Time series analysis in meteorology and climatology: an introduction

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 understandingspectrum windows. The applications section includes real data sets for students to analyse. Scalar variables are used for ease of understanding for exampleair 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. INDICE: Series foreword viiPreface ix1. Fourier analysis 11.1 Overview andterminology 21.2 Analysis and synthesis 61.3 Example data sets 141.4 Statistical properties of the periodogram 231.5 Further important topics in Fourier analysis 47Appendix 1.A Subroutine foranx 83Appendix 1.B Sum of complex exponentials 86Appendix 1.C Distribution of harmonic variances 86Appendix 1.D Derivation of Equation 1.42 92Problems 93References 992. Linear systems 1012.1 Input-output relationships 1022.2 Evaluation of the convolution integral 1042.3 Fourier transforms for analog data 1102.4 The delta function 1132.5 Special input functions 1182.6 The frequency response function 1222.7 Fourier transform of the convolution integral 1282.8 Linear systems in series 1302.9 Ideal interpolation formula 132Problems 137References 1423. Filtering data 1433.1 Recursive and nonrecursive filtering 1443.2 Commonly used digital nonrecursive filters 1503.3 Filter design 1593.4 Lanczos filtering 161Appendix 3.A Convolution of two running mean filters 173Appendix 3.B Derivation of Equation 3.20 176Appendix 3.C Subroutine sigma 177Problems 180References 1824. Autocorrelation 1834.1 Definition and properties 1844.2 Formulas for the acvf and acf 1884.3 The acvf and acf for stationary digital processes 1924.4 The acvf and acf for selected processes 1954.5 Statistical formulas 2014.6 Confidence limits for the population mean 2064.7 Variance of the acvf and acf estimators 211Appendix 4.A Generating a normal random variable 215Problems 216References 2215. Lagged-product spectrum analysis 2235.1 The variance density spectrum 2235.2 Relationship between the variance density spectrum and the acvf 2265.3 Spectra of random processes 2305.4 Spectra of selected processes 2325.5 Smoothing the spectrum 236Appendix 5.A Proof of Equation 5.11 239Appendix 5.B Proof of Equation 5.12 240Problems 241References 243Index 245

• ISBN: 978-1-119-95310-4
• Editorial: John Wiley & Sons
• Encuadernacion: Rústica
• Páginas: 262
• Fecha Publicación: 21/02/2012
• Nº Volúmenes: 1
• Idioma: Inglés