Statistical Analysis in Climate Research

by Hans von Storch , Francis W. Zwiers

• ISBN13: 9780521450713
• ISBN10: 0521450713
• Format: Hardcover
• Copyright: 1999-08-13
• Publisher: Cambridge University Press

Summary

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 specialized 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.

Table of Contents

Preface	ix
Thanks	x
Introduction	1	(16)
The Statistical Description	1	(1)
Some Typical Problems and Concepts	2	(15)
I Fundamentals	17	(78)
Probability Theory	19	(32)
Introduction	19	(1)
Probability	20	(1)
Discrete Random Variables	21	(2)
Examples of Discrete Random Variables	23	(3)
Discrete Multivariate Distributions	26	(3)
Continuous Random Variables	29	(4)
Example of Continuous Random Variables	33	(5)
Random Vectors	38	(7)
Extreme Value Distributions	45	(6)
Distributions of Climate Variables	51	(18)
Atmospheric Variables	52	(11)
Some Other Climate Variables	63	(6)
Concepts in Statistical Inference	69	(10)
General	69	(5)
Random Samples	74	(2)
Statistics and Sampling Distributions	76	(3)
Estimation	79	(16)
General	79	(1)
Examples of Estimators	80	(4)
Properties of Estimators	84	(6)
Interval Estimators	90	(3)
Bootstrapping	93	(2)
II Confirmation and Analysis	95	(46)
Overview	97	(2)
The Statistical Test of a Hypothesis	99	(30)
The Concept of Statistical Tests	99	(1)
The Structure and Terminology of a Test	100	(4)
Monte Carlo Simulation	104	(2)
On Establishing Statistical Significance	106	(2)
Multivariate Problems	108	(3)
Tests of the Mean	111	(7)
Test of Variances	118	(3)
Field Significance Tests	121	(1)
Univariate Recurrence Analysis	122	(4)
Multivariate Recurrence Analysis	126	(3)
Analysis of Atmospheric Circulation Problems	129	(12)
Validating a General Circulation Model	129	(2)
Analysis of a GCM Sensitivity Experiment	131	(2)
Identification of a Signal in Observed Data	133	(3)
Detecting the `Co2 Signal'	136	(5)
III Fitting Statistical Models	141	(52)
Overview	143	(2)
Regression	145	(26)
Introduction	145	(1)
Correlation	146	(4)
Fitting and Diagnosing Simple Regression Models	150	(10)
Multiple Regression	160	(6)
Model Selection	166	(2)
Some Other Topics	168	(3)
Analysis of Variance	171	(22)
Introduction	171	(2)
One Way Analysis of Variance	173	(8)
Two Way Analysis of Variance	181	(3)
Two Way ANOVA with Mixed Effects	184	(7)
Tuning a Basin Scale Ocean Model	191	(2)
IV Time Series	193	(96)
Overview	195	(2)
Time Series and Stochastic Processes	197	(20)
General Discussion	197	(2)
Basic Definitions and Examples	199	(4)
Auto-regressive Processes	203	(8)
Stochastic Climate Models	211	(2)
Moving Average Processes	213	(4)
Parameters of Univariate and Bivariate Time Series	217	(34)
The Auto-covariance Function	217	(5)
The Spectrum	222	(6)
The Cross-covariance Function	228	(6)
The Cross-spectrum	234	(7)
Frequency--Wavenumber Analysis	241	(10)
Estimating Covariance Functions and Spectra	251	(38)
Non-parametric Estimation of the Auto-correlation Function	252	(3)
Identifying and Fitting Auto-regressive Models	255	(8)
Estimating the Spectrum	263	(18)
Estimating the Cross-correlation Function	281	(1)
Estimating the Cross-spectrum	282	(7)
V Eigen Techniques	289	(78)
Overview	291	(2)
Empirical Orthogonal Functions	293	(24)
Definition of Empirical Orthogonal Functions	294	(5)
Estimation of Empirical Orthogonal Functions	299	(2)
Inference	301	(3)
Examples	304	(1)
Rotation of EOFs	305	(7)
Singular Systems Analysis	312	(5)
Canonical Correlation Analysis	317	(18)
Definition of Canonical Correlation Patterns	317	(5)
Estimating Canonical Correlation Patterns	322	(1)
Examples	323	(4)
Redundancy Analysis	327	(8)
POP Analysis	335	(18)
Principal Oscillation Patterns	335	(4)
Examples	339	(6)
POPs as a Predictive Tool	345	(1)
Cyclo-stationary POP Analysis	346	(4)
State Space Models	350	(3)
Complex Eigentechniques	353	(14)
Introduction	353	(1)
Hilbert Transform	353	(4)
Complex and Hilbert EOFs	357	(10)
VI Other Topics	367	(40)
Overview	369	(2)
Specific Statistical Concepts in Climate Research	371	(20)
The Decorrelation Time	371	(3)
Potential Predictability	374	(4)
Composites and Associated Correlation Patterns	378	(4)
Teleconnections	382	(2)
Time Filters	384	(7)
Forecast Quality Evaluation	391	(16)
The Skill of Categorcal Forecasts	392	(3)
The Skill of Quantitative Forecasts	395	(4)
The Murphy--Epstein Decomposition	399	(3)
Issues in the Evaluation of Forecast Skill	402	(3)
Cross-validation	405	(2)
VII Appendices	407	(48)
A Notation	409	(4)
B Elements of Linear Analysis	413	(3)
C Fourier Analysis and Fourier Transform	416	(3)
D Normal Density and Cumulative Distribution Function	419	(2)
E The X2 Distribution	421	(2)
F Student's t Distribution	423	(1)
G The F Distribution	424	(7)
H Table-Look-Up Test	431	(6)
I Critical Values for the Mann--Whitney Test	437	(6)
J Quantiles of the Squared-ranks Test Statistic	443	(3)
K Quantiles of the Spearman Rank Correlation Coefficient	446	(1)
L Correlations and Probability Statements	447	(4)
M Some Proofs of Theorems and Equations	451	(4)
References	455