Time Series Data Analysis in Oceanography

483 Pages·2022·16.067 MB·English

by  Chunyan Li

TIME SERIES DATA ANALYSIS IN OCEANOGRAPHY
Chunyan Li is a course instructor with years of experience in teaching physical
oceanography, estuarine dynamics, weather analysis, calculus, and time series
analysis. This book is for students and researchers interested in oceanography
and other subjects in the Earth sciences who are looking for complete coverage
of the theory and practice of time series data analysis using MATLAB. This
textbook provides an introduction to the topic’s core theory with examples and
exercises, many drawn directly from the author’s own teaching and research
experiences. The book discusses many concepts, including time; distance on
Earth; wind, current, and wave data formats; finding a subset of moving
platform-based data along planned or random transects; error propagation; Taylor
series expansion for error estimates; the least squares method; base functions and
linear independence of base functions; tidal harmonic analysis; Fourier series and
the generalized Fourier transform; discrete Fourier transform and fast Fourier
transform; power spectrum, cospectrum, and coherence; convolution and digital
filteringtechniques;samplingtheorems;finitesamplingeffects,windowfunctions,
andreductionofsidelobeeffects;rotaryspectrumanalysisforvelocityvectortime
series; short-term Fourier transform; wavelet analysis; and EOF analysis.
chunyan li is a professor in the Department of Oceanography and Coastal
Sciences, College of the Coast and Environment at Louisiana State University.
HeisDirectoroftheWave–Current–SurgeInformationSystem(WAVCIS),partof
the Gulf Coastal Ocean Observing System (GCOOS), which collects real-time
meteorological and oceanographic data. Li’s research focuses on coastal physical
oceanography, estuarine dynamics, ocean observations, atmospheric–oceanic
observing systems, storm surge, and severe weather-induced ocean response. He
haspublished120peer-reviewedpapers,manyofwhichhaveinvolvedoceantime
seriesanalysisandassociatedtheoriesanddynamicalprocessesinestuariesandthe
coastal ocean.

TIME SERIES DATA ANALYSIS IN
OCEANOGRAPHY
Applications Using MATLAB
CHUNYAN LI
LouisianaStateUniversity
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www.cambridge.org
Informationonthistitle:www.cambridge.org/9781108474276
DOI:10.1017/9781108697101
©ChunyanLi2022
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2022
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloging-in-PublicationData
Names:Li,Chunyan(Oceanographer),author.
Title:Timeseriesdataanalysisinoceanography:applicationsusingMATLAB/ChunyanLi.
Description:Cambridge,UnitedKingdom;NewYork,NY:CambridgeUniversityPress,2022.|Includes
bibliographicalreferencesandindex.
Identifiers:LCCN2021037860(print)|LCCN2021037861(ebook)|ISBN9781108474276(hardback)|
ISBN9781108697101(epub)
Subjects:LCSH:Oceanography–Statisticalmethods.|Time-seriesanalysis.|MATLAB|BISAC:SCIENCE/
EarthSciences/Oceanography
Classification:LCCGC10.4.S7L52022(print)|LCCGC10.4.S7(ebook)|DDC551.46072/7–dc23
LCrecordavailableathttps://lccn.loc.gov/2021037860
LCebookrecordavailableathttps://lccn.loc.gov/2021037861
ISBN978-1-108-47427-6Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracy
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Contents
Preface page xiii
Acknowledgments xv
1 Introduction 1
About Chapter 1 1
1.1 Some Definitions and Concepts 1
1.2 Background Knowledge 6
1.3 About Wind, Current, and Wave Directions in 2-D 10
Review Questions for Chapter 1 17
Exercises for Chapter 1 18
2 Introduction to MATLAB 19
About Chapter 2 19
2.1 MATLAB: A Matrix Lab 19
2.2 More on MATLAB 21
2.3 Programming Efficiency 26
2.4 MATLAB Built-In Functions and Constants 27
2.5 Examples of Working with Spatial Data 36
2.6 Selection of Data from Moving Platforms 43
Review Questions for Chapter 2 49
Exercises for Chapter 2 49
3 Time and MATLAB Functions for Time 53
About Chapter 3 53
3.1 Time Is of the Essence 53
3.2 MATLAB Functions for Time Strings, Time Vectors, or
Time Conversion 54
3.3 Caution on Using Local Time 57
v
vi Table of Contents
3.4 Solar Time, Mean Solar Time, and Greenwich Mean
Time (GMT) 59
3.5 Stellar or Sidereal Time 61
3.6 The Difference between Stellar and Solar Times 61
3.7 Coordinated Universal Time (UTC) 62
3.8 The Angular Speed of the Earth’s Rotation 63
3.9 Julian Day Number 63
3.10 Julian Century 66
3.11 Time and Longitude 66
3.12 GPS Data 67
3.13 Interpolation 70
3.14 Elapsed Time Computation 73
Selected MATLAB Commands in This Chapter 75
Review Questions for Chapter 3 76
Exercises for Chapter 3 76
4 Deterministic and Random Functions 78
About Chapter 4 78
4.1 Deterministic Functions 78
4.2 Random Process and Ergodic Process 80
4.3 Covariance Functions and Correlation Function 85
Review Questions for Chapter 4 89
Exercises for Chapter 4 89
5 Error and Variability Propagation 90
About Chapter 5 90
5.1 Source of Error 90
5.2 An Example of Overflow Error for a Large Value 93
5.3 An Example of Overflow Error 94
5.4 Absolute and Relative Errors 95
5.5 Relative Errors of Subtraction and Addition 95
5.6 Relative Errors of Multiplication and Division 98
5.7 Variability Propagation 99
5.8 Examples 100
5.9 Note on Relative Error 105
Review Questions for Chapter 5 106
Exercises for Chapter 5 107
6 Taylor Series Expansion and Application in Error Estimate 110
About Chapter 6 110
6.1 Taylor Series Expansion 110
Table of Contents vii
6.2 The Essence of Taylor Series Expansion 114
6.3 Some Examples 114
6.4 Some Examples of Taylor Series Expansion 116
6.5 An Example Using Taylor Series Expansion for
Error Estimate 117
6.6 Taylor Series Expansion for Two Variables 120
6.7 Taylor Series Expansion for Multiple Variables 122
6.8 An Example of Taylor Series Expansion for an Array
of Functions with Multiple Variables 124
Review Questions for Chapter 6 128
Exercises for Chapter 6 128
7 Spherical Trigonometry and Distance Computation 130
About Chapter 7 130
7.1 Need for Spherical Trigonometry 130
7.2 A Few Definitions 131
7.3 The Measure of “Distance” in Spherical Trigonometry 133
7.4 Laws in Spherical Trigonometry 136
7.5 Calculation When the Angle Is Small 139
Review Questions for Chapter 7 141
Exercises for Chapter 7 141
8 A System of Linear Equations and Least Squares Method 143
About Chapter 8 143
8.1 Linear Equations and Matrix Operation 143
8.2 A MATLAB Example to Solve an Equation 148
8.3 Inverse Matrix 149
8.4 A Different Approach of MATLAB 150
8.5 A Concept of Rank for Matrix 152
8.6 A General Discussion on the Solution of Linear Equations 153
8.7 Examples of Least Squares Method 157
8.8 Coefficient of Determination of Linear Models 163
Review Questions for Chapter 8 163
Exercises for Chapter 8 164
9 Base Functions and Linear Independence 165
About Chapter 9 165
9.1 Base Functions 165
9.2 Linear Dependence and Linear Independence 166
9.3 An Example of Simple Tide 168
9.4 Examples of Improper Base Functions 172
viii Table of Contents
9.5 More Discussion 173
Review Questions for Chapter 9 176
Exercises for Chapter 9 177
10 Generic Least Squares Method and Orthogonal Functions 178
About Chapter 10 178
10.1 Inner (Dot) Product 178
10.2 Generic Least Squares Method 181
10.3 Generic Least Squares Method 182
10.4 Geometric Meaning of Least Squares Method 186
Review Questions for Chapter 10 189
Exercises for Chapter 10 189
11 Harmonic Analysis of Tide 190
About Chapter 11 190
11.1 About Tides 190
11.2 Harmonic Analysis of Tides 194
11.3 Appendix: Tide-Generating Force 199
Review Questions for Chapter 11 205
Exercises for Chapter 11 205
12 Fourier Series 207
About Chapter 12 207
12.1 Linear Combination of Sinusoidal Functions 207
12.2 Least Squares Method for Continuous Functions 210
12.3 The Convergence of Fourier Series 218
12.4 Some Comments on Fourier Series 220
12.5 Examples of Fourier Series and Gibbs Effect 221
12.6 Additional Properties of Fourier Series 226
Review Questions for Chapter 12 228
Exercises for Chapter 12 228
13 Fourier Transform 230
About Chapter 13 230
13.1 Periodic Function and Discrete Spectrum 230
13.2 From Fourier Series to Fourier Transform 232
13.3 Power Distribution in Frequency Domain 237
13.4 Recap: From Least Squares Method to Fourier Transform 239
Review Questions for Chapter 13 240
Exercises for Chapter 13 240
Table of Contents ix
14 Discrete Fourier Transform and Fast Fourier Transform 242
About Chapter 14 242
14.1 The Discrete Fourier Transform 242
14.2 The Fast Fourier Transform 247
Review Questions for Chapter 14 264
Exercises for Chapter 14 264
15 Properties of Fourier Transform 267
About Chapter 15 267
15.1 Additive Property 267
15.2 Symmetric Properties 268
15.3 Similarity Property 269
15.4 Time Delay Property 271
15.5 Frequency Delay Property 271
15.6 Time Derivative Property 272
15.7 Frequency Derivative Property 272
15.8 Time Integration Property 273
15.9 Frequency Integration Property 274
15.10 Time Convolution Property 274
15.11 Frequency Convolution Property 275
15.12 Complex Conjugate Property 276
15.13 Integral Form of Parseval Formula 277
Review Questions for Chapter 15 277
Exercises for Chapter 15 277
16 More Discussion on the Harmonic Analysis and Fourier Analysis 279
About Chapter 16 279
16.1 Comparison between Harmonic and Fourier Analysis 279
16.2 Examples 283
16.3 Summary 304
Review Questions for Chapter 16 306
Exercises for Chapter 16 306
17 Effect of Finite Sampling 308
About Chapter 17 308
17.1 The Effect of Truncation 308
17.2 The Effect of Discrete Sampling 323
17.3 Discussion on Aliasing 328
18 Power Spectrum, Cospectrum, and Coherence 331
About Chapter 18 331