A comprehensive introduction to the most commonly used statistical methods relevant in atmospheric, oceanic and climate sciences. Each method is described step-by-step using plain language, and illustrated with concrete examples, with relevant statistical and scientific concepts explained as needed. Particular attention is paid to nuances and pitfalls, with sufficient detail to enable the reader to write relevant code. Topics covered include hypothesis testing, time series analysis, linear regression, data assimilation, extreme value analysis, Principal Component Analysis, Canonical Correlation Analysis, Predictable Component Analysis, and Covariance Discriminant Analysis. The specific statistical challenges that arise in climate applications are also discussed, including model selection problems associated with Canonical Correlation Analysis, Predictable Component Analysis, and Covariance Discriminant Analysis. Requiring no previous background in statistics, this is a highly accessible textbook and reference for students and early-career researchers in the climate sciences.
1. Basic Concepts in Probability and Statistics
2. Hypothesis Tests
3. Confidence Intervals
4. Statistical Tests Based on Ranks
5. Introduction to Stochastic Processes
6. The Power Spectrum
7. Introduction to Multivariate Methods
8. Linear Regression: Least Squares Estimation
9. Linear Regression: Inference
10. Model Selection
11. Screening: A Pitfall in Statistics
12. Principal Component Analysis
13. Field Significance
14. Multivariate Linear Regression
15. Canonical Correlation Analysis
16. Covariance Discriminant Analysis
17. Analysis of Variance and Predictability
18. Predictable Component Analysis
19. Extreme Value Theory
20. Data Assimilation
21. Ensemble Square Root Filters
Timothy M. DelSole is a Professor in the Department of Atmospheric, Oceanic, and Earth Sciences, and a Senior Scientist at the Center for Oceanic Atmospheric, and Land Studies, at George Mason University, Virginia. He has published over one hundred peer-reviewed papers in climate science and served as co-Editor-in-Chief of the Journal of Climate.
Michael Tippett is an Associate Professor at Columbia University. His research includes forecasting El Niño and relating extreme weather (tornadoes and hurricanes) with climate, now and in the future. He analyzes data from computer models and weather observations to find patterns that improve understanding, facilitate prediction, and help manage risk.