Statistical Methods in the Atmospheric Sciences
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Table of contents
- COVERCover
- Statistical Methods in the Atmospheric Sciencesiii
- Copyright Pageiv
- Contentsv
- Preface to the First Editionxv
- Preface to the Second Editionxvii
- PART I: Preliminaries1
- CHAPTER 1. Introduction3
- 1.1 What Is Statistics?3
- 1.2 Descriptive and Inferential Statistics3
- 1.3 Uncertainty about the Atmosphere4
- CHAPTER 2. Review of Probability7
- 2.1 Background7
- 2.2 The Elements of Probability7
- 2.3 The Meaning of Probability9
- 2.4 Some Properties of Probability11
- 2.5 Exercises18
- PART II: Univariate Statistics21
- CHAPTER 3. Empirical Distributions and Exploratory Data Analysis23
- 3.1 Background23
- 3.2 Numerical Summary Measures25
- 3.3 Graphical Summary Techniques28
- 3.4 Reexpression42
- 3.5 Exploratory Techniques for Paired Data49
- 3.6 Exploratory Techniques for Higher-Dimensional Data59
- 3.7 Exercises69
- CHAPTER 4. Parametric Probability Distributions71
- 4.1 Background71
- 4.2 Discrete Distributions73
- 4.3 Statistical Expectations82
- 4.4 Continuous Distributions85
- 4.5 Qualitative Assessments of the Goodness of Fit111
- 4.6 Parameter Fitting Using Maximum Likelihood114
- 4.7 Statistical Simulation120
- 4.8 Exercises128
- CHAPTER 5. Hypothesis Testing131
- 5.1 Background131
- 5.2 Some Parametric Tests138
- 5.3 Nonparametric Tests156
- 5.4 Field Significance and Multiplicity170
- 5.5 Exercises176
- CHAPTER 6. Statistical Forecasting179
- 6.1 Background179
- 6.2 Linear Regression180
- 6.3 Nonlinear Regression201
- 6.4 Predictor Selection207
- 6.5 Objective Forecasts Using Traditional Statistical Methods217
- 6.6 Ensemble Forecasting229
- 6.7 Subjective Probability Forecasts245
- 6.8 Exercises252
- CHAPTER 7. Forecast Verification255
- 7.1 Background255
- 7.2 Nonprobabilistic Forecasts of Discrete Predictands260
- 7.3 Nonprobabilistic Forecasts of Continuous Predictands276
- 7.4 Probability Forecasts of Discrete Predictands282
- 7.5 Probability Forecasts for Continuous Predictands302
- 7.6 Nonprobabilistic Forecasts of Fields304
- 7.7 Verification of Ensemble Forecasts314
- 7.8 Verification Based on Economic Value321
- 7.9 Sampling and Inference for Verification Statistics326
- 7.10 Exercises332
- CHAPTER 8. Time Series337
- 8.1 Background337
- 8.2 Time Domain„I. Discrete Data339
- 8.3 Time Domain„II. Continuous Data352
- 8.4 Frequency Domain„I. Harmonic Analysis371
- 8.5 Frequency Domain„II. Spectral Analysis381
- 8.6 Exercises399
- PART III: Multivariate Statistics401
- CHAPTER 9. Matrix Algebra and Random Matrices403
- 9.1 Background to Multivariate Statistics403
- 9.2 Multivariate Distance406
- 9.3 Matrix Algebra Review408
- 9.4 Random Vectors and Matrices426
- 9.5 Exercises432
- CHAPTER 10. The Multivariate Normal (MVN) Distribution435
- 10.1 Definition of the MVN435
- 10.2 Four Handy Properties of the MVN437
- 10.3 Assessing Multinormality440
- 10.4 Simulation from the Multivariate Normal Distribution444
- 10.5 Inferences about a Multinormal Mean Vector448
- 10.6 Exercises462
- CHAPTER 11. Principal Component (EOF) Analysis463
- 11.1 Basics of Principal Component Analysis463
- 11.2 Application of PCA to Geophysical Fields475
- 11.3 Truncation of the Principal Components481
- 11.4 Sampling Properties of the Eigenvalues and Eigenvectors486
- 11.5 Rotation of the Eigenvectors492
- 11.6 Computational Considerations499
- 11.7 Some Additional Uses of PCA501
- 11.8 Exercises507
- CHAPTER 12. Canonical Correlation Analysis (CCA)509
- 12.1 Basics of CCA509
- 12.2 CCA Applied to Fields517
- 12.3 Computational Considerations522
- 12.4 Maximum Covariance Analysis526
- 12.5 Exercises528
- CHAPTER 13. Discrimination and Classification529
- 13.1 Discrimination vs. Classification529
- 13.2 Separating Two Populations530
- 13.3 Multiple Discriminant Analysis (MDA)538
- 13.4 Forecasting with Discriminant Analysis544
- 13.5 Alternatives to Classical Discriminant Analysis545
- 13.6 Exercises547
- CHAPTER 14. Cluster Analysis549
- 14.1 Background549
- 14.2 Hierarchical Clustering551
- 14.3 Nonhierarchical Clustering559
- 14.4 Exercises561
- APPENDIX A. Example Data Sets565
- Table A.1. Daily precipitation and temperature data for Ithaca and Canandaigua, New York, for Januar566
- Table A.2. January precipitation data for Ithaca, New York, 1933–1982567
- Table A.3. June climate data for Guayaquil, Ecuador, 1951–1970567
- APPENDIX B. Probability Tables569
- Table B.1. Cumulative Probabilities for the Standard Gaussian Distribution570
- Table B.2. Quantiles of the Standard Gamma Distribution571
- Table B.3. Right-tail quantiles of the Chi-square distribution572
- APPENDIX C. Answers to Exercises579
- References587
- Index611
Praise for the First Edition:
"I recommend this book, without hesitation, as either a reference or course text...Wilks' excellent book provides a thorough base in applied statistical methods for atmospheric sciences."--BAMS (Bulletin of the American Meteorological Society)
Fundamentally, statistics is concerned with managing data and making inferences and forecasts in the face of uncertainty. It should not be surprising, therefore, that statistical methods have a key role to play in the atmospheric sciences. It is the uncertainty in atmospheric behavior that continues to move research forward and drive innovations in atmospheric modeling and prediction.
This revised and expanded text explains the latest statistical methods that are being used to describe, analyze, test and forecast atmospheric data. It features numerous worked examples, illustrations, equations, and exercises with separate solutions. Statistical Methods in the Atmospheric Sciences, Second Edition will help advanced students and professionals understand and communicate what their data sets have to say, and make sense of the scientific literature in meteorology, climatology, and related disciplines.
* Presents and explains techniques used in atmospheric data summarization, analysis, testing, and forecasting
* Features numerous worked examples and exercises
* Covers Model Output Statistic (MOS) with an introduction to the Kalman filter, an approach that tolerates frequent model changes
* Includes a detailed section on forecast verification
New in this Edition:
* Expanded treatment of resampling tests and coverage of key analysis techniques
* Updated treatment of ensemble forecasting
* Edits and revisions throughout the text plus updated references
"I recommend this book, without hesitation, as either a reference or course text...Wilks' excellent book provides a thorough base in applied statistical methods for atmospheric sciences."--BAMS (Bulletin of the American Meteorological Society)
Fundamentally, statistics is concerned with managing data and making inferences and forecasts in the face of uncertainty. It should not be surprising, therefore, that statistical methods have a key role to play in the atmospheric sciences. It is the uncertainty in atmospheric behavior that continues to move research forward and drive innovations in atmospheric modeling and prediction.
This revised and expanded text explains the latest statistical methods that are being used to describe, analyze, test and forecast atmospheric data. It features numerous worked examples, illustrations, equations, and exercises with separate solutions. Statistical Methods in the Atmospheric Sciences, Second Edition will help advanced students and professionals understand and communicate what their data sets have to say, and make sense of the scientific literature in meteorology, climatology, and related disciplines.
* Presents and explains techniques used in atmospheric data summarization, analysis, testing, and forecasting
* Features numerous worked examples and exercises
* Covers Model Output Statistic (MOS) with an introduction to the Kalman filter, an approach that tolerates frequent model changes
* Includes a detailed section on forecast verification
New in this Edition:
* Expanded treatment of resampling tests and coverage of key analysis techniques
* Updated treatment of ensemble forecasting
* Edits and revisions throughout the text plus updated references