Time Series Analysis in Meteorology and Climatology An Introduction

by Duchon, Claude; Hale, Robert

• ISBN13: 9780470971994
• ISBN10: 0470971991
• Edition: 1st
• Format: Hardcover
• Copyright: 2011-12-30
• Publisher: Wiley

Summary

Time Series Analysis in Meteorology and Climatology provides an accessible overview of this notoriously difficult subject. Clearly structured throughout, the authors develop sufficient theoretical foundation to understand the basis for applying various analytical methods to a time series and show clearly how to interpret the results. Taking a unique approach to the subject, the authors use a combination of theory and application to real data sets to enhance student understanding throughout the book. This book is written for those students that have a data set in the form of a time series and are confronted with the problem of how to analyse this data. Each chapter covers the various methods that can be used to carry out this analysis with coverage of the necessary theory and its application. In the theoretical section topics covered include; the mathematical origin of spectrum windows, leakage of variance and understanding spectrum windows. The applications section includes real data sets for students to analyse. Scalar variables are used for ease of understanding for example air temperatures, wind speed and precipitation. Students are encouraged to write their own computer programmes and data sets are provided to enable them to recognize quickly whether their programme is working correctly- one data set is provided with artificial data and the other with real data where the students are required to physically interpret the results of their periodgram analysis. Based on the acclaimed and long standing course at the University of Oklahoma, the book is distinct in its approach to the subject matter in that it is written specifically for readers in meteorology and climatology and uses a mix of theory and application to real data sets.

Author Biography

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	p. vii
Preface	p. ix
Fourier analysis	p. 1
Overview and terminology	p. 2
Analysis and synthesis	p. 6
Example data sets	p. 14
Statistical properties of the periodogram	p. 23
Further important topics in Fourier analysis	p. 47
Subroutine foranx	p. 83
Sum of complex exponentials	p. 86
Distribution of harmonic variances	p. 86
Derivation of Equation 1.42	p. 92
Problems	p. 93
References	p. 99
Linear systems	p. 101
Input-output relationships	p. 102
Evaluation of the convolution integral	p. 104
Fourier transforms for analog data	p. 110
The delta function	p. 113
Special input functions	p. 118
The frequency response function	p. 122
Fourier transform of the convolution integral	p. 128
Linear systems in series	p. 130
Ideal interpolation formula	p. 132
Problems	p. 137
References	p. 142
Filtering data	p. 143
Recursive and nonrecursive filtering	p. 144
Commonly used digital nonrecursive filters	p. 150
Filter design	p. 159
Lanczos filtering	p. 161
Convolution of two running mean filters	p. 173
Derivation of Equation 3.20	p. 176
Subroutine sigma	p. 177
Problems	p. 180
References	p. 182
Autocorrelation	p. 183
Definition and properties	p. 184
Formulas for the acvf and acf	p. 188
The acvf and acf for stationary digital processes	p. 192
The acvf and acf for selected processes	p. 195
Statistical formulas	p. 201
Confidence limits for the population mean	p. 206
Variance of the acvf and acf estimators	p. 211
Generating a normal random variable	p. 215
Problems	p. 216
References	p. 221
Lagged-product spectrum analysis	p. 223
The variance density spectrum	p. 223
Relationship between the variance density spectrum and the acvf	p. 226
Spectra of random processes	p. 230
Spectra of selected processes	p. 232
Smoothing the spectrum	p. 236
Proof of Equation 5.11	p. 239
Proof of Equation 5.12	p. 240
Problems	p. 241
References	p. 243
Index	p. 245
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