Time Series Analysis in Meteorology and Climatology: An Introduction(7 Advancing Weather and Climate Science)

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 and part of the RMetS Advancing Weather and Climate Science Series, this 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.

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 the acvf 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

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

Review :
“In summary, I unequivocally endorse this book as a valuable contribution to the literature of time series analysis in the geosciences. It is clear and includes examples that make it accessible for students; knowledgeable practitioners will also gain new insights from this book.”  (Bulletin of the American Meteorological Society, 1 September 2012)