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The material that makes up this book evolved from notes prepared for an undergraduate class that has been taught by the authors at MIT over a period of ten years or so. During this time, many people, especially the students taking the class and those assisting in its teaching, have contributed to the evolution of the material and to the correction of errors in both the text and the problem sets. We have also benefited from the advice of our colleagues at MIT and Harvard; we especially thank Ed Boyle, Kerry Emanuel, Mick Follows, Peter Huybers, Lodovica Illari, Julian Sachs, Eli Tziperman and Carl Wunsch for generously giving their time to provide comments on early drafts of the text.

Responsibility for the accuracy of the final text rests, of course, with the authors alone.

We would also like to thank Benno Blumenthal for his advice in using the IRI/LDEO Climate Data Library, Gordon (Bud) Brown for help with the laboratory equipment and Russell Windman for his advice on the book design and final preparation of the photographs and figures.

John Marshall and R. Alan Plumb

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0.1 Outline, scope, and rationale of the book xiii 0.2 Preface xiv

0.2.1 Natural fluid dynamics xv

0.2.2 Rotating fluid dynamics: GFD Lab 0 xvii

0.2.3 Holicism xix

1. Characteristics of the atmosphere 1

1.1 Geometry 1

1.2 Chemical composition of the atmosphere 2

1.3 Physical properties of air 4

1.3.2 Moist air 5

1.3.3 GFD Lab I: Cloud formation on adiabatic expansion 7

1.4 Problems 7

2. The global energy balance 9

2.1 Planetary emission temperature 9

2.2 The atmospheric absorption spectrum 13

2.3 The greenhouse effect 14

2.3.1 A simple greenhouse model 14

2.3.2 A leaky greenhouse 16

2.3.3 A more opaque greenhouse 16

2.3.4 Climate feedbacks 19

2.4 Further reading 20

2.5 Problems 20

3. The vertical structure of the atmosphere 23

3.1 Vertical distribution of temperature and greenhouse gases 23

3.1.1 Typical temperature profile 23

3.1.2 Atmospheric layers 24

3.2 The relationship between pressure and density: hydrostatic balance 26

3.3 Vertical structure of pressure and density 28

3.3.1 Isothermal atmosphere 28

3.3.2 Non-isothermal atmosphere 28

3.3.3 Density 29

3.4 Further reading 29

3.5 Problems 29

4. Convection 31

4.1 The nature of convection 32

4.1.1 Convection in a shallow fluid 32

4.1.2 Instability 33

4.2 Convection in water 34

4.2.1 Buoyancy 34

4.2.2 Stability 35

4.2.3 Energetics 36

4.2.4 GFD Lab II: Convection 36

4.3 Dry convection in a compressible atmosphere 39

4.3.1 The adiabatic lapse rate (in unsaturated air) 39

4.3.2 Potential temperature 41

4.4 The atmosphere under stable conditions 42

4.4.1 Gravity waves 42

4.4.2 Temperature inversions 44

4.5 Moist convection 46

4.5.1 Humidity 47

4.5.2 Saturated adiabatic lapse rate 49

4.5.3 Equivalent potential temperature 50

4.6 Convection in the atmosphere 50

4.6.1 Types of convection 51

4.6.2 Where does convection occur? 55

4.7 Radiative-convective equilibrium 56

4.8 Further reading 57

4.9 Problems 57

5. The meridional structure of the atmosphere 61

5.1 Radiative forcing and temperature 62

5.1.1 Incoming radiation 62

5.1.2 Outgoing radiation 63

5.1.3 The energy balance of the atmosphere 64

5.1.4 Meridional structure of temperature 64

5.2 Pressure and geopotential height 67

5.3 Moisture 70

5.4 Winds 73

5.4.1 Distribution of winds 74

5.5 Further reading 78

5.6 Problems 78

6. The equations of fluid motion 81

6.1 Differentiation following the motion 82

6.2 Equation of motion for a nonrotating fluid 84

6.2.1 Forces on a fluid parcel 84

6.2.2 The equations of motion 86

6.2.3 Hydrostatic balance 87

6.3 Conservation of mass 87

6.3.1 Incompressible flow 88

6.3.2 Compressible flow 88

6.4 Thermodynamic equation 89

6.5 Integration, boundary conditions, and restrictions in application 89

6.6 Equations of motion for a rotating fluid 90

6.6.1 GFD Lab III: Radial inflow 90

6.6.2 Transformation into rotating coordinates 93

6.6.3 The rotating equations of motion 94

6.6.4 GFD Labs IV and V: Experiments with Coriolis forces on a parabolic rotating table 96

6.6.5 Putting things on the sphere 100

6.6.6 GFD Lab VI: An experiment on the Earth's rotation 103

6.7 Further reading 104

6.8 Problems 104

7. Balanced flow 109

7.1 Geostrophic motion 110

7.1.1 The geostrophic wind in pressure coordinates 112

7.1.2 Highs and lows; synoptic charts 114

7.1.3 Balanced flow in the radial-inflow experiment 116

7.2 The Taylor-Proudman theorem 117 7.2.1 GFD Lab VII: Taylor columns 118

7.3 The thermal wind equation 119

7.3.1 GFD Lab VIII: The thermal wind relation 120

7.3.2 The thermal wind equation and the Taylor-Proudman theorem 122

7.3.3 GFD Lab IX: cylinder "collapse" under gravity and rotation 123

7.3.4 Mutual adjustment of velocity and pressure 125

7.3.5 Thermal wind in pressure coordinates 126

7.4 Subgeostrophic flow: the Ekman layer 129

7.4.1 GFD Lab X: Ekman layers: frictionally-induced cross-isobaric flow 130

7.4.2 Ageostrophic flow in atmospheric highs and lows 130

7.4.3 Planetary-scale ageostrophic flow 133

7.5 Problems 135

8. The general circulation of the atmosphere 139

8.1 Understanding the observed circulation 140

8.2 A mechanistic view of the circulation 141

8.2.1 The tropical Hadley circulation 142

8.2.2 The extratropical circulation and GFD Lab XI: Baroclinic instability 145

8.3 Energetics of the thermal wind equation 149

8.3.1 Potential energy for a fluid system 149

8.3.2 Available potential energy 150

8.3.3 Release of available potential energy in baroclinic instability 152

8.3.4 Energetics in a compressible atmosphere 153

8.4 Large-scale atmospheric energy and momentum budget 154

8.4.1 Energy transport 154

8.4.2 Momentum transport 156

8.5 Latitudinal variations of climate 157

8.6 Further reading 158

8.7 Problems 159

9. The ocean and its circulation 163

9.1 Physical characteristics of the ocean 164

9.1.1 The ocean basins 164

9.1.2 The cryosphere 165

9.1.3 Properties of seawater; equation of state 165

9.1.4 Temperature, salinity, and temperature structure 168

9.1.5 The mixed layer and thermocline 171

9.2 The observed mean circulation 176

9.3 Inferences from geostrophic and hydrostatic balance 182

9.3.1 Ocean surface structure and geostrophic flow 183

9.3.2 Geostrophic flow at depth 184

9.3.3 Steric effects 186

9.3.4 The dynamic method 187

9.4 Ocean eddies 188

9.4.1 Observations of ocean eddies 188

9.5 Further reading 189

9.6 Problems 190

10. The wind-driven circulation 197

10.1 The wind stress and Ekman layers 198

10.1.1 Balance of forces and transport in the Ekman layer 199

10.1.2 Ekman pumping and suction and GFD Lab XII 201

10.1.3 Ekman pumping and suction induced by large-scale wind patterns 203

10.2 Response of the interior ocean to Ekman pumping 206

10.2.1 Interior balances 206

10.2.2 Wind-driven gyres and western boundary currents 206

10.2.3 Taylor-Proudman on the sphere 207

10.2.4 GFD Lab XIII: Wind-driven ocean gyres 211

10.3 The depth-integrated circulation: Sverdrup theory 213

10.3.1 Rationalization of position, sense of circulation, and volume transport of ocean gyres 214

10.4 Effects of stratification and topography 216 10.4.1 Taylor-Proudman in a layered ocean 217

10.5 Baroclinic instability in the ocean 218

10.6 Further reading 220

10.7 Problems 220

11. The thermohaline circulation of the ocean 223

11.1 Air-sea fluxes and surface property distributions 224

11.1.1 Heat, freshwater, and buoyancy fluxes 224

11.1.2 Interpretation of surface temperature distributions 231

11.1.3 Sites of deep convection 232

11.2 The observed thermohaline circulation 234

11.2.1 Inferences from interior tracer distributions 234

11.2.2 Time scales and intensity of thermohaline circulation 239

11.3 Dynamical models of the thermohaline circulation 239

11.3.1 Abyssal circulation schematic deduced from Taylor-Proudman on the sphere 239

11.3.2 GFD Lab XIV: The abyssal circulation 241

11.3.3 Why western boundary currents? 243

11.3.4 GFD Lab XV: Source sink flow in a rotating basin 245

11.4 Observations of abyssal ocean circulation 245

11.5 The ocean heat budget and transport 247

11.5.1 Meridional heat transport 248

11.5.2 Mechanisms of ocean heat transport and the partition of heat transport between the atmosphere and ocean 251

11.6 Freshwater transport by the ocean 255

11.7 Further reading 256

11.8 Problems 256

12. Climate and climate variability 259

12.1 The ocean as a buffer of temperature change 261 12.1.1 Nonseasonal changes in SST 262

12.2 ElNino and the Southern Oscillation 264

12.2.1 Interannual variability 264

12.2.2 "Normal" conditions—equatorial upwelling and the Walker circulation 266

12.2.3 ENSO 269

12.2.4 Other modes of variability 273

12.3 Paleoclimate 273

12.3.1 Climate over Earth history 275

12.3.2 Paleotemperatures over the past 70 million years: the ô18O record 277

12.3.3 Greenhouse climates 280

12.3.4 Cold climates 280

12.3.5 Glacial-interglacial cycles 282

12.3.6 Global warming 291

12.4 Further reading 292

12.5 Problems 292

Appendices 295

A.1 Derivations 295

A.1.1 The Planck function 295

A.1.2 Computation of available potential energy 296

A.1.3 Internal energy for a compressible atmosphere 296

A.2 Mathematical definitions and notation 296 A.2.1 Taylor expansion 296 A.2.2 Vector identities 297 A.2.3 Polar and spherical coordinates 298 A.3 Use of foraminifera shells in paleoclimate 298 A.4 Laboratory experiments 299 A.4.1 Rotating tables 299 A.4.2 List of laboratory experiments 300 A.5 Figures and access to data over the web 302

References 303

Textbooks and reviews 303

Other references 303

References to paleo-data sources 304

Index 307

Online companion site:


This is an introductory text on the circulation of the atmosphere and ocean, with an emphasis on global scales. It has been written for undergraduate students who have no prior knowledge of meteorology and oceanography or training in fluid mechanics. We believe that the text will also be of use to beginning graduate students in the field of atmospheric, oceanic, and climate science. By the end of the book we hope that readers will have a good grasp of what the atmosphere and ocean look like on the large scale, and, through application of the laws of mechanics and thermodynamics, why they look like they do. We will also place our observations and understanding of the present climate in the context of how climate has evolved and changed over Earth's history.

The book is roughly divided in to three equal parts. The first third deals exclusively with the atmosphere (Chapters 1 to 5), the last third with the ocean and its role in climate (Chapters 9 to 12). Sandwiched in between we develop the necessary fluid dynamical background (Chapter 6 and 7). Our discussion of the general circulation of the atmosphere (Chapter 8), follows the dynamical chapters. The text can be used in a number of ways. It has been written so that those interested primarily in the atmosphere might focus on Chapters 1 to 8. Those interested in the ocean can begin at Chapter 9, referring back as necessary to the dynamical Chapters 6 and 7. It is our hope, however, that many will be interested in learning about both fluids. Indeed, one of the joys of working on this text—and using it as background material for undergraduate courses taught at the Massachusetts Institute of Technology (MIT)—has been our attempt to discuss the circulation of the atmosphere and ocean in a single framework and in the same spirit.

In our writing we have been led by observations rather than theory. We have not written a book about fluid dynamics illustrated by atmospheric and oceanic phenomena. Rather we hope that the observations take the lead, and theory is introduced when it is needed. Advanced dynamical ideas are only used if we deem it essential to bring order to the observations. We have also chosen not to unnecessarily formalize our discussion. Yet, as far as is possible, we have offered rigorous physical discussions expressed in mathematical form: we build (nearly) everything up from first principles, our explanations of the observations are guided by theory, and these guiding principles are, we hope, clearly espoused.

The majority of the observations described and interpreted here are available electronically via the companion Web site, We make much use of the remarkable database and web-browsing facilities developed at the Lamont Doherty Earth Observatory of Columbia University. Thus the raw data presented by figures on the pages of the book can be accessed and manipulated over the web, as described in Section A.5.

One particularly enjoyable aspect of the courses from which this book sprang has been the numerous laboratory experiments carried out in lectures as demonstrations, or studied in more detail in undergraduate laboratory courses. We hope that some of this flavor comes through on the written page. We have attempted to weave the experiments into the body of the text so that, in the spirit of the best musicals, the 'song and dance routines' seem natural rather than forced. The experiments we chose to describe are simple and informative, and for the most part do not require sophisticated apparatus. Video loops of the experiments can be viewed over the Web, but there is no real substitute for carrying them out oneself. We encourage you to try. Details of the equipment required to carry out the experiments, including the necessary rotating turntables, can be found in Section A.4.

Before getting on to the meat of our account, we now make some introductory remarks about the nature of the problems we are concerned with.

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