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Tables of Contents for Data Analysis Methods in Physical Oceanography
Chapter/Section Title
Page #
Page Count
Preface
xi
Acknowledgments
xv
Data Acquisition and Recording
1
158
Introduction
1
1
Basic sampling requirements
2
6
Sampling interval
3
1
Sampling duration
4
2
Sampling accuracy
6
1
Burst sampling versus continuous sampling
6
1
Regularly versus irregularly sampled data
7
1
Independent realizations
8
1
Temperature
8
25
Mercury thermometers
9
3
The mechanical bathythermograph (MBT)
12
2
Resistance thermometers (expendable bathythermograph: XBT)
14
4
Salinity/conductivity-temperature-depth profilers
18
1
Dynamic response of temperature sensors
19
3
Response times of CTD systems
22
1
Temperature calibration of STD/CTD profilers
23
1
Sea surface temperature
24
6
The modern digital thermometer
30
2
Potential temperature and density
32
1
Salinity
33
9
Salinity and electrical conductivity
34
5
The practical salinity scale
39
3
Nonconductive methods
42
1
Depth or pressure
42
13
Hydrostatic pressure
42
1
Free-fall velocity
43
5
Echo sounding
48
6
Other depth sounding methods
54
1
Seal-level measurement
55
13
Tide and pressure gauges
58
4
Satellite altimetry
62
1
Inverted echo sounder (IES)
63
4
Wave height and direction
67
1
Eulerian currents
68
34
Early current meter technology
70
1
Rotor-type current meters
70
8
Nonmechanical current meters
78
5
Profiling acoustic Doppler current meters (ADCM)
83
11
Comparisons of current meters
94
1
Electromagnetic methods
95
1
Other methods of current measurement
96
1
Mooring logistics
97
2
Acoustic releases
99
3
Lagrangian current measurements
102
17
Drift cards and bottles
103
1
Modern drifters
104
3
Processing satellite-tracked drifter data
107
2
Drifter response
109
6
Other types of surface drifters
115
1
Subsurface floats
116
3
Surface displacements in satellite imagery
119
1
Wind
119
6
Precipitation
125
2
Chemical tracers
127
18
Conventional tracers
128
10
Light attenuation and scattering
138
4
Oxygen isotope: δ18O
142
1
Helium-3; helium/heat ratio
143
2
Transient chemical tracers
145
14
Tritium
146
3
Radiocarbon
149
4
Chlorofluorocarbons
153
2
Radon-222
155
2
Sulfur hexafluoride
157
1
Strontium-90
158
1
Data Processing and Presentation
159
34
Introduction
159
1
Calibration
160
1
Interpolation
161
1
Data presentation
162
31
Introduction
162
5
Vertical profiles
167
3
Vertical sections
170
2
Horizontal maps
172
5
Map projections
177
4
Characteristic or property versus property diagrams
181
4
Time-series presentation
185
2
Histograms
187
1
New directions in graphical presentation
187
6
Stastical Methods and Error Handling
193
112
Introduction
193
1
Sample distributions
194
3
Probability
197
4
Cumulative probability functions
200
1
Moments and expected values
201
6
Unbiased estimators and moments
203
1
Moment generating functions
204
3
Common probability density functions
207
4
Central limit theorem
211
3
Estimation
214
2
Confidence intervals
216
8
Confidence interval for μ (σ known)
217
1
Confidence interval for μ (σ unknown)
218
1
Confidence interval for σ2
219
1
Goodness-of-fit test
220
4
Selecting the sample size
224
1
Confidence intervals for altimeter bias estimates
225
2
Estimation methods
227
6
Minimum variance unbiased estimation
228
1
Method of moments
229
1
Maximum likelihood
230
3
Linear estimation (regression)
233
10
Method of least squares
234
4
Standard error of the estimate
238
1
Multivariate regression
239
1
A computational example of matrix regression
240
2
Polynomial curve fitting with least squares
242
1
Relationship between least-squares and maximum likelihood
242
1
Relationship between regression and correlation
243
6
The effects of random errors on correlation
244
1
The maximum likelihood correlation estimator
245
1
Correlation and regression: cause and effect
246
3
Hypothesis testing
249
8
Significance levels and confidence intervals for correlation
253
1
Analysis of variance and the F-distribution
254
3
Effective degrees of freedom
257
9
Trend estimates and the integral time scale
261
5
Editing and despiking techniques: the nature of errors
266
11
Identifying and removing errors
266
7
Propagation of error
273
1
Dealing with numbers: the statistics of roundoff
274
3
Gauss-Markov theorem
277
1
Interpolation: filling the data gaps
277
13
Equally and unequally spaced data
277
2
Interpolation methods
279
7
Interpolating gappy records: practical examples
286
4
Covariance and the covariance matrix
290
4
Convariance and structure functions
291
1
A computational example
291
2
Multivariate distributions
293
1
Bootstrap and jackknife methods
294
11
Bootstrap method
295
6
Jackknife method
301
4
The Spatial Analyses of Data Fields
305
66
Traditional block and bulk averaging
305
4
Objective analysis
309
10
Objective mapping: examples
314
5
Empirical orthogonal functions
319
25
Principal axes of a single vector time series (scatter plot)
325
3
EOF computation using the scatter matrix method
328
4
EOF computation using singular value decomposition
332
2
An example: deep currents near a mid-ocean ridge
334
2
Interpretation of EOFs
336
4
Variations on conventional EOF analysis
340
4
Normal mode analysis
344
12
Vertical normal modes
344
3
An example: normal modes of semidiurnal frequency
347
3
Coastal-trapped waves (CTWs)
350
6
Inverse methods
356
15
General inverse theory
356
5
Inverse theory and absolute currents
361
5
The IWEX internal wave problem
366
4
Summary of inverse methods
370
1
Time-series Analysis Methods
371
198
Basic concepts
371
2
Stochastic processes and stationarity
373
1
Correlation functions
374
6
Fourier analysis
380
12
Mathematical formulation
381
3
Discrete time series
384
3
A computational example
387
1
Fourier analysis for specified frequencies
388
2
The fast Fourier transform
390
2
Harmonic analysis
392
12
A least-squares methods
392
3
A computational example
395
2
Harmonic analysis of tides
397
1
Choice of constituents
398
1
A computational example for tides
399
3
Complex demodulation
402
2
Spectral analysis
404
60
Spectra of deterministic and stochastic processes
409
4
Spectra of discrete series
413
4
Conventional spectral methods
417
8
Spectra of vector series
425
7
Effect of sampling on spectral estimates
432
9
Smoothing spectral estimates (windowing)
441
9
Smoothing spectra in the frequency domain
450
4
Confidence intervals on spectra
454
1
Zero-padding and prewhitening
455
5
Spectral analysis of unevenly spaced time series
460
1
General spectral bandwidth and Q of the system
461
1
Summary of the standard spectral analysis approach
461
3
Spectral analysis (parametric methods)
464
16
Some basic concepts
467
1
Autoregressive power spectral estimation
468
10
Maximum likelihood spectral estimation
478
2
Cross-spectral analysis
480
21
Cross-correlation functions
480
2
Cross-covariance method
482
1
Fourier transform method
482
2
Phase and cross-amplitude functions
484
1
Coincident and quadrature spectra
485
1
Coherence spectrum (coherency)
486
4
Frequency response of a linear system
490
5
Rotary cross-spectral analysis
495
6
Wavelet analysis
501
15
The wavelet transform
502
2
Wavelet algorithms
504
1
Oceanographic examples
505
3
The S-transformation
508
3
The multiple filter technique
511
5
Digital filters
516
41
Introduction
518
Basic concepts
517
2
Ideal filters
519
8
Design of oceanographic filters
527
5
Running-mean filters
532
3
Godin-type filters
535
1
Lanczos-window cosine filters
536
7
Butterworth filters
543
8
Frequency-domain (transform) filtering
551
6
Fractals
557
12
The scaling exponent method
561
1
The yardstick method
562
1
Box counting method
563
1
Correlation dimension
564
1
Dimensions of multifractal functions
564
3
Predictability
567
2
Appendices
569
28
Appendix A Units in physical oceanography
570
2
Appendix B Glossary of statistical terminology
572
4
Appendix C Means, variances and moment-generating functions for some common continuous variables
576
1
Appendix D Statistical tables
577
8
Appendix E Correlation coefficents at the 5% and 1% levels of significance for various degrees of freedom v
585
1
Appendix F Approximations and nondimensional numbers in physical oceanography
586
7
Appendix G Convolution
593
4
References
597
24
Index
621