Stephen Griffies

Fundamentals of Ocean Climate Models (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book sets forth the physical, mathematical, and numerical foundations of computer models used to understand and predict the global ocean climate system. Aimed at students and researchers of ocean and climate science who seek to understand the physical content of ocean model equations and numerical methods for their solution, it is largely general in formulation and employs modern mathematical techniques. It also highlights certain areas of cutting-edge research.

Stephen Griffies presents material that spans a broad spectrum of issues critical for modern ocean climate models. Topics are organized into parts consisting of related chapters, with each part largely self-contained. Early chapters focus on the basic equations arising from classical mechanics and thermodynamics used to rationalize ocean fluid dynamics. These equations are then cast into a form appropriate for numerical models of finite grid resolution. Basic discretization methods are described for commonly used classes of ocean climate models. The book proceeds to focus on the parameterization of phenomena occurring at scales unresolved by the ocean model, which represents a large part of modern oceanographic research. The final part provides a tutorial on the tensor methods that are used throughout the book, in a general and elegant fashion, to formulate the equations.

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Produktdetails

• Verlag: Verso
• Erscheinungstermin: 5. Juni 2018
• Englisch
• ISBN-13: 9780691187129
• Artikelnr.: 52920221

Autorenporträt

Stephen Griffies is head of the Oceans and Climate Group at the National Oceanic and Atmospheric Administration's Geophysical Fluid Dynamics Laboratory in Princeton, New Jersey. He is a principal developer of the Modular Ocean Model, which is widely used by ocean and climate scientists worldwide

Inhaltsangabe

FOREWORD XIII
PREFACE XV
ACKNOWLEDGMENTS XXV
ABOUT THE COVER XXVII
LIST OF SYMBOLS XXIX
Chapter 1. OCEAN CLIMATE MODELS 1
1.1 Ocean models as tools for ocean science 1
1.2 Ocean climate models 2
1.3 Challenges of climate change 3
PART 1. FUNDAMENTAL OCEAN EQUATIONS 5
Chapter 2. BASICS OF OCEAN FLUID MECHANICS 7
2.1 Some fundamental ocean processes 7
2.2 The continuum hypothesis 9
2.3 Kinematics of fluid motion 10
2.4 Kinematical and dynamical approximations 16
2.5 Averaging over scales and realizations 20
2.6 Numerical discretization 21
2.7 Chapter summary 22
Chapter 3. KINEMATICS 24
3.1 Introduction 24
3.2 Mathematical preliminaries 24
3.3 The divergence theorem and budget analyses 29
3.4 Volume and mass conserving kinematics 31
3.5 Chapter summary 40
Chapter 4. DYNAMICS 42
4.1 Introduction 42
4.2 Motion on a rotating sphere 43
4.3 Principles of continuum dynamics 47
4.4 Dynamics of fluid parcels 51
4.5 Hydrostatic pressure 56
4.6 Dynamics of hydrostatic fluid columns 58
4.7 Fluid motion in a rapidly rotating system 62
4.8 Vertical stratification 68
4.9 Vorticity and potential vorticity 70
4.10 Particle dynamics on a rotating sphere 75
4.11 Symmetry and conservation laws 80
4.12 Chapter summary 83
Chapter 5. THERMO-HYDRODYNAMICS 87
5.1 General types of ocean tracers 87
5.2 Basic equilibrium thermodynamics 91
5.3 Energy of a fluid parcel 95
5.4 Global mechanical energy balance 105
5.5 Basic non-equilibrium thermodynamics 110
5.6 Thermodynamical tracers 111
5.7 Ocean density 114
5.8 Chapter summary 118
Chapter 6. GENERALIZED VERTICAL COORDINATES 121
6.1 Introduction 121
6.2 Concerning the choice of vertical coordinate 122
6.3 Generalized surfaces 128
6.4 Local orthonormal coordinates 130
6.5 Mathematics of generalized vertical coordinates 131
6.6 Metric tensors 136
6.7 The dia-surface velocity component 138
6.8 Conservation of mass and volume for parcels 141
6.9 Kinematic boundary conditions 143
6.10 Primitive equations 145
6.11 Transformation of SGS tracer flux components 147
6.12 Chapter summary 149
PART 2. AVERAGED DESCRIPTIONS 153
Chapter 7. CONCERNI NG UNRESOLVED PHYSICS 155
7.1 Represented dynamics and parameterized physics 155
7.2 Lateral (neutral) and vertical processes 157
7.3 Basic mechanisms for dianeutral transport 159
7.4 Dianeutral transport in models 161
7.5 Numerically induced spurious dianeutral transport 166
7.6 Chapter summary 167
Chapter 8. EULERIAN AVERAGED EQUATIONS 169
8.1 Introduction 169
8.2 The nonhydrostatic shallow ocean equations 171
8.3 Averaged kinematics 173
8.4 Averaged kinematics over finite domains 174
8.5 Averaged tracer 179
8.6 Averaged momentum budget 182
8.7 Summary of the Eulerian averaged equations 183
8.8 Mapping to ocean model variables 185
8.9 Chapter summary 187
Chapter 9. KINEMATICS OF AN ISENTROPIC ENSEMBLE 189
9.1 Parameterizing mesoscale eddies 189
9.2 Advection and skewsion 191
9.3 Volume conservation 194
9.4 Ensemble mean tracer equation 203
9.5 Quasi-Stokes transport in z-models 206
9.6 Chapter summary 212
PART 3. SEMI-DISCRETE EQUATIONS AND ALGORITHMS 215
Chapter 10. DISCRETIZATION BASICS 217
10.1 Discretization methods 217
10.2 An introduction to Arakawa grids 218
10.3 Time stepping 219
10.4 Chapter summary 221
Chapter 11. MASS AND TRACER BUDGETS 222
11.1 Summary of the continuous model equations 222
11.2 Tracer and mass/volume compatibility 223
11.3 Mass budget for a grid cell 223
11.4 Mass budget for a discrete fluid column 227
11.5 Tracer budget for a grid cell 228
11.6 Fluxes for turbulence mixed layer schemes 232
11.7 Flux plus restore boundary conditions 233
11.8 Z-like vertical coordinate models 234
11.9 Chapter summary 235
Chapter 12. ALGORITHMS FOR HYDROSTATIC OCEAN MODELS 237
12.1 Summary of the continuous model equations 237
12.2 Budget of linear momentum for a grid cell 238
12.3 Strategies for time stepping momentum 244
12.4 A leap-frog algorithm 248
12.5 Discretization of time tendencies 251
12.6 A time staggered algorithm 258
12.7 Barotropic updates with a predictor-corrector 262
12.8 Stability considerations 265
12.9 Smoothing the surface height in B-grid models 277
12.10 Rigid lid streamfunction method 278
12.11 Chapter summary 280
PART 4. NEUTRAL PHYSICS 281
Chapter 13. BASICS OF NEUTRAL PHYSICS 283
13.1 Concerning the utility of neutral physics 283
13.2 Notation and summary of scalar budgets 286
13.3 Compatibility in the mean field budgets 287
13.4 The SGS tracer transport tensor 288
13.5 Advection and skewsion 290
13.6 Neutral tracer fluxes 291
13.7 Chapter summary and a caveat on the conjecture 294
Chapter 14. NEUTRAL TRANSPORT OPERATORS 296
14.1 Neutral diffusion 296
14.2 Gent-McWilliams stirring 304
14.3 Summarizing the neutral physics fluxes 308
14.4 Flow-dependent diffusivities 309
14.5 Biharmonic operators 317
14.6 Chapter summary and some challenges 326
Chapter 15. NEUTRAL PHYSICS NEAR THE SURFACE BOUNDARY 328
15.1 Linear stability for neutral diffusion 328
15.2 Linear stability for GM stirring 332
15.3 Neutral physics near boundaries 333
15.4 Chapter summary and caveats 343
Chapter 16. FUNCTIONAL DISCRETIZATION OF NEUTRAL PHYSICS 345
16.1 Foundations for discrete neutral physics 345
16.2 Introduction to the discretization 350
16.3 A one-dimensional warm-up 352
16.4 Elements of the discrete dissipation functional 354
16.5 Triad stencils and some more notation 361
16.6 The discrete diffusion operator 363
16.7 Diffusive flux components 367
16.8 Further issues of numerical implementation 371
16.9 Chapter summary 374
PART 5. HORIZONTAL FRICTION 377
Chapter 17. HORIZONTAL FRICTION IN MODELS 379
17.1 Boussinesq and non-Boussinesq friction 379
17.2 Introduction and general framework 379
17.3 Properties of the stress tensor 380
17.4 Properties of the viscosity tensor 387
17.5 Transverse isotropy 389
17.6 Transverse anisotropy 393
17.7 Generalized orthogonal coordinates 396
17.8 Dissipation functional 398
17.9 Biharmonic friction 402
17.10 Some mathematical details 404
17.11 Chapter summary 407
Chapter 18. CHOOSING THE HORIZONTAL VISCOSITY 409
18.1 Stability and resolution considerations 409
18.2 Comparing Laplacian and biharmonic mixing 415
18.3 Smagorinsky viscosity 416
18.4 Background viscosity 420
18.5 Viscosities for anisotropic friction 421
18.6 Chapter summary 422
Chapter 19. FUNCTIONAL DISCRETIZATION OF FRICTION 424
19.1 Comments on notation 424
19.2 Summary of the various formulations 425
19.3 Horizontal friction discretization 426
19.4 Laplacian plus metric form of isotropic friction 436
19.5 Chapter summary 439
PART 6. TENSOR ANALYSIS 441
Chapter 20. ELEMENTARY TENSOR ANALYSIS 443
20.1 Introduction 443
20.2 Some practical motivation 444
20.3 Coordinates and vectors 446
20.4 The metric and coordinate transformations 448
20.5 Transformations of a vector 451
20.6 One-forms 452
20.7 Mapping between vectors and one-forms 454
20.8 Transformation of a one-form 454
20.9 Arbitrary tensors and their transformations 455
20.10 Tensorial properties of the gradient operator 456
20.11 The invariant volume element 457
20.12 Determinants and the Levi-Civita symbol 459
20.13 Surfaces embedded in Euclidean space 461
20.14 Chapter summary 464
Chapter 21. CALCULUS ON CURVED MANIFOLDS 466
21.1 Fundamental character of tensor equations 466
21.2 Covariant differentiation 468
21.3 Covariant derivative of a second order tensor 470
21.4 Christoffel symbols in terms of the metric 471
21.5 Covariant divergence of a vector 471
21.6 Covariant divergence of a second order tensor 472
21.7 Covariant Laplacian of a scalar 473
21.8 Covariant curl of a vector 473
21.9 Covariant Laplacian of a vector 473
21.10 Integral theorems 474
21.11 Orthogonal curvilinear coordinates 474
21.12 Summary of curvilinear tensor analysis 481
PART 7. EPILOGUE 487
Chapter 22. SOME CLOSING COMMENTS AND CHALLENGES 489
BIBLIOGRAPHY 493
Index 511