Time Series Analysis in Climatology and Related Sciences

253 Pages·2021·10.25 MB·English

by  Victor Privalsky

Progress in Geophysics
Victor Privalsky
Time Series
Analysis
in Climatology
and Related
Sciences
Progress in Geophysics
Series Editor
AlexanderB.Rabinovich,P.P.ShirshovInstituteofOceanology,RussianAcademy
of Sciences, Moskva, Russia
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More information about this series at http://www.springer.com/series/15922
Victor Privalsky
Time Series Analysis
in Climatology and Related
Sciences
123
Victor Privalsky
Water Problems Institute
Russian Academy of Sciences
Moscow,Russia
ISSN 2523-8388 ISSN 2523-8396 (electronic)
Progressin Geophysics
ISBN978-3-030-58054-4 ISBN978-3-030-58055-1 (eBook)
https://doi.org/10.1007/978-3-030-58055-1
©SpringerNatureSwitzerlandAG2021
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To the memory of my daughter Maria
Privalsky and my teacher Akiva Yaglom
Acknowledgements
The author is sincerely indebted to Alexander Benilov, Sergei Dobrovolski,
M.Fortus,MaxMalkin,SergeiMuzylev,JulieRich,andTatyanaVyruchalkinafor
their valuable help.
Special thanks are to Alexander Rabinovich for recommending this book to
Springer.
vii
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Basics of Scalar Random Processes. . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 Basic Statistical Characteristics . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Deterministic Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Random Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Covariance and Correlation Functions . . . . . . . . . . . . . . . . . . . 15
2.5 Spectral Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.6 Examples of Geophysical Time Series and Their Statistics . . . . 19
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Time and Frequency Domain Models of Scalar Time Series. . . . . . 27
3.1 Nonparametric Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Parametric Models of Time Series . . . . . . . . . . . . . . . . . . . . . . 29
3.3 Parametric Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 Determining the Order of Autoregressive Models . . . . . . . . . . . 34
3.5 Comparison of Autoregressive and Nonparametric Spectral
Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.6 Advantages and Disadvantages of Autoregressive Analysis
(Scalar Case) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4 Practical Analysis of Time Series . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1 Selecting the Sampling Interval . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2 Linear Trend and Its Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3 Testing for Stationarity and Ergodicity. . . . . . . . . . . . . . . . . . . 48
4.4 Linear Filtering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
ix
x Contents
4.5 Frequency Resolution of Autoregressive Spectral Analysis . . . . 55
4.6 Example of AR Analysis in Time and Frequency Domains. . . . 58
Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5 Stochastic Models and Spectra of Climatic and Related Time
Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.1 Properties of Climate Indices. . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2 Properties of Time Series of Spatially Averaged Surface
Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.3 Quasi-Biennial Oscillation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.4 Other Oscillations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6 Statistical Forecasting of Geophysical Processes . . . . . . . . . . . . . . . 75
6.1 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.2 Method of Extrapolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.3 Example 1. Global Annual Temperature. . . . . . . . . . . . . . . . . . 82
6.4 Example 2. Quasi-Biennial Oscillation . . . . . . . . . . . . . . . . . . . 85
6.5 Example 3. ENSO Components. . . . . . . . . . . . . . . . . . . . . . . . 88
6.6 Example 4. Madden–Julian Oscillation. . . . . . . . . . . . . . . . . . . 91
Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7 Bivariate Time Series Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.1 Elements of Bivariate Time Series Analysis . . . . . . . . . . . . . . . 98
7.1.1 Bivariate Autoregressive Models in Time Domain . . . . 98
7.1.2 Bivariate Autoregressive Models in Frequency
Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
7.1.3 Reliability of Autoregressive Estimates
of Frequency-Dependent Quantities. . . . . . . . . . . . . . . 106
7.2 Granger Causality and Feedback . . . . . . . . . . . . . . . . . . . . . . . 107
7.3 On Properties of Software for Analysis of Multivariate
Time Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
8 Teleconnection Research and Bivariate Extrapolation . . . . . . . . . . 113
8.1 Example 1. The ENSO Teleconnection . . . . . . . . . . . . . . . . . . 114
8.2 Example 2. Teleconnections Between ENSO and AST . . . . . . . 120
8.2.1 Time Domain Analysis—ENSO and Spatially
Averaged Temperature . . . . . . . . . . . . . . . . . . . . . . . . 120
8.2.2 Frequency Domain Analysis . . . . . . . . . . . . . . . . . . . . 126
8.3 Example 3. Bivariate Extrapolation of Madden–Julian
Oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Contents xi
Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
9 Reconstruction of Time Series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
9.2 Methods of Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
9.2.1 Traditional Correlation/Regression Reconstruction
(CRR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
9.2.2 Autoregressive Reconstruction Method (ARR). . . . . . . 142
9.3 Verification of the Autoregressive Reconstruction Method. . . . . 144
9.3.1 Reconstruction Example: A Climatic Type Process. . . . 145
9.4 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 150
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
10 Frequency Domain Structure and Feedbacks in QBO
Time Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
11 Verification of General Circulation Models. . . . . . . . . . . . . . . . . . . 163
11.1 Verifying the Structure of ENSO. . . . . . . . . . . . . . . . . . . . . . . 165
11.1.1 Linear Trend Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . 168
11.1.2 Mean Values and Standard Deviations. . . . . . . . . . . . . 168
11.1.3 Probability Density. . . . . . . . . . . . . . . . . . . . . . . . . . . 169
11.1.4 Time and Frequency Domain Properties . . . . . . . . . . . 169
11.2 Verification of ENSO Influence upon Global Temperature . . . . 174
11.3 Verifications of Properties of Surface Temperature Over
CONUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
11.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
12 Applications to Proxy Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
12.2 Greenland Ice Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
12.3 Antarctic Ice Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
12.4 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 201
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
13 Application to Sunspot Numbers and Total Solar Irradiance . . . . . 205
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
13.2 Properties of Sunspot Number Time Series. . . . . . . . . . . . . . . . 207
13.3 Properties of Total Solar Irradiance Time Series . . . . . . . . . . . . 212
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
14 Multivariate Time and Frequency Domain Analysis. . . . . . . . . . . . 221
14.1 Time Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
14.2 Frequency Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 223