Table of Contents

1. Introduction.
I. Fundamentals. 2. Probability Theory. 3. Distributions of Climate Variables. 4. Concepts in Statistical Inference. 5. Estimation.
II. Confirmation and Analysis. 6. The Statistical Test of a Hypothesis. 7. Analysis of Atmospheric Circulation Problems.
III. Fitting Statistical Models. 8. Regression. 9. Analysis of Variance.
IV. Time Series. 10. Time Series and Stochastic Processes. 11. Parameters of Univariate and Bivariate Time Series. 12. Estimating Covariance Functions and Spectra.
V. Eigen Techniques. 13. Empirical Orthogonal Functions. 14. Canonical Correlation Analysis. 15. POP Analysis. 16. Complex Eigentechniques.
VI. Other Topics. 17. Specific Statistical Concepts in Climate Research. 18. Forecast Quality Evaluation. B. Elements of Linear Analysis.
C. Fourier Analysis and Fourier Transform.
D. Normal Density and Cumulative Distribution Function.
E. The X[superscript 2] Distribution.
F. Student's t Distribution.
G. The F Distribution.
H. Table-Look-Up Test.
I. Critical Values for the Mann-Whitney Test.
J. Quantiles of the Squared-ranks Test Statistic.
K. Quantiles of the Spearman Rank Correlation Coefficient.
L. Correlations and Probability Statements.
M. Some Proofs of Theorems and Equations. Climatology is, to a large degree, the study of the statistics of our climate. The powerful tools of mathematical statistics therefore find wide application in climatological research. The purpose of this book is to help the climatologist understand the basic precepts of the statistician's art and to provide some of the background needed to apply statistical methodology correctly and usefully. The book is self contained: introductory material, standard advanced techniques, and the specialised techniques used specifically by climatologists are all contained within this one source. There are a wealth of real-world examples drawn from the climate literature to demonstrate the need, power and pitfalls of statistical analysis in climate research. Suitable for graduate courses on statistics for climatic, atmospheric and oceanic science, this book will also be valuable as a reference source for researchers in climatology, meteorology, atmospheric science, and oceanography.