simulation from the Multivariate Normal Distribution
11.5 Inferences about a Multinormal Mean Vector
11.6 Exercises

Chapter 12 Principal Component (EOF) Analysis
12.1 Basics of Principal Component Analysis
12.2 Application of PCA to Geophysical Fields
12.3 Truncation of the Principal Components
12.4 Sampling Properties of the Eigenvalues and Eigenvectors
12.5 Rotation of the Eigenvectors
12.6 Computational Considerations
12.7 Some Additional Uses of PCA
12.8 Exercises

Chapter 13 Canonical Correlation Analysis (CCA)
13.1 Basics of CCA
13.2 CCA Applied to Fields
13.3 Computational Considerations
13.4 Maximum Covariance Analysis (MCA)
13.5 Exercises

Chapter 14 Discrimination and Classification
14.1 Discrimination vs. Classification
14.2 Separating Two Populations
14.3 Multiple Discriminant Analysis (MDA)
14.4 Forecasting with Discriminant Analysis
14.5 Alternatives to Classical Discriminant Analysis
14.6 Exercises

Chapter 15 Cluster Analysis
15.1 Background
15.2 Hierarchical Clustering
15.3 Nonhierarchical Clustering
15.4 Exercises

Appendix A Example Data Sets
Appendix B Probability Tables
Appendix C Answers to Exercises
References
Index

Statistical Methods in the Atmospheric Sciences, Third Edition, explains the latest statistical methods used to describe, analyze, test, and forecast atmospheric data. This revised and expanded text is intended to help students understand and communicate what their data sets have to say, or to make sense of the scientific literature in meteorology, climatology, and related disciplines.

In this new edition, what was a single chapter on multivariate statistics has been expanded to a full six chapters on this important topic. Other chapters have also been revised and cover exploratory data analysis, probability distributions, hypothesis testing, statistical weather forecasting, forecast verification, and time series analysis. There is now an expanded treatment of resampling tests and key analysis techniques, an updated discussion on ensemble forecasting, and a detailed chapter on forecast verification. In addition, the book includes new sections on maximum likelihood and on statistical simulation and contains current references to original research. Students will benefit from pedagogical features including worked examples, end-of-chapter exercises with separate solutions, and numerous illustrations and equations.

This book will be of interest to researchers and students in the atmospheric sciences, including meteorology, climatology, and other geophysical disciplines.

• Accessible presentation and explanation of techniques for atmospheric data summarization, analysis, testing and forecasting
• Many worked examples
• End-of-chapter exercises, with answers provided

Researchers and students in the atmospheric sciences, including meteorology, climatology, and other geophysical disciplines