The modelling of ocean circulation is important not only for its own sake, but also in terms of the prediction of weather patterns and the effects of climate change. This book introduces the basic computational techniques necessary for all models of the ocean and atmosphere, and the conditions they must satisfy. It describes the workings of ocean models, the problems that must be solved in their construction, and how to evaluate computational results. Major emphasis is placed on examining ocean models critically, and determining what they do well and what they do poorly. Numerical analysis is introduced as needed, and exercises are included to illustrate major points. Developed from notes for a course taught in physical oceanography at the College of Oceanic and Atmospheric Sciences at Oregon State University, this book is ideal for graduate students of oceanography, geophysics, climatology and atmospheric science, and researchers in oceanography and atmospheric science.
Author(s): Robert N. Miller
Edition: 1
Year: 2007
Language: English
Pages: 252
Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 9
1 Introduction......Page 13
2.1 Simple discretizations of a linear advection equation......Page 15
2.2.1 Consistency, stability, convergence: the fundamentals......Page 20
2.3 Implicit methods......Page 26
2.4 Dissipation and dispersion......Page 27
2.5 A (very) brief introduction to finite-element methods......Page 32
2.6 Higher-order methods......Page 38
2.7 A first look at boundary-value problems......Page 40
2.8 Well- and ill-posed problems......Page 43
2.9 Exercises......Page 44
3.1 Introduction......Page 47
3.2 Discrete methods for the shallow-water equations......Page 53
3.3.1 Stability considerations for advection-diffusion equations......Page 58
3.3.2 Nonlinear instability......Page 60
3.4 Conservation laws and conservative difference schemes......Page 63
3.5 Artificial dissipation revisited......Page 71
3.7 Open-boundary conditions......Page 72
3.8.1 An early model of basin-scale circulation......Page 82
3.8.2 Stable and unstable equilibria in shallow-water models......Page 86
3.9 Choice of computational parameters: an example......Page 92
3.10 Exercises......Page 97
4.1 Specification of the primitive equation model......Page 99
4.2 Dissipation......Page 103
4.3.1 Derivation of a practical rigid lid PE model......Page 106
4.3.2 Examples with simple dynamics......Page 108
4.3.3 Stability restrictions......Page 111
4.4 Spinup of 3D models......Page 116
4.5 Consequences of discretization......Page 122
4.6 The importance of vertical resolution......Page 126
4.7 Example: Transport in the Drake Passage and the large-scale circulation......Page 130
4.8 Example: Separation of the Brazil current from the coast......Page 135
4.9 Generalized vertical coordinates......Page 146
4.10 Layer models......Page 158
4.11 Open-boundary conditions......Page 167
4.12 Finely resolved calculations......Page 168
4.13 Exercises......Page 175
5.1 Background and notation......Page 177
5.2.1 Vertical discretization......Page 179
5.4 Open-boundary models......Page 183
6.1 Introduction......Page 187
6.2 Example: A high-resolution two-dimensional model of upwelling circulation on the Oregon shelf......Page 189
6.3 Example: A three-dimensional calculation off the coast of California......Page 195
6.4 Example: A finite-element model......Page 203
6.5 Summary......Page 206
6.6 Exercises......Page 207
7.1 Introduction......Page 211
7.2 Waves in the equatorial ocean......Page 213
7.3 Simple models of the tropical oceans......Page 218
7.3.1 A simple gridded model of the tropical ocean......Page 223
7.3.2 Example: Application of a simple model of the tropical Pacific Ocean......Page 225
7.3.3 Simple models of the tropical Atlantic Ocean......Page 230
7.4.1 Comparisons to simple models......Page 232
7.4.2 Example: Dynamic balances in model equatorial undercurrents......Page 234
7.5 Conclusions......Page 239
7.6 Exercises......Page 241
References......Page 243
Index......Page 253
