Statistical Analysis in Climate Research,9780521450713

Statistical Analysis in Climate Research

by
ISBN13: 9780521450713
ISBN10: 0521450713
Format: Hardcover
Pub. Date: 1999-08-13
Publisher(s): Cambridge University Press
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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

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