EART164: PLANETARY ATMOSPHERES

Transcription

1 EART164: PLANETARY ATMOSPHERES Francis Nimmo

2 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 (~ 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 Earth Saturn (~300K)(~50 K) Temperature profiles in a young (T Tauri) stellar nebula, D Alessio et al., A.J 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.

4 Atmospheric Structure (1) Atmosphere is hydrostatic: Gas law gives us: RT P ( z) g( z) Combining these two (and neglecting latent heat): dp g P dz RT 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 dp dz e.g. what is the pressure at the top of Mt Everest? Most scale heights are in the range 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: P Scale height: H=RT/g dp dz RT ( z) g( z)

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 g dz C p dt L dx 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 dt dz g C p L 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) dx dt

8 troposphere stratosphere Simplified Structure z Incoming photons (short l, not absorbed) thin Outgoing photons (long l, easily absorbed) Effective radiating surface T X adiabat Convection T X T s T thick Absorbed at surface

9 More on the adiabat If no heat is exchanged, we have C p dt V dp Let s also define C p =C v +R and g=c p /C v A bit of work then yields an important result: g c P P ct g 1 or equivalently g 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 T eq S (1 A) 4 1/ 4 Adiabat (including condensation) dt dz g C p L dx dt Adiabatic relationship g P c

12 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 Phase boundary L H Pvap CL exp RT 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 H 2 O

14 Altitude (km) Giant planet clouds 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 dp dt s L H RT P s 2 t H gr 2

16 Black body basics 1. Planck function (intensity): B 3 2h 2 c e lmax h kt 1 1 Defined in terms of frequency or wavelength. Upwards (half-hemisphere) flux is 2p B 2. Wavelength & frequency: 3. Wien s law: 0.29 T e.g. Sun T=6000 K l max =0.5 m Mars T=250 K l max =12 m 4. Stefan-Boltzmann law F c l l max in cm 0 B d T 4 =5.7x10-8 in SI units

17 z Optical depth, absorption, opacity I-I di I=-Ia z a a=absorption coefft. (kg -1 m 2 ) =density (kg m -3 ) I = intensity I l l l The total absorption depends on and a, and how they vary with z. The optical depth t is a dimensionless measure of the total absorption over a distance d: d t = ar dz You can show (how?) that I=I 0 exp(-t) ò 0 dt dz = ar 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. I dz

18 We can then derive (very useful!): Radiative Diffusion a p d T T B z T z F ) ( ) ( 0 If we assume that a is constant and cheat a bit, we get a ) ( T z T z F Strictly speaking a is Rosseland mean opacity But this means we can treat radiation transfer as a heat diffusion problem big simplification

19 T Greenhouse effect 3 ( t) T 1 t A consequence of this model is that the surface is hotter than air immediately above it. We can derive the surface temperature T s : 4 0 T T 1 t s eq s 1 2 Earth 4 T eq Mars T eq (K) T 0 (K) T s (K) Inferred t Fraction transmitted T

20 -dt/dz rad Convection vs. Conduction Atmosphere can transfer heat depending on opacity and temperature gradient Competition with convection... 4 dt 3 T dt g e a 3 R dz 16 T dz -dt/dz ad C p Whichever is smaller wins Radiation dominates (low optical depth) crit Convection dominates (high optical depth) crit 16 3 a gt T R 4 e 3 C Does this equation make sense? p

21 Radiative time constant Atmospheric heat capacity (per m 2 ): H C p Radiative flux: Time constant: F 4 T e C p solar P g T ( 1 A) 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: T di F( z) Rad. time constant: l a l I dt dz = ar T 3 z l dz 3 ( t) T 1 t 2 F C p solar P g T ( 1 A) T a T0 1/ 4 T eq

24 Geostrophic balance In steady state, neglecting friction we can balance pressure gradients and Coriolis: L wind Coriolis H L v du dt 1 P 2sin x pressure isobars 1 P x fv F x Flow is perpendicular to the pressure gradient! 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?

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 R d is (why?) vprop Rd f Here v prop is the propagation velocity of the particular kind of feature we re interested in Taylor s analysis on p.171 is dimensionally incorrect E.g. gravity waves propagate with v prop =(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 du dt u Ro 2 L sin 1 P x u g T z ft y 2sin v F x

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

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 Re u l ~( l) 1/3 2 g dt g NB T dz C p ur / 1/ 2 l ~ F 3/ 2 1/ 2 dt dt g ~ C p H dz ad dz T 2

29 T eq and greenhouse Venus Earth Mars Titan Solar constant S (Wm -2 ) Bond albedo A T eq (K) T s (K) Greenhouse effect (K) Inferred t s T eq S (1 A) s eq s 1/ 4 T T 1 t 4 Recall that t a dz So if a=constant, then t = a x column density So a (wildly oversimplified) way of calculating T eq as P changes could use: Example: water on early Mars t a P g

30 Climate Evolution Drivers Driver Period Examples Seasonal 1-100s yr Pluto, Titan Spin / orbit variations 10s-100s kyr Earth, Mars Solar output Secular (faint young Sun); and 100s yr Earth Volcanic activity Secular(?); intermittent Venus(?), Mars(?), Earth Atmospheric loss Secular Mars, Titan Impacts Intermittent Mars? Greenhouse gases Various Venus, Earth Ocean circulation 10s Myr (plate tectonics) Earth Life Secular Earth 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, 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

33 Week 9 - Key equations 1/ 4 S (1 A) 4 4 T 4 3 eq Ts Teq 1 t s 4 MgSiO CO MgCO SiO t a P g l M nvth (1 ) V V 2 i 2 esc pr 2 i e l H p 2 a ext ext dm R F dt GM / R 0