EART 164 PLANETARY ATMOSPHERES Francis Nimmo F Nimmo

EART 164: PLANETARY ATMOSPHERES Francis Nimmo F. Nimmo EART 164 Spring 11

Sequence of events • 1. Nebular disk formation • 2. Initial coagulation (~10 km, ~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) F. Nimmo EART 164 Spring 11

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” Earth Saturn (~300 K)(~50 K) Temperature profiles in a young (T Tauri) stellar nebula, D’Alessio et al. , A. J. 1998 Condensation behaviour of most abundant elements of solar nebula e. g. C is stable as CO above 1000 K, CH 4 above 60 K, and then condenses to CH 4. 6 H 2 O. F. Nimmo EART 164 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, m is the mass of one mole, and RT/gm 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 F. Nimmo EART 164 Spring 11

Week 1 - Key concepts • • • Snow line Migration Troposphere/stratosphere Primary/secondary/tertiary atmosphere Emission/absorption Occultation Scale height Hydrostatic equilibrium Exobase Mean free path F. Nimmo EART 164 Spring 11

Week 1 - Key equations • Hydrostatic equilibrium: • Ideal gas equation: • Scale height: H=RT/gm F. Nimmo EART 164 Spring 11

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/d. T depends on the saturation curve and how much moisture is present (see Week 4) • E. g. Earth L=2. 3 k. J/kg and dx/d. T~2 x 10 -4 K-1 (say) gives a moist adiabat of 6. 5 K/km (cf. dry adiabat 10 K/km) F. Nimmo EART 164 Spring 11

z adiabat TX Incoming photons (short l, not absorbed) troposphere stratosphere Simplified Structure Ts T Outgoing photons thin (long l, easily absorbed) Effective radiating surface TX Convection thick Absorbed at surface F. Nimmo EART 164 Spring 11

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 F. Nimmo EART 164 Spring 11

Week 2 - Key concepts • • Solar constant, albedo Troposphere, stratosphere, tropopause Snowball Earth Adiabat, moist adiabat, lapse rate Greenhouse effect Metallic hydrogen Contractional heating Opacity F. Nimmo EART 164 Spring 11

Week 2 - Key Equations • Equilibrium temperature • Adiabat (including condensation) • Adiabatic relationship F. Nimmo EART 164 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 F. Nimmo EART 164 Spring 11

Phase boundary E. g. water CL=3 x 107 bar, LH=50 k. J/mol So at 200 K, Ps=0. 3 Pa, at 250 K, Ps=100 Pa H 2 O F. Nimmo EART 164 Spring 11

Altitude (km) Giant planet clouds Colours are due to trace constituents, probably sulphur compounds Different cloud decks, depending on condensation temperature F. Nimmo EART 164 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 F. Nimmo EART 164 Spring 11

Black body basics 1. Planck function (intensity): Defined in terms of frequency or wavelength. Upwards (half-hemisphere) flux is 2 p Bn 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. 7 x 10 -8 in SI units F. Nimmo EART 164 Spring 11

Optical depth, absorption, opacity I-DI Dz DI=-Iar Dz a=absorption coefft. (kg-1 m 2) r=density (kg m-3) I = intensity I • 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: • You can show (how? ) that I=I 0 exp(-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. F. Nimmo EART 164 Spring 11

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 F. Nimmo EART 164 Spring 11

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: Earth Mars Teq (K) 255 217 T 0 (K) 214 182 Ts (K) 288 220 Inferred t 0. 84 0. 08 Fraction transmitted 0. 43 0. 93 F. Nimmo EART 164 Spring 11

Convection vs. Conduction • Atmosphere can transfer heat depending on opacity and temperature gradient • Competition with convection. . . Whichever is smaller wins -d. T/dzad -d. T/dzrad Radiation dominates (low optical depth) rcrit Does this equation make sense? Convection dominates (high optical depth) F. Nimmo EART 164 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 F. Nimmo EART 164 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 F. Nimmo EART 164 Spring 11

Week 5 - Key equations Absorption: Optical depth: Greenhouse effect: Radiative Diffusion: Rad. time constant: F. Nimmo EART 164 Spring 11

Geostrophic balance • In steady state, neglecting friction we can balance pressure gradients and Coriolis: Flow is perpendicular to the pressure gradient! L wind L pressure Coriolis H isobars • 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? F. Nimmo EART 164 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 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=(g. H)1/2 F. Nimmo EART 164 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 F. Nimmo EART 164 Spring 11

Energy cascade (Kolmogorov) Energy in (e, W kg-1) ul, El l Energy viscously dissipated (e, W kg-1) • Approximate analysis (~) • In steady state, e is constant • Turbulent kinetic energy (per kg): El ~ ul 2 • 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? F. Nimmo EART 164 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 ul ~(e l)1/3 F. Nimmo EART 164 Spring 11

Teq and greenhouse Venus Earth Mars Titan Solar constant S (Wm-2) 2620 1380 594 15. 6 Bond albedo A 0. 76 0. 4 0. 15 0. 3 Teq (K) 229 245 217 83 Ts (K) 730 288 220 95 Greenhouse effect (K) 501 43 3 12 Inferred ts 136 1. 2 0. 08 0. 96 Recall that So if a=constant, then t = a x column density So a (wildly oversimplified) way of calculating Teq as P changes could use: Example: water on early Mars F. Nimmo EART 164 Spring 11

Climate Evolution Drivers Driver Period Examples Seasonal 1 -100 s yr Pluto, Titan Spin / orbit variations 10 s-100 s kyr Earth, Mars Solar output Secular (faint young Sun); and 100 s yr Earth Volcanic activity Secular(? ); intermittent Venus(? ), Mars(? ), Earth Atmospheric loss Secular Mars, Titan Impacts Intermittent Mars? Greenhouse gases Various Venus, Earth Ocean circulation 10 s Myr (plate tectonics) Earth Life Secular Earth Albedo changes can amplify (feedbacks) F. Nimmo EART 164 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) F. Nimmo EART 164 Spring 11

Week 9 - Key Concepts • Faint young Sun, albedo feedbacks, Urey cycle • Loss mechanisms (Jeans, Hydrodynamic, Energylimited, 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 F. Nimmo EART 164 Spring 11

Week 9 - Key equations F. Nimmo EART 164 Spring 11