Numerical Models of Oceans and Oceanic Processes
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Table of contents
- Cover
- Contentsvii
- List of Acronymsxv
- List of Symbolsxxiii
- Forewordxxvii
- Prefacexxx
- Prologuexxxiii
- Chapter 1. Introduction to Ocean Dynamics1
- 1.1 Types, Advantages, and Limitations of Ocean Models15
- 1.2 Recent Examples21
- 1.3 Governing Equations28
- 1.4 Vorticity Conservation46
- 1.5 Nondimensional Numbers and Scales of Motion48
- 1.6 Geostrophic Flow and Thermal Wind56
- 1.7 Inertial Motions59
- 1.8 Ekman Layers60
- 1.9 Sverdrup Transport71
- 1.10 Western Boundary Intensification (Stommel Solution)75
- 1.11 Gyre Scale Circulation (Munk Solution)80
- 1.12 Barotropic Currents over Topography90
- 1.13 Baroclinic Transport over Topography92
- 1.14 Coastal Upwelling and Fronts96
- 1.15 Mesoscale Eddies and Variability100
- 1.16 Thermohaline Circulation and Box (Reservoir) Models110
- 1.17 Numerical Models121
- Chapter 2. Introduction to Numerical Solutions127
- 2.1 Introduction129
- 2.2 Ordinary Differential Equations137
- 2.3 Partial Differential Equations141
- 2.4 Elliptic Equations and Steady-State Problems151
- 2.5 Time Dependent Problems168
- 2.6 Finite-Difference (Grid Point) Methods186
- 2.7 Spectral (Spectral Transform) Methods211
- 2.8 Finite-Element Methods216
- 2.9 Parameterization of Subgrid Scale Processes223
- 2.10 Lateral Open Boundary Conditions225
- 2.11 Computational Issues231
- 2.12 Examples233
- Chapter 3. Equatorial Dynamics and Reduced Gravity Models Solutions247
- 3.1 Oceanic Dynamical Response to Forcing248
- 3.2 Governing Equations253
- 3.3 Equatorial Waves259
- 3.4 Equatorial Currents271
- 3.5 Reduced Gravity Model of Equatorial Processes275
- Chapter 4. Midlatitude Dynamics and Quasi-Geostrophic Models291
- 4.1 Linear Motions292
- 4.2 Continuous Stratification310
- 4.3 Geostrophic Adjustment and Instabilities313
- 4.4 Spinup324
- 4.5 Quasi-Geostrophic Models327
- Chapter 5. High-Latitude Dynamics and Sea-Ice Models337
- 5.1 Salient Features of Ice Cover337
- 5.2 Momentum Equations for Sea Ice346
- 5.3 Constitutive Law for Sea Ice (Ice Rheology)348
- 5.4 Continuity Equations for Sea Ice360
- 5.5 Response of Sea Ice to Storm Passage361
- 5.6 Numerics363
- Chapter 6. Tides and Tidal Modeling375
- 6.1 Description of Tides379
- 6.2 Formulation: Tidal Potential387
- 6.3 Body, Load, Atmospheric, and Radiational Tides399
- 6.4 Dynamical Theory of Tides: Laplace Tidal Equations410
- 6.5 Equilibrium Theory of Tides417
- 6.6 Tidal Analysis: Orthotides418
- 6.7 Tidal Currents424
- 6.8 Global Tidal Models429
- 6.9 Regional Tidal Models440
- 6.10 Geophysical Implications441
- 6.11 Changes in Earth's Rotation457
- 6.12 Baroclinic (Internal) Tides471
- 6.13 Long-Period Tides480
- 6.14 Shallow Water Tides and Residual Currents486
- 6.15 Summary490
- Chapter 7. Coastal Dynamics and Barotropic Models493
- 7.1 Wind- and Buoyancy-Driven Currents496
- 7.2 Tidal Motions498
- 7.3 Continental Shelf Waves499
- 7.4 Modeling Shelf Circulation512
- 7.5 Barotropic Models513
- Chapter 8. Data and Data Processing529
- 8.1 In Situ Observational Data532
- 8.2 Remotely Sensed Data554
- 8.3 NWP Products569
- 8.4 Preprocessing of Observational Data and Postprocessing of Model Output571
- Chapter 9. Sigma-Coordinate Regional and Coastal Models577
- 9.1 Introduction579
- 9.2 Governing Equations585
- 9.3 Vertical Mixing591
- 9.4 Boundary Conditions593
- 9.5 Mode Splitting596
- 9.6 Numerics599
- 9.7 Numerical Problems611
- 9.8 Applications614
- 9.9 Code Structure619
- Chapter 10. Multilevel Basin Scale and Global Models627
- 10.1 Introduction628
- 10.2 Governing Equations629
- 10.3 Isopycnal Diffusion640
- 10.4 Architecture and Other Model Features645
- 10.5 Applications647
- 10.6 Hybrid s-Coordinate Models649
- 10.7 Regional z-Level Models659
- Chapter 11. Layered and Isopycnal Models661
- 11.1 Layered Models662
- 11.2 Isopycnal Models668
- Chapter 12. Ice–Ocean Coupled Models675
- 12.1 Sea-Ice Models676
- 12.2 Coupled Ice–Ocean Models689
- Chapter 13. Ocean–Atmosphere Coupled Models699
- 13.1 Coupling between the Ocean and the Atmosphere703
- 13.2 Coupled Ocean–Atmosphere General Circulation Models708
- 13.3 Regional Coupled Ocean–Atmosphere Models719
- Chapter 14. Data Assimilation and Nowcasts/Forecasts729
- 14.1 Introduction730
- 14.2 Direct Insertion734
- 14.3 Nudging735
- 14.4 Statistical Assimilation Schemes736
- 14.5 Variational Methods747
- 14.6 Predictability of Nonlinear Systems„Low Order Paradigms753
- 14.7 Nowcasts/Forecasts in the Gulf of Mexico769
- Appendix A. Equations of State777
- A.1 Equation of State for the Ocean777
- A.2 Equation of State for the Atmosphere779
- Appendix B. Wavelet Transforms783
- B.1 Introduction786
- B.2 Examples808
- B.3 Wavelet Transforms and Stochastic Processes812
- B.4 Two-Dimensional Wavelet Transforms813
- B.5 Cross Wavelet Transforms (CrWT)815
- B.6 Error Analysis818
- Appendix C. Empirical Orthogonal Functions and Empirical Normal Modes819
- C.1 Empirical Orthogonal Functions820
- C.2 Empirical Normal Modes842
- Appendix D Units and Constants851
- D.1 Useful Quantities851
- D.2 Important Scales and Quantities858
- D.3 Useful Websites862
- References865
- Biographies911
- Index915
- List of Volumes in the Series937
- Color Plate Section941
Oceans play a pivotal role in our weather and climate. Ocean-borne commerce is vital to our increasingly close-knit global community. Yet we do not fully understand the intricate details of how they function, how they interact with the atmosphere, and what the limits are to their biological productivity and their tolerance to wastes. While satellites are helping us to fill in the gaps, numerical ocean models are playing an important role in increasing our ability to comprehend oceanic processes, monitor the current state of the oceans, and to a limited extent, even predict their future state.
Numerical Models of Oceans and Oceanic Processes is a survey of the current state of knowledge in this field. It brings together a discussion of salient oceanic dynamics and processes, numerical solution methods, and ocean models to provide a comprehensive treatment of the topic. Starting with elementary concepts in ocean dynamics, it deals with equatorial, mid-latitude, high latitude, and coastal dynamics from the perspective of a modeler. A comprehensive and up-to-date chapter on tides is also included. This is followed by a discussion of different kinds of numerical ocean models and the pre- and post-processing requirements and techniques. Air-sea and ice-ocean coupled models are described, as well as data assimilation and nowcast/forecasts. Comprehensive appendices on wavelet transforms and empirical orthogonal functions are also included.
This comprehensive and up-to-date survey of the field should be of interest to oceanographers, atmospheric scientists, and climatologists. While some prior knowledge of oceans and numerical modeling is helpful, the book includes an overview of enough elementary material so that along with its companion volume, Small Scale Processes in Geophysical Flows, it should be useful to both students new to the field and practicing professionals.
* Comprehensive and up-to-date review
* Useful for a two-semester (or one-semester on selected topics) graduate level course
* Valuable reference on the topic
* Essential for a better understanding of weather and climate
Numerical Models of Oceans and Oceanic Processes is a survey of the current state of knowledge in this field. It brings together a discussion of salient oceanic dynamics and processes, numerical solution methods, and ocean models to provide a comprehensive treatment of the topic. Starting with elementary concepts in ocean dynamics, it deals with equatorial, mid-latitude, high latitude, and coastal dynamics from the perspective of a modeler. A comprehensive and up-to-date chapter on tides is also included. This is followed by a discussion of different kinds of numerical ocean models and the pre- and post-processing requirements and techniques. Air-sea and ice-ocean coupled models are described, as well as data assimilation and nowcast/forecasts. Comprehensive appendices on wavelet transforms and empirical orthogonal functions are also included.
This comprehensive and up-to-date survey of the field should be of interest to oceanographers, atmospheric scientists, and climatologists. While some prior knowledge of oceans and numerical modeling is helpful, the book includes an overview of enough elementary material so that along with its companion volume, Small Scale Processes in Geophysical Flows, it should be useful to both students new to the field and practicing professionals.
* Comprehensive and up-to-date review
* Useful for a two-semester (or one-semester on selected topics) graduate level course
* Valuable reference on the topic
* Essential for a better understanding of weather and climate