Ocean Wave Data Analysis: Introduction to Time Series Analysis, Signal Processing, and Wave Prediction

Order at Amazon: https://www.amazon.com/dp/0692109978

In this book, readers learn about:

• Linear wave theory
• Time-series of oceancoastal wave
• Wave data analysis in time domain (zero-crossing method)
• Wave data analysis in frequency domain (spectral analysis method)
• Window functions and digital filtering
• Analysis of water pressure and wave orbital velocity
• Wavenumber, wavelength, directional wave spectrum, wind sea, and swell waves
• Non-dimensional wave variables
• Wind and bathymetry data
• Water wave spectrums
• Parametric wave models
• Parametric hurricane models
• SWAN wave modelMATLAB and Python Codes are provided throughout the book to calculate different wave properties

1 Introduction to Wave Theory 1

1.1 Linear wave theory 1

1.2 Basic relations 2

1.3 Wave characteristics based on water depth 3

1.4 Dispersion relation 3

1.5 Wave phase velocity (Celerity) 4

1.6 Group wave velocity 5

1.7 Water particle motion under the wave 5

1.8 Water pressure under the wave 6

1.9 Wave energy and power 7

1.10 Wave radiation stress (momentum flux) 8

1.11 Higher order wave theory 9

1.12 Stokes waves 10

1.13 Cnoidal waves 12

1.14 Solitary waves 12

2 Introduction to Time Series: Data Acquisition and Preparation 13

2.1 Sampling frequency 13

2.2 Data sampling in burst and continuous modes 15

2.3 Sampling duration 15

2.4 Data quality control 17

2.4.1 de-spiking 17

2.4.2 Unacceptable data removal 18

2.4.3 Missing data 18

2.5 de-trending data 18

3 Introduction to Time Domain Data Analysis: Zero-Crossing Method 21

3.1 Random sea 21

3.2 Zero-crossing method 22

3.3 Wave properties from zero-crossing method 24

4 Introduction to frequency domain data analysis: spectral analysis method 29

4.1 Relationships between time and frequency domains 29

4.2 Fourier analysis 31

4.3 Power spectral density 35

4.4 Periodogram method 38

4.5 Frequency ordering 40

4.6 Power spectral density calculation code 41

4.7 Calculating a power spectral density using MATLAB/Octave and Python/SciPy functions 48

4.8 Calculating wave properties from a spectral analysis method 49

4.9 Wave properties calculation code 50

4.10 Peak wave frequency from weighted integral of wave power spectrum 52

4.11 MATLAB, GNU Octave and Python 54

5 Window Functions, Digital Filters and Data Smoothing 57

5.1 Window function 57

5.2 Digital filters 59

5.2.1 Low-pass filter 61

5.2.2 High-pass filter 63

5.2.3 Band-pass filter 65

5.2.4 Band-reject filter 67

5.2.5 Low-pass filter code 69

5.2.6 High-pass filter code 75

5.3 Filter application in the time domain 77

5.4 Filter application in the frequency domain 78

5.5 Filtering a power spectral density 81

5.6 Data smoothing 82

5.7 Smoothing a power spectral density (periodogram) 84

5.8 Calculating a power spectral density using MATLAB/Octave and Python/SciPy functions 85

5.9 Code for smoothing a power spectral density using convolution 90

6 Pressure Data Analysis 93

6.1 Pressure data correction to account for dynamic pressure attenuation in depth 93

6.2 Obtaining water surface elevation from measured pressure data in the time domain 97

6.3 Obtaining a power spectral density of the water surface elevation from measured pressure data in the frequency domain 99

6.4 Lower limit for a pressure response factor 100

6.5 Theoretical method to define an acceptable minimum value for a pressure response factor 102

6.6 Practical methods to define an acceptable minimum value for a pressure response factor 106

6.6.1 Practical method to define fmaxpcorr and Kpmin in the time domain 106

6.6.2 Practical methods to define fmaxpcorr and Kpmin in the frequency domain 107

6.6.3 Some guidelines on defining a constant fcH, an adaptive fmaxpcorr, and an adaptive Kpmin in the frequency domain 109

6.6.4 Step by step procedure to obtain a water surface elevation power spectral density from measured pressure data in the frequency domain 112

6.7 Accuracy of using a pressure response factor to convert pressure data to water surface elevation 115

6.8 Wave spectrum diagnostic tail 117

7 Velocity Data Analysis 123

7.1 Wave orbital and mean velocity (current velocity) 124

7.2 Obtaining water surface elevation from measured velocity data in the time domain 127

7.3 Obtaining a power spectral density of the water surface elevation from measured velocity data in the frequency domain 129

7.4 Lower limit for an orbital velocity conversion factor 130

7.5 Theoretical method to define an acceptable minimum value for an orbital velocity conversion factor 132

7.6 Practical methods to define an acceptable minimum value for an orbital velocity conversion factor 136

7.6.1 Practical method to define fmaxuvcorr and Kuvmin in the time domain 137

7.6.2 Practical methods to define fmaxuvcorr and Kuvmin in the frequency domain 137

7.6.3 Some guidelines on defining a constant fcH, an adaptive fmaxuvcorr, and an adaptive Kuvmin in the frequency domain 139

7.6.4 Step by step procedure to obtain a water surface elevation power spectral density from measured velocity data in the frequency domain 142

7.7 Accuracy of using an orbital velocity conversion factor to convert velocity data to water surface elevation 145

7.8 Wave spectrum diagnostic tail 146

8 Calculating Secondary Wave Properties 151

8.1 Calculating wavenumber and wavelength 151

8.2 Relationship between wave properties in the time and frequency domains 157

8.3 Calculating wave properties from the linear wave theory 158

8.4 Wave height and wave period distributions 160

8.5 Directional wave spectra 163

8.6 Generating a time series from a power spectral density 170

8.7 Wind Sea and swell waves partitioning 172

9 Wave Modeling and Prediction 177

9.1 Non-dimensional variables 177

9.2 Geographic coordinate system 179

9.3 Wind data 181

9.3.1 Wind gust factor (wind velocity averaging) 182

9.3.2 Wind velocity profile 185

9.3.3 Wind direction averaging 188

9.4 Sustained wind 188

9.5 Wind fetch 190

9.6 Bathymetry data 192

9.7 Water wave power spectra 193

9.7.1 Bretschneider (1959) spectrum in deep water 195

9.7.2 Pierson and Moskowitz (1964) spectrum in fully developed deep water 195

9.7.3 JONSWAP (1973) spectrum in deep water 196

9.7.4 Donelan (1985) spectrum for deep water 197

9.7.5 TMA (1985) spectrum in depth-limited water 198

9.7.6 Generating wave power spectra numerically 200

9.8 Parametric wave models 201

9.8.1 Fetch-limited wave growth, duration-limited wave growth and equivalent wind fetch 202

9.8.2 Fully developed condition 203

9.8.3 Asymptotic limit 204

9.8.4 Mean water depth along a wind fetch 204

9.8.5 Steps to calculate wave properties using parametric models 205

9.9 Parametric wave model equations 208

9.9.1 SMB parametric wave model in deep water 208

9.9.2 Wilson (1965) parametric wave model in deep water 210

9.9.3 JONSWAP (1973) parametric wave model in deep water 211

9.9.4 Shore Protection Manual, SPM, (1984), parametric wave model in deep water 213

9.9.5 Kahma and Calkoen (1992) parametric wave model in deep water 214

9.9.6 Hwang and Wang (2004) parametric wave model in deep water 214

9.9.7 Coastal Engineering Manual, CEM (2015), parametric wave model in deep water 215

9.9.8 Shore Protection Manual, SPM, (1984), parametric wave model in depth-limited water 217

9.9.9 Young and Verhagen (1996a) parametric wave model in depth-limited water 219

9.9.10 Karimpour et al. (2017) parametric wave model in depth-limited water 220

9.10 Parametric hurricane models 224

9.10.1 Hurricane wind velocity and pressure models 224

9.10.2 Hurricane historical data 226

9.10.3 Hurricane maximum wind velocity 226

9.10.4 Hurricane wind velocity adjustment for height and duration 226

9.10.5 Hurricane wind velocity inflow angle 227

9.10.6 Hurricane wind velocity adjustment for hurricane forward motion 228

9.11 SWAN wave model 230

9.11.1 Preparing a computational grid for SWAN 231

9.11.2 Preparing depth data for SWAN 233

9.11.3 Preparing water level data for SWAN 235

9.11.4 Preparing wind data for SWAN 236

9.11.5 Preparing a command input file for SWAN 238

9.11.6 Start SWAN simulation 244

9.12 Goodness of fit 245

Notation 249

References 265

Index 287

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Ocean Wave Data Analysis: Introduction to Time Series Analysis, Signal Processing, and Wave Prediction

Copyright (c) 2022 Arash Karimpour

All rights reserved

Ocean Wave Data Analysis: Introduction to Time Series Analysis, Signal Processing, and Wave Prediction © 2018 by Arash Karimpour is licensed under CC BY-NC-SA 4.0 (https://creativecommons.org/licenses/by-nc-sa/4.0/)