Data Analysis Methods in Physical Oceanography (eBook)

Cover 1
Contents 5
Preface 11
Acknowledgments 15
Data Acquisition and Recording 17
Introduction 17
Basic Sampling Requirements 18
Sampling Interval 19
Sampling Duration 20
Sampling Accuracy 22
Burst Sampling Versus Continuous Sampling 22
Regularly Versus Irregularly Sampled Data 23
Independent Realizations 24
Temperature 24
Mercury Thermometers 25
The Mechanical Bathythermograph (MBT) 28
Resistance Thermometers (Expendable Bathythermograph: XBT) 30
Salinity/Conductivity-Temperature-Depth Profilers 33
Dynamic Response of Temperature Sensors 34
Response Times of CTD Systems 38
Temperature Calibration of STD/CTD Profilers 39
Sea Surface Temperature 40
Ship Measurements 40
Satellite-Sensed Sea Surface Temperature (Radiation Temperature) 42
The Modern Digital Thermometer 46
Potential Temperature and Density 47
Salinity 49
Salinity and Electrical Conductivity 50
A Comparison of Two Modern CTDs 52
The Practical Salinity Scale 55
Nonconductive Methods 58
Depth of Pressure 58
Hydrostatic Pressure 58
Free-Fall Velocity 59
Echo Sounding 64
Height above the Bottom 68
Other Depth Sounding Methods 70
Laser Induced Detection and Ranging (LIDAR) 70
Synthetic Aperture Radar (SAR) 70
Satellite Altimetry 70
Sea-Level Measurement 71
Specifics of Sea-Level Variability 72
Tide and Pressure Gauges 74
Satellite Altimetry 78
Inverted Echo Sounder (IES) 79
Wave Height and Direction 83
Eulerian Currents 84
Early Current Meter Technology 86
Rotor-Type Current Meters 86
The RCM Series of Current Meters 86
The Vector Averaging Current Meter (VACM) 89
Problems with the Savonious Rotor 90
Vector Measuring Current Meter (VMCM) 93
Nonmechanical Current Meters 94
Acoustic Current Meters (ACM) 94
Electromagnetic Current Meters (ECM) 95
Profiling Acoustic Doppler Current Meters (ADCM) 99
Acoustic Backscatter 108
Comparisons of Current Meters 110
Electromagnetic Methods 111
Other Methods of Current Measurement 112
Mooring Logistics 113
Acoustic Releases 115
Lagrangian Current Measurements 118
Drift Cards and Bottles 119
Modern Drifters 120
Processing Satellite-Tracked Drifter Data 123
Drifter Response 125
Other Types of Surface Drifters 131
Subsurface Floats 132
Surface Displacements in Satellite Imagery 135
Wind 135
Precipitation 141
Chemical Tracers 143
Conventional Tracers 144
Temperature and Salinity 144
Dissolved Oxygen 145
Nutrients 149
Silicate 153
Light Attenuation and Scattering 154
Oxygen Isotope: Gamma18O 158
Helium-3 Helium/Heat Ratio
Transient Chemical Tracers 161
Tritium 162
Radiocarbon 165
Chlorofluorocarbons 169
Radon-222 171
Sulfur Hexafluoride 173
Strontium-90 174
Data Processing and Presentation 175
Introduction 175
Calibration 176
Interpolation 177
Data Presentation 178
Introduction 178
Vertical Profiles 183
Vertical Sections 186
Horizontal Maps 188
Map Projections 193
Characteristic or Property Versus Property Diagrams 197
Time-Series Presentation 201
Histograms 203
New Directions in Graphical Presentation 203
Statistical Methods and Error Handling 209
Introduction 209
Sample Distributions 210
Probability 213
Cumulative Probability Functions 216
Moments and Expected Values 217
Unbiased Estimators and Moments 219
Moment Generating Functions 220
Common Probability Density Functions 223
Central Limit Theorem 227
Estimation 230
Confidence Intervals 232
Confidence Interval for mu (Sigma known) 233
Confidence Interval for Mu (Sigma Unknown) 234
Confidence Interval for Sigma2 235
Goodness-of-Fit Test 236
Selecting the Sample Size 240
Confidence Intervals for Altimeter Bias Estimates 241
Estimation Methods 243
Minimum Variance Unbiased Estimation 244
Method of Moments 245
Maximum Likelihood 246
Linear Estimation (Regression) 249
Method of Least Squares 250
Standard Error of the Estimate 254
Multivariate Regression 255
A Computational Example of Matrix Regression 256
Polynomial Curve Fitting with Least Squares 258
Relationship between Least-Squares and Maximum Likelihood 258
Relationship between Regression and Correlation 259
The Effects of Random Errors on Correlation 260
The Maximum Likelihood Correlation Estimator 261
Correlation and Regression: Cause and Effect 262
Hypothesis Testing 265
Significance Levels and Confidence Intervals for Correlation 269
Analysis of Variance and the F-Distribution 270
Effective Degrees of Freedom 273
Trend Estimates and the Integral Time Scale 277
Editing and Despiking Techniques: The Nature of Errors 280
Identifying and Removing Errors 282
Propagation of Error 289
Dealing with Numbers: The Statistics of Roundoff 290
Gauss-Markov Theorem 292
Interpolation: Filling the Data Gaps 293
Equally and Unequally Spaced Data 293
Interpolation Methods 295
Linear Interpolation 295
Polynomial Interpolation 295
Lagrange's Method 296
Spline Interpolation 297
Interpolating Gappy Records: Practical Examples 301
Interpolating Gappy Records for Time-Series Analysis 302
Interpolating Satellite-Tracked Positional Data 303
Interpolation Records from Nearby Stations 306
Covariance and the Covariance Matrix 306
Covariance and Structure Functions 306
A Computational Example 307
Multivariate Distributions 309
The Bootstrap and Jackknife Methods 310
Bootstrap Method 311
Jackknife Method 317
The Spatial Analyses of Data Fields 321
Traditional Block and Bulk Averaging 321
Objective Analysis 325
Objective Mapping: Examples 330
Empirical Orthogonal Functions 335
Principal Axes of a Single Vector Time Series (Scatter Plot) 341
EOF Computation using the Scatter Matrix Method 344
EOF Computation using Singular Value Decomposition 348
An Example: Deep Currents Near a Mid-Ocean Ridge 350
Interpretation of EOFs 352
Variations on Conventional EOF Analysis 356
Normal Mode Analysis 360
Vertical Normal Modes 360
An Example: Normal Modes of Semidiurnal Frequency 363
Coastal-Trapped Waves (CTWs) 366
Inverse Methods 372
General Inverse Theory 372
Inverse Theory and Absolute Currents 377
The Beta Spiral Method 378
Wunsch's Method 380
The IWEX Internal Wave Problem 382
Summary of Inverse Methods 386
Time-Series Analysis Methods 387
Basic Concepts 387
Stochastic Processes and Stationarity 389
Correlation Functions 390
Fourier Analysis 396
Mathematical Formulation 397
Discrete Time Series 400
A Computational Example 403
Fourier Analysis for Specified Frequencies 404
The Fast Fourier Transform 406
Harmonic Analysis 408
A Least-Squares Method 408
A Computational Example 411
Harmonic Analysis of Tides 413
Choice of Constituents 414
A Computational Example for Tides 415
Complex Demodulation 418
Spectral Analysis 420
Spectra of Deterministic and Stochastic Processes 425
Spectra of Discrete Series 429
Conventional Spectral Methods 433
The Autocorrelation Method 433
The Periodogram Method 435
The Power Spectral Density for Periodic Data 438
Variance-Preserving Spectra 438
The Chi-Squared Property of Spectral Estimators 440
Spectra of Vector Series 441
Cartesian Component Rotary Spectra 442
Rotary Component Spectra 443
Rotary Spectra (Via Cartesian Components) 448
Effect of Sampling on Spectral Estimates 448
Effect of Finite Record Length 448
Aliasing 450
Nyquist Frequency Sampling 453
Frequency Resolution 454
Smoothing Spectral Estimates (Windowing) 456
Desired Window Qualities 458
Rectangular (Box-Car) and Triangular Windows 459
Hanning and Hamming Windows (50% Overlap) 461
Kaiser-Bessel Window (75% Overlap) 464
Smoothing Spectra in the Frequency Domain 466
Band Averaging 466
Block Averaging 467
Confidence Intervals on Spectra 469
Confidence Intervals on a Logarithmic Scale 470
Fidelity and Stability 471
Zero-Padding and Prewhitening 471
Spectral Analysis of Unevenly Spaced Time Series 474
General Spectral Bandwidth and Q of the System 476
Summary of the Standard Spectral Analysis Approach 477
Spectral Analysis (Parametric Methods) 480
Some Basic Concepts 481
Autoregressive Power Spectral Estimation 484
Autoregressive Parameter Estimation 485
Order of the Autoregressive Process 487
Maximum Entropy Method (MEM) 489
An Autoregressive Model of Global Temperatures 490
Maximum Likelihood Spectral Estimation 493
Cross-Spectral Analysis 494
Cross-Correlation Functions 496
Cross-Covariance Method 497
Fourier Transform Method 498
Phase and Cross-Amplitude Functions 499
Coincident and Quadrature Spectra 501
Relationship of Co- and Quad-Spectra to Cross-Covariance 502
Coherence Spectrum (Coherency) 502
Confidence Levels 504
Frequency Response of a Linear System 506
Multi-Input Systems Cross-Spectral Analysis 506
Rotary Cross-Spectral Analysis 510
Rotary Analysis for a Pair of Time Series 512
Wavelet Analysis 516
The Wavelet Transform 517
Wavelet Algorithms 518
Oceanographic Examples 520
The S-Transformation 521
The Multiple Filter Technique 525
Theoretical Considerations 525
Digital Filters 530
Introduction 530
Basic Concepts 531
Ideal Filters 534
Bandwidth 535
Gibbs' Phenomenon 538
Recoloring 541
Design of Oceanographic Filters 542
Frequency Versus Time Domain Filtering 542
Filter Cascades 543
Running-Mean Filters 545
Godin-Type Filters 548
Lanczos-Window Cosine Filters 549
Cosine Filters 551
The Lanczos Window 552
Practical Filter Design 554
The Hanning (Von Hann) Window 555
Butterworth Filters 556
High-Pass and Band-Pass Filters 558
Digital Formulation 559
Tangent Versus Sine Filters 561
Filter Design 562
Filter Coefficients 562
Frequency-Domain (Transform) Filtering 565
Truncation Effects 570
Fractals 570
The Scaling Exponent Method 573
The Yardstick Method 574
Box Counting Method 577
Correlation Dimension 577
Dimensions of Multifractal Functions 579
Predictability 580
Appendices 585
Units in Physical Oceanography 586
Glossary of Statistical Terminology 588
Means, Variances and Moment-Generating Functions for Some Common Continuous Variables 592
Statistical Tables 593
Correlation Coefficents at the 5% and 1% Levels of Significance for Various Degrees of Freedom v 601
Approximations and Nondimensional Numbers in Physical Oceanography 602
Convolution 609
Convolution and Fourier Transforms 609
Convolution of Discrete Data 609
Convolution as Truncation of an Infinite Time Series 610
Deconvolution 612
References 613
Index 637