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EART164: PLANETARY ATMOSPHERES

Francis Nimmo. EART164: PLANETARY ATMOSPHERES. 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).

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EART164: PLANETARY ATMOSPHERES

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  1. Francis Nimmo EART164: PLANETARY ATMOSPHERES

  2. Sequence of events • 1. Nebular disk formation • 2. Initial coagulation (~10km, ~105 yrs) • 3. Orderly growth (to Moon size, ~106 yrs) • 4. Runaway growth (to Mars size, ~107 yrs), gas blowoff • 5. Late-stage collisions (~107-8 yrs)

  3. Temperature and Condensation Nebular conditions can be used to predict what components of the solar nebula will be present as gases or solids: Mid-plane Photosphere “Snow line” “Snow line” Saturn (~50 K) Earth (~300K) Condensation behaviour of most abundant elements of solar nebula e.g. C is stable as CO above 1000K, CH4 above 60K, and then condenses to CH4.6H2O. From Lissauer and DePater, Planetary Sciences Temperature profiles in a young (T Tauri) stellar nebula, D’Alessio et al., A.J. 1998

  4. Atmospheric Structure (1) • Atmosphere is hydrostatic: • Gas law gives us: • Combining these two (and neglecting latent heat): Here R is the gas constant, m is the mass of one mole, and RT/gmis 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. Week 1 - Key concepts • Snow line • Migration • Troposphere/stratosphere • Primary/secondary/tertiary atmosphere • Emission/absorption • Occultation • Scale height • Hydrostatic equilibrium • Exobase • Mean free path

  6. Week 1 - Key equations • Hydrostatic equilibrium: • Ideal gas equation: • Scale height: H=RT/gm

  7. Moist adiabats • 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 L is the latent heat (J/kg), dx is the incremental mass fraction condensing out Cp ~ 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. Simplified Structure Incoming photons (short l, not absorbed) Outgoing photons (long l, easily absorbed) z thin stratosphere Effective radiating surface TX troposphere Convection adiabat thick T Absorbed at surface TX Ts

  9. More on the adiabat • If no heat is exchanged, we have • Let’s also define Cp=Cv+R and g=Cp/Cv • A bit of work then yields an important result: or equivalently Here c is a constant • These equations are only true for adiabatic situations

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

  11. Week 2 - Key Equations • Equilibrium temperature • Adiabat (including condensation) • Adiabatic relationship

  12. Week 3 - Key Concepts Cycles: ozone, CO, SO2 Noble gas ratios and atmospheric loss (fractionation) Outgassing (40Ar, 4He) D/H ratios and water loss Dynamics can influence chemistry Photodissociation and loss (CH4, H2O etc.) Non-solar gas giant compositions Titan’s problematic methane source

  13. Phase boundary E.g. water CL=3x107 bar, LH=50 kJ/mol So at 200K, Ps=0.3 Pa, at 250 K, Ps=100 Pa H2O

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

  15. 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. Black body basics 1. Planck function (intensity): Defined in terms of frequency or wavelength. Upwards (half-hemisphere) flux is 2pBn 2. Wavelength & frequency: 3. Wien’s law: lmax in cm e.g. Sun T=6000 K lmax=0.5 mm Mars T=250 K lmax=12 mm 4. Stefan-Boltzmann law s=5.7x10-8 in SI units

  17. Optical depth, absorption, opacity I-DI a=absorption coefft. (kg-1 m2) r=density (kg m-3) I = intensity • The total absorption depends on r and a, and how they vary with z. • The optical depth t is a dimensionless measure of the total absorption over a distance d: Dz DI=-IarDz I • You can show (how?) that I=I0exp(-t) • So the optical depth tells you how many factors of e the incident light has been reduced by over the distance d. • Large t = light mostly absorbed.

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

  19. Greenhouse effect A consequence of this model is that the surface is hotter than air immediately above it. We can derive the surface temperature Ts:

  20. Convection vs. Conduction • Atmosphere can transfer heat depending on opacity and temperature gradient • Competition with convection . . . Whichever is smaller wins -dT/dzad Radiation dominates (low optical depth) -dT/dzrad rcrit Does this equation make sense? Convection dominates (high optical depth)

  21. Radiative time constant Atmospheric heat capacity (per m2): Radiative flux: Time constant: E.g. for Earth time constant is ~ 1 month For Mars time constant is a few days

  22. 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. Week 5 - Key equations Absorption: Optical depth: Greenhouse effect: Radiative Diffusion: Rad. time constant:

  24. Geostrophic balance • In steady state, neglecting friction we can balance pressure gradients and Coriolis: Flow is perpendicular to the pressure gradient! L L wind • 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? pressure Coriolis isobars H

  25. 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 Rd is (why?) Taylor’s analysis on p.171 is dimensionally incorrect • Here vprop is the propagation velocity of the particular kind of feature we’re interested in • E.g. gravity waves propagate with vprop=(gH)1/2

  26. 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. Energy cascade (Kolmogorov) Energy in (e, W kg-1) • Approximate analysis (~) • In steady state, e is constant • Turbulent kinetic energy (per kg): El ~ ul2 • Turnover time: tl ~l /ul • Dissipation rate e ~El/tl • So ul ~(e l)1/3(very useful!) • At what length does viscous dissipation start to matter? ul, El l Energy viscously dissipated (e, W kg-1)

  28. 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 ul ~(e l)1/3

  29. Teq and greenhouse Recall that So if a=constant, then t = a x column density So a (wildly oversimplified) way of calculating Teqas P changes could use: Example: water on early Mars

  30. Climate Evolution Drivers Albedo changes can amplify (feedbacks)

  31. 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. 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 (CO2 and H2O) Snowball Earth

  33. Week 9 - Key equations

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