Principles of Planetary Climate

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 13
Remarks on notation and terminology......Page 15
How to use this book......Page 16
Prerequisites and suggested syllabi......Page 19
Acknowledgements......Page 22
Notation......Page 23
1.2 Close to home......Page 29
1.3 Into deepest time: Faint Young Sun and habitability of the Earth......Page 34
1.4 Goldilocks in space: Earth, Mars, and Venus......Page 42
1.5 Other Solar System planets and satellites......Page 47
1.6 Farther afield: extrasolar planets......Page 49
1.7.1 Overview of proxy data......Page 55
1.7.2 Isotopic proxies......Page 57
1.7.3 Hydrogen and oxygen isotopes in sea water and marine sediments......Page 62
1.7.4 Forams to the rescue......Page 64
1.8 The Proterozoic climate revisited: Snowball Earth......Page 67
1.9 The hothouse/icehouse dichotomy......Page 73
1.9.1 The past 70 million years......Page 74
1.9.2 Hothouse and icehouse climates over the Phanerozoic......Page 78
1.10 Pleistocene glacial–interglacial cycles......Page 80
1.10.2 Ice-core records......Page 81
1.11 Holocene climate variation......Page 84
1.12 Back to home: global warming......Page 86
1.13 The fate of the Earth and the lifetime of biospheres......Page 94
1.14.1 Your computational toolkit......Page 96
1.14.2 Basic physics and chemistry......Page 101
1.14.3 Stable isotope calculations......Page 103
1.15 For further reading......Page 106
2.2 A few observations......Page 109
2.3.1 The equation of state for an ideal gas......Page 112
2.3.2 Specific heat and conservation of energy......Page 116
2.3.3 Entropy, reversibility, and potential temperature; the Second Law......Page 117
2.4 Static stability of inhomogeneous mixtures......Page 121
2.5 The hydrostatic relation......Page 124
2.6 Thermodynamics of phase change......Page 126
2.7 The moist adiabat......Page 131
2.7.2 Mixtures of condensable with non-condensable gases......Page 134
2.7.3 Moist static energy......Page 139
2.8 Workbook......Page 140
2.8.1 Basic dry thermodynamics......Page 141
2.8.2 Potential temperature, dry adiabats and inhomogeneous atmospheres......Page 143
2.8.3 Data Lab: Analysis of temperature soundings......Page 145
2.8.4 The hydrostatic relation......Page 148
2.8.5 Latent heat and Clausius–Clapeyron......Page 150
2.8.6 Moist adiabats......Page 156
2.9 For further reading......Page 160
3.1 Overview......Page 162
3.2 Blackbody radiation......Page 163
3.3 Radiation balance of planets......Page 171
3.4 Ice-albedo feedback......Page 181
3.4.1 Faint Young Sun, Snowball Earth and hysteresis......Page 187
3.4.2 Climate sensitivity, radiative forcing and feedback......Page 191
3.5 Partially absorbing atmospheres......Page 193
3.6 Optically thin atmospheres: the skin temperature......Page 197
3.7.1 Basic concepts......Page 202
3.7.2 The Planck function......Page 203
3.7.3 Basic energy balance......Page 206
3.7.4 The greenhouse effect......Page 208
3.7.5 Ice-albedo feedback, hysteresis and bifurcation......Page 211
3.7.6 Kirchhoff’s law, emissivity, absorptivity......Page 212
3.8 For further reading......Page 213
4.1 Overview......Page 215
4.2.1 Optical thickness and the Schwarzschild equations......Page 216
4.2.2 Some special solutions of the two-stream equations......Page 222
4.3 The gray gas model......Page 227
4.3.2 Radiative properties of an all-troposphere dry atmosphere......Page 228
4.3.3 A first look at the runaway greenhouse......Page 233
4.3.4 Pure radiative equilibrium for a gray gas atmosphere......Page 237
4.3.5 Effect of atmospheric solar absorption on pure radiative equilibrium......Page 240
4.4.1 Overview: OLR through thick and thin......Page 244
4.4.2 The absorption spectrum of real gases......Page 248
4.4.3 I walk the line......Page 254
4.4.4 Behavior of the band-averaged transmission function......Page 259
4.4.5 Dealing with multiple greenhouse gases......Page 266
4.4.6 A homebrew radiation model......Page 269
4.4.7 Spectroscopic properties of selected greenhouse gases......Page 271
Carbon dioxide......Page 272
Water vapor......Page 277
Methane......Page 281
Diatomic molecules and general considerations......Page 283
Carbon dioxide continuum......Page 285
Water vapor continuum......Page 287
4.4.9 Condensed substances: clouds......Page 290
4.5 Real gas OLR for all-troposphere atmospheres......Page 291
4.5.1 CO2 and dry air......Page 292
4.5.2 Pure CO2 atmospheres: Present and Early Mars, and Venus......Page 294
4.5.3 Water vapor feedback......Page 297
4.5.4 Greenhouse effect of CO2 vs. CH4......Page 306
4.6 Another look at the runaway greenhouse......Page 309
4.7 Pure radiative equilibrium for real gas atmospheres......Page 317
4.8 Tropopause height for real gas atmospheres......Page 327
4.9 The lesson learned......Page 330
4.10.1 Basic gray gas calculations......Page 331
4.10.2 Pure radiative equilibrium......Page 333
4.10.3 Real gas basics......Page 335
4.10.4 Calculations with polynomial OLR fits......Page 336
4.10.5 Real gas and semigray radiation computations......Page 337
4.10.6 Tropopause height......Page 339
4.11 For further reading......Page 341
5.1 Overview......Page 344
5.2 Basic concepts......Page 346
5.3 Scattering by molecules: Rayleigh scattering......Page 358
5.4 Scattering by particles......Page 361
5.5 The two-stream equations with scattering......Page 366
5.6 Some basic solutions......Page 368
5.7 Numerical solution of the two-stream equations......Page 376
5.8 Water and ice clouds......Page 382
5.9 Things that go bump in the night: Infrared scattering with gaseous absorption......Page 387
5.10 Effects of atmospheric solar absorption......Page 390
5.10.1 Near-IR and visible absorption......Page 391
5.10.2 Ultraviolet absorption......Page 400
5.11 Albedo of snow and ice......Page 402
5.12.1 Scattering basics......Page 403
5.12.2 Use and derivation of basic two-stream solutions......Page 404
5.12.3 Numerical two-stream solutions......Page 408
5.12.4 Absorption of stellar radiation......Page 410
5.13 For further reading......Page 411
6.1 Overview......Page 414
6.2.2 The behavior of the longwave back-radiation......Page 416
6.2.3 Radiatively driven ground–air temperature difference......Page 419
6.3 Basic models of turbulent exchange......Page 423
6.3.1 Sensible heat flux......Page 424
6.3.2 Latent heat flux......Page 425
6.4 Similarity theory for the surface layer......Page 430
6.5 Joint effect of the fluxes on surface conditions......Page 437
6.6 Global warming and the surface budget fallacy......Page 441
6.7 Mass balance and melting......Page 443
6.8 Precipitation–temperature relations......Page 445
6.9 Simple models of sea ice in equilibrium......Page 448
6.10.1 Basic surface balance calculations......Page 453
6.10.2 Evaporation and sublimation......Page 455
6.10.4 Radiative-convective equilibrium coupled to a surface budget......Page 456
6.11 For further reading......Page 459
7.1 Overview......Page 460
7.3 Distribution of incident solar radiation......Page 461
7.4.1 Thermal inertia for a mixed layer ocean......Page 472
7.4.2 Thermal inertia of a solid surface......Page 479
7.5 Some elementary orbital mechanics......Page 485
7.6 Effect of long-term variation of orbital parameters......Page 490
7.6.1 Milankovic cycles on Earth......Page 491
7.6.2 Milankovic cycles on Mars......Page 495
7.7.1 Formation and inhibition of polar sea ice......Page 497
7.7.2 Continental climates on hothouse Earth......Page 500
7.7.3 Snowball Earth......Page 501
7.7.5 Mars, present and past......Page 502
7.7.6 Nearly airless bodies......Page 505
7.7.7 Titan......Page 506
7.7.8 Gas and ice giants......Page 507
7.7.9 Habitability of planets with extreme orbital configurations......Page 508
7.8.1 Distribution of insolation......Page 509
7.8.2 Thermal inertia......Page 513
7.8.3 The diffusion equation and its uses......Page 516
7.8.4 Orbital mechanics and eccentricity......Page 517
7.8.5 Simulation of planetary seasonal cycles......Page 520
7.8.6 A little data analysis......Page 523
7.9 For further reading......Page 524
8.1 Overview......Page 525
8.2 About chemical reactions......Page 527
8.3 Silicate weathering and atmospheric CO2......Page 531
8.4 Partitioning of constituents between atmosphere and ocean......Page 542
8.5 About ultraviolet......Page 550
8.6.1 Photodissociation stirs the pot......Page 551
8.6.2 OH: a radical’s life......Page 558
8.6.3 A planet’s first CO2......Page 561
8.7 Escape of an atmosphere to space......Page 562
8.7.1 Basic concepts......Page 563
8.7.2 Diffusion-limited escape......Page 578
8.7.3 Non-thermal escape......Page 580
8.7.4 Hydrodynamic escape......Page 583
Equations for 1D compressible transonic flow......Page 584
Adiabatic escape......Page 587
Re-interpretation of the transonic rule in terms of energetics......Page 590
Escape driven by EUV heating......Page 593
Effects of heat diffusion......Page 599
Wrap-up and summary of hydrodynamic escape......Page 602
8.7.5 Erosion by solar wind......Page 603
8.7.6 Impact erosion......Page 605
8.8.1 Silicate weathering......Page 615
8.8.2 Ocean–atmosphere partitioning......Page 618
8.8.3 Atmospheric chemistry......Page 620
8.8.4 Atmospheric escape......Page 621
8.9 For further reading......Page 625
9.2 Horizontal heat transport......Page 627
9.2.1 A little fluid mechanics......Page 629
9.2.2 Some observations......Page 633
9.2.3 Scale analysis of atmospheric heat transport......Page 638
9.2.4 Formulation of energy balance models......Page 641
9.2.5 Equilibrium solution of diffusive energy balance models......Page 642
9.2.6 Limitations of diffusive energy balance models......Page 646
9.3 Dynamics of relative humidity......Page 647
9.4 Dynamics of static stability......Page 649
9.5 Afterword: endings and beginnings......Page 650
9.6.1 Basic concepts......Page 656
9.6.2 Diffusive energy balance models......Page 658
9.7 For further reading......Page 661
Index......Page 663