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Statistical Methods in the Atmospheric Sciences, Fifth Edition provides a thorough and structured exploration of the statistical techniques essential for analyzing atmospheric data. The book begins with foundational concepts in probability, setting the stage for more advanced topics. It then covers univariate statistics, including empirical distributions, parametric probability models, and both frequentist and Bayesian inference methods, offering tools for rigorous data analysis and interpretation. The text also addresses statistical forecasting and ensemble forecasting, which are crucial for predicting atmospheric phenomena, along with methods for verifying forecast accuracy. Time series analysis is explored in detail, enabling readers to understand temporal dependencies in atmospheric data. The book advances into multivariate statistics, presenting matrix algebra and random matrices as mathematical foundations. It discusses the multivariate normal distribution, principal component analysis (EOF), and multivariate analysis of vector pairs to handle complex, multidimensional atmospheric datasets. Techniques for discrimination, classification, and cluster analysis are also examined, providing methods for categorizing and interpreting atmospheric patterns. Supplementary materials include example data sets, probability tables, and a glossary of symbols and acronyms, along with answers to exercises that reinforce learning.
This comprehensive new edition equips researchers, students, and professionals with the statistical knowledge and practical skills necessary to analyze atmospheric data effectively and to contribute to advancements in meteorology and climate science.
List of contents
1. Introduction
2. Review of Probability II Univariate Statistics
3. Empirical Distributions and Exploratory Data Analysis
4. Parametric Probability Distributions
5. Frequentist Statistical Inference
6. Bayesian Inference
7. Statistical Forecasting
8. Ensemble Forecasting
9. Forecast Verification
10. Time Series III Multivariate Statistics
11. Matrix Algebra and Random Matrices
12. The Multivariate Normal (MVN) Distribution
13. Principal Component (EOF) Analysis
14. Multivariate Analysis of Vector Pairs
15. Discrimination and Classification
16. Cluster Analysis
Appendix
A. Example Data Sets
B. Probability Tables
C. Symbols and Acronyms
D. Answers to Exercises
About the author
Daniel S. Wilks has been a member of the Atmospheric Sciences faculty at Cornell University since 1987. His research focuses on the application of statistical methods for quantification and analysis of uncertainty in meteorological and climatological data and forecasts. Dr. Wilks has taught courses on statistics in the atmospheric sciences and has been author or coauthor of more than 100 peer-reviewed research articles.
