1. F.Nimmo EART164 Spring 11 Francis Nimmo EART164: PLANETARY ATMOSPHERES

2. F.Nimmo EART164 Spring 11 Sequence of events 1. Nebular disk formation 2. Initial coagulation (~10km, ~10 5 yrs) 3. Orderly growth (to Moon size, ~10 6 yrs) 4. Runaway growth (to Mars size, ~10 7 yrs), gas blowoff 5. Late-stage collisions (~10 7-8 yrs)

3. F.Nimmo EART164 Spring 11 Temperature and Condensation Temperature profiles in a young (T Tauri) stellar nebula, D’Alessio et al., A.J. 1998 Nebular conditions can be used to predict what components of the solar nebula will be present as gases or solids: Condensation behaviour of most abundant elements of solar nebula e.g. C is stable as CO above 1000K, CH 4 above 60K, and then condenses to CH 4.6H 2 O. From Lissauer and DePater, Planetary Sciences Mid-plane Photosphere Earth (~300K) Saturn (~50 K) “Snow line”

4. F.Nimmo EART164 Spring 11 Atmospheric Structure (1) Atmosphere is hydrostatic: Gas law gives us: Combining these two (and neglecting latent heat): Here R is the gas constant,  is the mass of one mole, and RT/g  is the pressure scale height of the (isothermal) atmosphere (~10 km) which tells you how rapidly pressure decreases with height e.g. what is the pressure at the top of Mt Everest? Most scale heights are in the range 10-30 km

5. F.Nimmo EART164 Spring 11 Snow line Migration Troposphere/stratosphere Primary/secondary/tertiary atmosphere Emission/absorption Occultation Scale height Hydrostatic equilibrium Exobase Mean free path Week 1 - Key concepts

6. F.Nimmo EART164 Spring 11 Hydrostatic equilibrium: Week 1 - Key equations Ideal gas equation: Scale height: H=RT/g 

7. F.Nimmo EART164 Spring 11 In many cases, as an air parcel rises, some volatiles will condense out This condensation releases latent heat So the change in temperature with height is decreased compared to the dry case Moist adiabats L is the latent heat (J/kg), dx is the incremental mass fraction condensing out C p ~ 1000 J/kg K for dry air on Earth The quantity dx/dT depends on the saturation curve and how much moisture is present (see Week 4) E.g. Earth L=2.3 kJ/kg and dx/dT~2x10 -4 K -1 (say) gives a moist adiabat of 6.5 K/km (cf. dry adiabat 10 K/km)

8. F.Nimmo EART164 Spring 11 Simplified Structure thin thick Incoming photons (short  not absorbed) Effective radiating surface T X Outgoing photons (long  easily absorbed) Convection T z TsTs TXTX adiabat troposphere stratosphere Absorbed at surface

9. F.Nimmo EART164 Spring 11 If no heat is exchanged, we have Let’s also define C p =C v +R and  =C p /C v A bit of work then yields an important result: More on the adiabat or equivalently Here c is a constant These equations are only true for adiabatic situations

10. F.Nimmo EART164 Spring 11 Solar constant, albedo Troposphere, stratosphere, tropopause Snowball Earth Adiabat, moist adiabat, lapse rate Greenhouse effect Metallic hydrogen Contractional heating Opacity Week 2 - Key concepts

11. F.Nimmo EART164 Spring 11 Week 2 - Key Equations Equilibrium temperature Adiabatic relationship Adiabat (including condensation)

12. F.Nimmo EART164 Spring 11 Week 3 - Key Concepts Cycles: ozone, CO, SO 2 Noble gas ratios and atmospheric loss (fractionation) Outgassing ( 40 Ar, 4 He) D/H ratios and water loss Dynamics can influence chemistry Photodissociation and loss (CH 4, H 2 O etc.) Non-solar gas giant compositions Titan’s problematic methane source

13. F.Nimmo EART164 Spring 11 Phase boundary H2OH2O E.g. water C L =3x10 7 bar, L H =50 kJ/mol So at 200K, P s =0.3 Pa, at 250 K, P s =100 Pa

14. F.Nimmo EART164 Spring 11 Giant planet clouds Altitude (km) Different cloud decks, depending on condensation temperature Colours are due to trace constituents, probably sulphur compounds

15. F.Nimmo EART164 Spring 11 Week 4 - Key concepts Saturation vapour pressure, Clausius-Clapeyron Moist vs. dry adiabat Cloud albedo effects Giant planet cloud stacks Dust sinking timescale and thermal effects

16. F.Nimmo EART164 Spring 11 max in cm e.g. Sun T=6000 K  max =0.5  m Mars T=250 K max =12  m  =5.7x10 -8 in SI units Black body basics 1. Planck function (intensity): Defined in terms of frequency or wavelength. Upwards (half-hemisphere) flux is 2  B 2. Wavelength & frequency: 3. Wien’s law: 4. Stefan-Boltzmann law

17. F.Nimmo EART164 Spring 11 The total absorption depends on  and , and how they vary with z. The optical depth  is a dimensionless measure of the total absorption over a distance d: Optical depth, absorption, opacity I I-  I zz  I=-I   z  =absorption coefft. (kg -1 m 2 )  =density (kg m -3 ) I = intensity You can show (how?) that I=I 0 exp(-  ) So the optical depth tells you how many factors of e the incident light has been reduced by over the distance d. Large  = light mostly absorbed.

18. F.Nimmo EART164 Spring 11 We can then derive (very useful!): Radiative Diffusion If we assume that  is constant and cheat a bit, we get Strictly speaking  is Rosseland mean opacity But this means we can treat radiation transfer as a heat diffusion problem – big simplification

19. F.Nimmo EART164 Spring 11 Greenhouse effect EarthMars T eq (K)255217 T 0 (K)214182 T s (K)288220 Inferred  0.840.08 Fraction transmitted0.430.93 A consequence of this model is that the surface is hotter than air immediately above it. We can derive the surface temperature T s :

20. F.Nimmo EART164 Spring 11 Atmosphere can transfer heat depending on opacity and temperature gradient Competition with convection... Convection vs. Conduction Does this equation make sense? Radiation dominates (low optical depth) Convection dominates (high optical depth)  crit Whichever is smaller wins -dT/dz ad -dT/dz rad

21. F.Nimmo EART164 Spring 11 Radiative time constant Atmospheric heat capacity (per m 2 ): Radiative flux: Time constant: E.g. for Earth time constant is ~ 1 month For Mars time constant is a few days

22. F.Nimmo EART164 Spring 11 Week 5 - Key Concepts Black body radiation, Planck function, Wien’s law Absorption, emission, opacity, optical depth Intensity, flux Radiative diffusion, convection vs. conduction Greenhouse effect Radiative time constant

23. F.Nimmo EART164 Spring 11 Week 5 - Key equations Absorption: Optical depth: Radiative Diffusion: Rad. time constant: Greenhouse effect:

24. F.Nimmo EART164 Spring 11 Geostrophic balance In steady state, neglecting friction we can balance pressure gradients and Coriolis: The result is that winds flow along isobars and will form cyclones or anti-cyclones What are wind speeds on Earth? How do they change with latitude? L L H isobars pressure Coriolis wind Flow is perpendicular to the pressure gradient!

25. F.Nimmo EART164 Spring 11 Rossby deformation radius Short distance flows travel parallel to pressure gradient Long distance flows are curved because of the Coriolis effect (geostrophy dominates when Ro<1) The deformation radius is the changeover distance It controls the characteristic scale of features such as weather fronts At its simplest, the deformation radius R d is (why?) Here v prop is the propagation velocity of the particular kind of feature we’re interested in E.g. gravity waves propagate with v prop =(gH) 1/2 Taylor’s analysis on p.171 is dimensionally incorrect

26. F.Nimmo EART164 Spring 11 Week 6 - Key Concepts Hadley cell, zonal & meridional circulation Coriolis effect, Rossby number, deformation radius Thermal tides Geostrophic and cyclostrophic balance, gradient winds Thermal winds

27. F.Nimmo EART164 Spring 11 Energy cascade (Kolmogorov) Approximate analysis (~) In steady state,  is constant Turbulent kinetic energy (per kg): E l ~ u l 2 Turnover time: t l ~l /u l Dissipation rate  ~E l /t l So u l ~(  l) 1/3 (very useful!) At what length does viscous dissipation start to matter? Energy in ( , W kg -1 ) Energy viscously dissipated ( , W kg -1 ) u l, E l l

28. F.Nimmo EART164 Spring 11 Week 7 - Key Concepts Reynolds number, turbulent vs. laminar flow Velocity fluctuations, Kolmogorov cascade Brunt-Vaisala frequency, gravity waves Rossby waves, Kelvin waves, baroclinic instability Mixing-length theory, convective heat transport u l ~(  l) 1/3

29. F.Nimmo EART164 Spring 11 VenusEarthMarsTitan Solar constant S (Wm -2 )2620138059415.6 Bond albedo A0.760.40.150.3 T eq (K)22924521783 T s (K)73028822095 Greenhouse effect (K)50143312 Inferred  s 1361.20.080.96 T eq and greenhouse Recall that So if  =constant, then  =  x column density So a (wildly oversimplified) way of calculating T eq as P changes could use: Example: water on early Mars

30. F.Nimmo EART164 Spring 11 Climate Evolution Drivers DriverPeriodExamples Seasonal1-100s yrPluto, Titan Spin / orbit variations10s-100s kyrEarth, Mars Solar outputSecular (faint young Sun); and 100s yr Earth Volcanic activitySecular(?); intermittentVenus(?), Mars(?), Earth Atmospheric lossSecularMars, Titan ImpactsIntermittentMars? Greenhouse gasesVariousVenus, Earth Ocean circulation10s Myr (plate tectonics)Earth LifeSecularEarth Albedo changes can amplify (feedbacks)

31. F.Nimmo EART164 Spring 11 Atmospheric loss An important process almost everywhere Main signature is in isotopes (e.g. C,N,Ar,Kr) Main mechanisms: –Thermal (Jeans) escape –Hydrodynamic escape –Blowoff (EUV, X-ray etc.) –Freeze-out –Ingassing & surface interactions (no fractionation?) –Impacts (no fractionation)

32. F.Nimmo EART164 Spring 11 Week 9 - Key Concepts Faint young Sun, albedo feedbacks, Urey cycle Loss mechanisms (Jeans, Hydrodynamic, Energy- limited, Impact-driven, Freeze-out, Surface interactions, Urey cycle) and fractionation Orbital forcing, Milankovitch cycles “Warm, wet Mars”? Earth bombardment history Runaway greenhouses (CO 2 and H 2 O) Snowball Earth

33. F.Nimmo EART164 Spring 11 Week 9 - Key equations