Numerical Models of Oceans and Oceanic Processes (eBook)

Cover 1
Contents 8
List of Acronyms 16
List of Symbols 24
Foreword 28
Preface 31
Prologue 34
Chapter 1. Introduction to Ocean Dynamics 38
1.1 Types, Advantages, and Limitations of Ocean Models 52
1.2 Recent Examples 58
1.3 Governing Equations 65
1.4 Vorticity Conservation 83
1.5 Nondimensional Numbers and Scales of Motion 85
1.6 Geostrophic Flow and Thermal Wind 93
1.7 Inertial Motions 96
1.8 Ekman Layers 97
1.9 Sverdrup Transport 108
1.10 Western Boundary Intensification (Stommel Solution) 112
1.11 Gyre Scale Circulation (Munk Solution) 117
1.12 Barotropic Currents over Topography 127
1.13 Baroclinic Transport over Topography 129
1.14 Coastal Upwelling and Fronts 133
1.15 Mesoscale Eddies and Variability 137
1.16 Thermohaline Circulation and Box (Reservoir) Models 147
1.17 Numerical Models 158
Chapter 2. Introduction to Numerical Solutions 164
2.1 Introduction 166
2.2 Ordinary Differential Equations 174
2.3 Partial Differential Equations 178
2.4 Elliptic Equations and Steady-State Problems 188
2.5 Time Dependent Problems 205
2.6 Finite-Difference (Grid Point) Methods 223
2.7 Spectral (Spectral Transform) Methods 248
2.8 Finite-Element Methods 253
2.9 Parameterization of Subgrid Scale Processes 260
2.10 Lateral Open Boundary Conditions 262
2.11 Computational Issues 268
2.12 Examples 270
Chapter 3. Equatorial Dynamics and Reduced Gravity Models Solutions 284
3.1 Oceanic Dynamical Response to Forcing 285
3.2 Governing Equations 290
3.3 Equatorial Waves 296
3.4 Equatorial Currents 308
3.5 Reduced Gravity Model of Equatorial Processes 312
Chapter 4. Midlatitude Dynamics and Quasi-Geostrophic Models 328
4.1 Linear Motions 329
4.2 Continuous Stratification 347
4.3 Geostrophic Adjustment and Instabilities 350
4.4 Spinup 361
4.5 Quasi-Geostrophic Models 364
Chapter 5. High-Latitude Dynamics and Sea-Ice Models 374
5.1 Salient Features of Ice Cover 374
5.2 Momentum Equations for Sea Ice 383
5.3 Constitutive Law for Sea Ice (Ice Rheology) 385
5.4 Continuity Equations for Sea Ice 397
5.5 Response of Sea Ice to Storm Passage 398
5.6 Numerics 400
Chapter 6. Tides and Tidal Modeling 412
6.1 Description of Tides 416
6.2 Formulation: Tidal Potential 424
6.3 Body, Load, Atmospheric, and Radiational Tides 436
6.4 Dynamical Theory of Tides: Laplace Tidal Equations 447
6.5 Equilibrium Theory of Tides 454
6.6 Tidal Analysis: Orthotides 455
6.7 Tidal Currents 461
6.8 Global Tidal Models 466
6.9 Regional Tidal Models 477
6.10 Geophysical Implications 478
6.11 Changes in Earth's Rotation 494
6.12 Baroclinic (Internal) Tides 508
6.13 Long-Period Tides 517
6.14 Shallow Water Tides and Residual Currents 523
6.15 Summary 527
Chapter 7. Coastal Dynamics and Barotropic Models 530
7.1 Wind- and Buoyancy-Driven Currents 533
7.2 Tidal Motions 535
7.3 Continental Shelf Waves 536
7.4 Modeling Shelf Circulation 549
7.5 Barotropic Models 550
Chapter 8. Data and Data Processing 566
8.1 In Situ Observational Data 569
8.2 Remotely Sensed Data 591
8.3 NWP Products 606
8.4 Preprocessing of Observational Data and Postprocessing of Model Output 608
Chapter 9. Sigma-Coordinate Regional and Coastal Models 614
9.1 Introduction 616
9.2 Governing Equations 622
9.3 Vertical Mixing 628
9.4 Boundary Conditions 630
9.5 Mode Splitting 633
9.6 Numerics 636
9.7 Numerical Problems 648
9.8 Applications 651
9.9 Code Structure 656
Chapter 10. Multilevel Basin Scale and Global Models 664
10.1 Introduction 665
10.2 Governing Equations 666
10.3 Isopycnal Diffusion 677
10.4 Architecture and Other Model Features 682
10.5 Applications 684
10.6 Hybrid s-Coordinate Models 686
10.7 Regional z-Level Models 696
Chapter 11. Layered and Isopycnal Models 698
11.1 Layered Models 699
11.2 Isopycnal Models 705
Chapter 12. Ice–Ocean Coupled Models 712
12.1 Sea-Ice Models 713
12.2 Coupled Ice–Ocean Models 726
Chapter 13. Ocean–Atmosphere Coupled Models 736
13.1 Coupling between the Ocean and the Atmosphere 740
13.2 Coupled Ocean–Atmosphere General Circulation Models 745
13.3 Regional Coupled Ocean–Atmosphere Models 756
Chapter 14. Data Assimilation and Nowcasts/Forecasts 766
14.1 Introduction 767
14.2 Direct Insertion 771
14.3 Nudging 772
14.4 Statistical Assimilation Schemes 773
14.5 Variational Methods 784
14.6 Predictability of Nonlinear Systems„Low Order Paradigms 790
14.7 Nowcasts/Forecasts in the Gulf of Mexico 806
Appendix A. Equations of State 814
A.1 Equation of State for the Ocean 814
A.2 Equation of State for the Atmosphere 816
Appendix B. Wavelet Transforms 820
B.1 Introduction 823
B.2 Examples 845
B.3 Wavelet Transforms and Stochastic Processes 849
B.4 Two-Dimensional Wavelet Transforms 850
B.5 Cross Wavelet Transforms (CrWT) 852
B.6 Error Analysis 855
Appendix C. Empirical Orthogonal Functions and Empirical Normal Modes 856
C.1 Empirical Orthogonal Functions 857
C.2 Empirical Normal Modes 879
Appendix D Units and Constants 888
D.1 Useful Quantities 888
D.2 Important Scales and Quantities 895
D.3 Useful Websites 899
References 902
Biographies 948
Index 952
List of Volumes in the Series 974
Color Plate Section 978