Statistical Methods in the Atmospheric Sciences: An Introduction
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Table of contents
- PageCover
- Contentsv
- Prefacexi
- Chapter 1. Introduction1
- 1.1 What Is Statistics?1
- 1.2 Descriptive and Inferential Statistics2
- 1.3 Uncertainty about the Atmosphere2
- 1.4 An Aside on Notation4
- Chapter 2. Review of Probability6
- 2.1 Background6
- 2.2 The Elements of Probability7
- 2.3 The Meaning of Probability9
- 2.4 Some Properties of Probability10
- Exercises19
- Chapter 3. Empirical Distributions and Exploratory Data Analysis21
- 3.1 Background21
- 3.2 Numerical Summary Measures24
- 3.3 Graphical Summary Techniques27
- 3.4 Reexpression36
- 3.5 Exploratory Techniques for Paired Data44
- 3.6 Exploratory Techniques for Higher-Dimensional Data54
- Exercises62
- Chapter 4. Theoretical Probability Distributions64
- 4.1 Background64
- 4.2 Discrete Distributions66
- 4.3 Statistical Expectations74
- 4.4 Continous Distribution76
- 4.5 Multivariate Probability Distributions99
- 4.6 Qualitative Assessments of the Goodness of Fit104
- 4.7 Parameter Fitting Using Maximum Likelihood108
- Exercises111
- Chapter 5. Hypothesis Testing114
- 5.1 Background114
- 5.2 Some Parametric Tests121
- 5.3 Nonparametric Tests137
- 5.4 Field Significance and Multiplicity151
- Exercises157
- Chapter 6. Statistical Weather Forecasting159
- 6.1 Background159
- 6.2 Review of Least-Squares Regression160
- 6.3 Objective Forecasts„Without NWP181
- 6.4 Objective Forecasts„With NWP199
- 6.5 Probabilistic Field (Ensemble) Forecasts210
- 6.6 Subjective Probability Forecasts221
- Exercises230
- Chapter 7. Forecast Verification233
- 7.1 Background233
- 7.2 Categorical Forecasts of Discrete Predictands238
- 7.3 Categorical Forecasts of Continuous Predictands250
- 7.4 Probability Forecasts258
- 7.5 Categorical Forecasts of Fields272
- Exercises281
- Chapter 8. Time Series284
- 8.1 Background284
- 8.2 Time Domain. I. Discrete Data287
- 8.3 Time Domain. II. Continuous Data302
- 8.4 Frequency Domain. I. Harmonic Analysis325
- 8.5 Frequency Domain. II. Spectral Analysis341
- Exercises357
- Chapter 9. Methods for Multivariate Data359
- 9.1 Background359
- 9.2 Matrix Algebra Notation360
- 9.3 Principal-Component (EOF) Analysis373
- 9.4 Canonical Correlation Analysis398
- 9.5 Discriminant Analysis408
- 9.6 Cluster Analysis419
- Exercises427
- Appendix A. Example Data Sets429
- Appendix B. Probability Tables432
- Appendix C. Answers to Exercises439
- References444
- Index455
- International Geophysics Series465
This book introduces and explains the statistical methods used to describe, analyze, test, and forecast atmospheric data. It will be useful to students, scientists, and other professionals who seek to make sense of the scientific literature in meteorology, climatology, or other geophysical disciplines, or to understand and communicate what their atmospheric data sets have to say. The book includes chapters on exploratory data analysis, probability distributions, hypothesis testing, statistical weather forecasting, forecast verification, time(series analysis, and multivariate data analysis. Worked examples, exercises, and illustrations facilitate understanding of the material; an extensive and up-to-date list of references allows the reader to pursue selected topics in greater depth.
Key Features
* Presents and explains techniques used in atmospheric data summarization, analysis, testing, and forecasting
* Includes extensive and up-to-date references
* Features numerous worked examples and exercises
* Contains over 130 illustrations
Key Features
* Presents and explains techniques used in atmospheric data summarization, analysis, testing, and forecasting
* Includes extensive and up-to-date references
* Features numerous worked examples and exercises
* Contains over 130 illustrations