Contents

Preface i

Contents 2

1 The Big Questions 3

1.1 Overview 3

1.2 Close to home 3

1.3 Into deepest time: Faint Young Sun and habitability of the Earth 8

1.4 Goldilocks in space: Earth,Mars and Venus 15

1.5 Other Solar System planets and satellites 20

1.6 Farther afield: Extrasolar planets 22

1.7 Digression: About climate proxies 28

1.7.1 Overview of proxy data 28

1.7.2 Isotopic proxies 29

1.7.3 Hydrogen and Oxygen isotopes in sea water and marine sediments 34

1.7.4 Forams to the rescue 37

1.8 The Proterozoic climate revisited:Snowball Earth 39

1.9 The hothouse/icehouse dichotomy 45

1.9.1 The past 70 million years 45

1.9.2 Hothouse and icehouse climates over the Phanerozoic 50

1.10 Pleistocene Glacial-Interglacial cycles 51

1.10.1 The Marine Sediment Record 53

1.10.2 Ice core records 55

1.11 Holocene climate variation 57

1.12 Back to home: Global Warming 59

1.13 The fate of the Earth,the lifetime of biospheres 67

1.14 For Further Reading 68

2 Thermodynamics in a Nutshell 71

2.1 Overview 71

2.2 A few observations 71

2.3 Dry thermodynamics of an ideal gas 74

2.3.1 The equation of state for an ideal gas 74

2.3.2 Specific heat and conservation of energy 78

2.3.3 Entropy, reversibility and Potential temperature; The Second Law 79

2.4 Static stability of inhomogeneous mixtures 82

2.5 The hydrostatic relation 85

2.6 Thermodynamics of phase change 87

2.7 The moist adiabat 92

2.7.1 One-component condensible atmospheres 92

2.7.2 Mixtures of condensible with noncondensible gases 95

2.7.3 Moist static energy 99

2.8 For Further Reading 101

3 Elementary models of radiation balance 103

3.1 Overview 103

3.2 Blackbody radiation 104

3.3 Radiation balance of planets 111

3.4 Ice-albedo feedback 123

3.4.1 Faint Young Sun, Snowball Earth and Hysteresis 128

3.4.2 Climate sensitivity, radiative forcing and feedback 133

3.5 Partially absorbing atmospheres 136

3.6 Optically thin atmospheres: The skin temperature 139

3.7 For Further Reading 144

4 Radiative transfer in temperature-stratified atmospheres 147

4.1 Overview 147

4.2 Basic Formulation of Plane Parallel Radiative Transfer 148

4.2.1 Optical thickness and the Schwarzschild equations 148

4.2.2 Some special solutions of the Two-Stream equations 153

4.3 The Grey Gas Model 158

4.3.1 OLR and back-radiation for an optically thin grey atmosphere 159

4.3.2 Radiative properties of an all-troposphere dry atmosphere 160

4.3.3 A first look at the runaway greenhouse 164

4.3.4 Pure radiative equilibrium for a grey gas atmosphere 168

4.3.5 Effect of atmospheric solar absorption on pure radiative equilibrium 171

4.4 Real gas radiation: Basic principles 174

4.4.1 Overview: OLR through thick and thin 174

4.4.2 The absorption spectrum of real gases 178

4.4.4 Behavior of the band-averaged transmission function 190

4.4.5 Dealing with multiple greenhouse gases 196

4.4.6 A homebrew radiation model 199

4.4.7 Spectroscopic properties of selected greenhouse gases 201

4.4.8 Collisional continuum absorption 212

4.4.9 Condensed substances: Clouds 218

4.5 Real gas OLR for all-troposphere atmospheres 220

4.5.1 CO2 and dry air 220

4.5.2 Pure CO2 atmospheres:Present and Early Mars, and Venus 222

4.5.3 Water vapor feedback 225

4.5.4 Greenhouse effect of CO2 vs CH4 233

4.6 Another look at the runaway greenhouse 236

4.7 Pure radiative equilibrium for real gas atmospheres 243

4.8 Tropopause height for real gas atmospheres 253

4.9 The lesson learned 256

4.10 For Further Reading 257

5 Scattering 261

5.1 Overview 261

5.2 Basic concepts 262

5.3 Scattering by molecules: Rayleigh scattering 274

5.4 Scattering by particles 277

5.5 The two-stream equations with scattering 282

5.6 Some basic solutions 284

5.7 Numerical solution of the two-stream equations 291

5.8 Water and ice clouds 297

5.9 Things that go bump in the night: Infrared-scattering with gaseous absorption . . 301

5.10 Effects of atmospheric solar absorption 302

5.10.1 Near-IR and visible absorption 303

5.10.2 Ultraviolet absorption 311

5.11 Albedo of snow and ice 314

5.12 For Further Reading 315

6 The Surface Energy Balance 317

6.1 Overview 317

6.2 Radiative exchange 319

6.2.1 Shortwave radiation 319

6.2.2 The behavior of the longwave back-radiation 319

6.2.3 Radiatively driven ground-air temperature difference 322

6.3 Basic models of turbulent exchange 325

6.3.1 Sensible heat flux 327

6.3.2 Latent heat flux 327

6.4 Similarity theory for the surface layer 332

6.5 Joint effect of the fluxes on surface conditions 339

6.6 Global warming and the surface budget fallacy 342

6.7 Mass balance and melting 344

6.8 Precipitation-temperature relations 346

6.9 Simple models of sea ice in equilibrium 349

6.10 For Further Reading 354

7 Variation of temperature with season and latitude 355

7.1 Overview 355

7.2 A few observations of the Earth 355

7.3 Distribution of incident solar radiation 356

7.4 Thermal Inertia 366

7.4.1 Thermal inertia for a mixed-layer ocean 366

7.4.2 Thermal inertia of a solid surface 370

7.4.3 Summary of thermal inertia effects 376

7.5 Some elementary orbital mechanics 376

7.6 Effect of long term variation of orbital parameters 381

7.6.1 Milankovic cycles on Earth 382

7.6.2 Milankovic cycles on Mars 386

7.7 A palette of planetary seasonal cycles 389

7.7.1 Formation and inhibition of polar sea ice 389

7.7.2 Continental climates on Hothouse Earth 389

7.7.3 Snowball Earth 389

7.7.4 Venus 389

7.7.5 Mars, present and past 389

7.7.6 Planets with high eccentricity or obliquity 390

7.8 For Further Reading 390

8 Evolution of the atmosphere 391

8.1 Overview 391

8.2 About chemical reactions 392

8.3 Silicate weathering and atmospheric CO2 396

8.4 Partitioning of CO2 between atmosphere and ocean 406

8.5 About Extreme Ultraviolet 406

8.6 A few words about atmospheric chemistry 407

8.7 Escape of an atmosphere to space 407

8.7.1 Basic concepts 408

8.7.2 Diffusion limited escape 422

8.7.3 Non-thermal escape 424

8.7.4 Hydrodynamic escape 427

8.7.5 Erosion by solar wind 445

8.7.6 Impact erosion 448

8.8 For Further Reading 457

9 A peek at dynamics 459

9.1 Overview 459

9.2 Horizontal heat transport 459

9.2.1 Formulation of energy balance models 459

9.2.2 Equilibrium energy balance models 460

9.2.3 WTG models of the tropics 460

9.3 Dynamics of relative humidity 460

9.4 Dynamics of static stability 460

Chapter 1

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