Statistical Methods in the Atmospheric Sciences

Statistical Methods in the Atmospheric Sciences

3rd Edition - May 20, 2011

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  • Author: Daniel Wilks
  • Hardcover ISBN: 9780123850225
  • eBook ISBN: 9780123850232

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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.

Key Features

  • 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

Table of Contents

  • 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


Product details

  • No. of pages: 704
  • Language: English
  • Copyright: © Academic Press 2011
  • Published: May 20, 2011
  • Imprint: Academic Press
  • Hardcover ISBN: 9780123850225
  • eBook ISBN: 9780123850232

About the Author

Daniel Wilks

Daniel S. Wilks has been a member of the Atmospheric Sciences faculty at Cornell University since 1987, and is the author of Statistical Methods in the Atmospheric Sciences (2011, Academic Press), which is in its third edition and has been continuously in print since 1995. Research areas include statistical forecasting, forecast postprocessing, and forecast evaluation.

Affiliations and Expertise

Department of Earth and Atmospheric Sciences, Cornell University, USA

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