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Time Series Analysis in Meteorology and Climatology: An Introduction / Edition 1

Time Series Analysis in Meteorology and Climatology: An Introduction / Edition 1

by Claude Duchon, Robert Hale


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Time Series Analysis in Meteorology and Climatology: An Introduction / Edition 1

Time Series Analysis in Meteorology and Climatology providesan accessible overview of this notoriously difficult subject.Clearly structured throughout, the authors develop sufficienttheoretical foundation to understand the basis for applying variousanalytical methods to a time series and show clearly how tointerpret the results. Taking a unique approach to the subject, theauthors use a combination of theory and application to real datasets to enhance student understanding throughout the book.

This book is written for those students that have a data set inthe form of a time series and are confronted with the problem ofhow to analyse this data. Each chapter covers the various methodsthat can be used to carry out this analysis with coverage of thenecessary theory and its application. In the theoretical sectiontopics covered include; the mathematical origin of spectrumwindows, leakage of variance and understanding spectrum windows.The applications section includes real data sets for students toanalyse. Scalar variables are used for ease of understanding forexample air temperatures, wind speed and precipitation.

Students are encouraged to write their own computer programmesand data sets are provided to enable them to recognize quicklywhether their programme is working correctly- one data set isprovided with artificial data and the other with real data wherethe students are required to physically interpret the results oftheir periodgram analysis.

Based on the acclaimed and long standing course at theUniversity of Oklahoma and part of the RMetS Advancing Weather andClimate Science Series, this book is distinct in its approachto the subject matter in that it is written specifically forreaders in meteorology and climatology and uses a mix of theory andapplication to real data sets.

Product Details

ISBN-13: 9780470971994
Publisher: Wiley
Publication date: 05/22/2012
Series: Advancing Weather and Climate Science Series
Pages: 262
Product dimensions: 6.80(w) x 9.70(h) x 0.70(d)

About the Author

Claude Edward Duchon, Professor Emeritus, School of Meteorology, University of Oklahoma

Robert C. Hale, Research Scientist, Cooperative Institute for Research in the Atmosphere, Colorado State University

Table of Contents

Series foreword vii

Preface ix

1. Fourier analysis 1

1.1 Overview and terminology 2

1.2 Analysis and synthesis 6

1.3 Example data sets 14

1.4 Statistical properties of the periodogram 23

1.5 Further important topics in Fourier analysis 47

Appendix 1.A Subroutine foranx 83

Appendix 1.B Sum of complex exponentials 86

Appendix 1.C Distribution of harmonic variances 86

Appendix 1.D Derivation of Equation 1.42 92

Problems 93

References 99

2. Linear systems 101

2.1 Input–output relationships 102

2.2 Evaluation of the convolution integral 104

2.3 Fourier transforms for analog data 110

2.4 The delta function 113

2.5 Special input functions 118

2.6 The frequency response function 122

2.7 Fourier transform of the convolution integral 128

2.8 Linear systems in series 130

2.9 Ideal interpolation formula 132

Problems 137

References 142

3. Filtering data 143

3.1 Recursive and nonrecursive filtering 144

3.2 Commonly used digital nonrecursive filters 150

3.3 Filter design 159

3.4 Lanczos filtering 161

Appendix 3.A Convolution of two running mean filters 173

Appendix 3.B Derivation of Equation 3.20 176

Appendix 3.C Subroutine sigma 177

Problems 180

References 182

4. Autocorrelation 183

4.1 Definition and properties 184

4.2 Formulas for the acvf and acf 188

4.3 The acvf and acf for stationary digital processes 192

4.4 The acvf and acf for selected processes 195

4.5 Statistical formulas 201

4.6 Confidence limits for the population mean 206

4.7 Variance of the acvf and acf estimators 211

Appendix 4.A Generating a normal random variable 215

Problems 216

References 221

5. Lagged-product spectrum analysis 223

5.1 The variance density spectrum 223

5.2 Relationship between the variance density spectrum and theacvf 226

5.3 Spectra of random processes 230

5.4 Spectra of selected processes 232

5.5 Smoothing the spectrum 236

Appendix 5.A Proof of Equation 5.11 239

Appendix 5.B Proof of Equation 5.12 240

Problems 241

References 243

Index 245

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