Transcript Slide 1

EART164: PLANETARY
ATMOSPHERES
Francis Nimmo
F.Nimmo EART164 Spring 11
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)
F.Nimmo EART164 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”
“Snow line”
Earth Saturn
(~300K)(~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 1000K, CH4 above 60K, and then
condenses to CH4.6H2O. F.Nimmo EART164 Spring 11
Atmospheric Structure (1)
• Atmosphere is hydrostatic:
RT
• Gas law gives us:
P
dP
dz
  ( 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
e.g. what is the pressure at the top of Mt Everest?
Most scale heights are in the range 10-30 km
F.Nimmo EART164 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 EART164 Spring 11
Week 1 - Key equations
• Hydrostatic equilibrium:
dP
dz
  ( z) g ( z)
RT
• Ideal gas equation: P 

• Scale height: H=RT/g
F.Nimmo EART164 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
 g dz  Cp dT  L dx
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
dT
g

dx
dz
C p  L dT
• 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)
F.Nimmo EART164 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 EART164 Spring 11
More on the adiabat
• If no heat is exchanged, we have C p dT  V dP
• Let’s also define Cp=Cv+R and g=Cp/Cv
• A bit of work then yields an important result:
P  c
g
or equivalently
P  cT
g
g 1
Here c is a constant
• These equations are only true for adiabatic situations
F.Nimmo EART164 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 EART164 Spring 11
Week 2 - Key Equations
 S (1  A) 

• Equilibrium temperature Teq  
 4 
1/ 4
• Adiabat (including
condensation)
• Adiabatic relationship
dT
g

dx
dz
C p  L dT
P  c
g
F.Nimmo EART164 Spring 11
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
F.Nimmo EART164 Spring 11
Phase boundary
Pvap
 LH 
 CL exp 

 RT 
E.g. water CL=3x107 bar, LH=50 kJ/mol
So at 200K, Ps=0.3 Pa, at 250 K, Ps=100 Pa
H2 O
F.Nimmo EART164 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 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
dPs LH Ps

2
dT
RT
t
H
gr 
2
F.Nimmo EART164 Spring 11
Black body basics
1. Planck function (intensity):
2h 3 1
B  2
h
c e kT  1
Defined in terms of frequency or wavelength.
Upwards (half-hemisphere) flux is 2p B
2. Wavelength & frequency:  
0.29
3. Wien’s law: lmax 
T
e.g. Sun T=6000 K lmax=0.5 m
Mars T=250 K lmax=12 m
c
l
lmax in cm

4
F

B
d



T
4. Stefan-Boltzmann law
 
=5.7x10-8 in SI units
0
F.Nimmo EART164 Spring 11
Optical depth, absorption, opacity
I-I
z
I=-Ia z
a=absorption coefft. (kg-1 m2)
=density (kg m-3)
I = intensity
dIl  a l I l dz
I
• 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
dt
t = ò 0 ar dz
= ar
dz
• You can show (how?) that I=I0 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 EART164 Spring 11
Radiative Diffusion
• We can then derive (very useful!):

4p T 1 B (T )
F ( z)  
d

3 z 0 a T
• If we assume that a is constant and cheat a
bit, we get
3
16 T T
F ( z)  
3 z a
• Strictly speaking a is Rosseland mean opacity
• But this means we can treat radiation transfer as
a heat diffusion problem – big simplification
F.Nimmo EART164 Spring 11
Greenhouse effect
 3 
T 4 (t )  T04 1  t 
 2 
1
4
T0  Teq4
2
A consequence of this model is that the surface is hotter than air
immediately above it. We can derive the surface temperature Ts:
 3 
Ts  T 1  t s 
 4 
4
4
eq
Earth
Mars
Teq (K)
255
217
T0 (K)
214
182
Ts (K)
288
220
Inferred t
0.84
0.08
Fraction transmitted
0.43
0.93
F.Nimmo EART164 Spring 11
Convection vs. Conduction
• Atmosphere can transfer heat depending on
opacity and temperature gradient
• Competition with convection . . .
4
dT
g
dT
3 Te


aR
3
dz
Cp
dz
16 T
Whichever is smaller wins
-dT/dzad
Radiation dominates
(low optical depth)
-dT/dzrad
crit
crit
3
16 gT

4
3 a RTe C p
Does this equation make sense?
Convection dominates
(high optical depth)
F.Nimmo EART164 Spring 11
Radiative time constant
Atmospheric heat capacity (per m2):
C p H
Radiative flux:
Te4
Time constant:
Cp
 T
P
g
Fsolar (1  A)
E.g. for Earth time constant is ~ 1 month
For Mars time constant is a few days
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
F.Nimmo EART164 Spring 11
Week 5 - Key equations
dIl  a l I l dz
dt
= ar
Optical depth:
dz
Absorption:
Greenhouse
effect:
 3 
T (t )  T 1  t 
 2 
Radiative
Diffusion:
16 T T
F ( z)  
3 z a
4
4
0
Cp
Rad. time constant:
1
T0  1/ 4 Teq
2
3
 T
P
g
Fsolar (1  A)
F.Nimmo EART164 Spring 11
Geostrophic balance
du
1 P

 fv  Fx
dt
 x
• In steady state, neglecting friction we can balance
pressure gradients and Coriolis:
1
P
Flow is perpendicular to
v
the pressure gradient!
2  sin  x
L
L
wind
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 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 Rd is (why?)
Rd 
v prop
f
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
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
u
Ro 
2 L sin 
du
1 P

 2 sin v  Fx
dt
 x
u
g T

z
fT y
F.Nimmo EART164 Spring 11
Energy cascade (Kolmogorov)
Energy in (, W kg-1)
ul, El
l
Energy viscously
dissipated (, W kg-1)
• Approximate analysis (~)
• In steady state,  is constant
• Turbulent kinetic energy
(per kg): El ~ ul2
• Turnover time: tl ~l /ul
• Dissipation rate  ~El/tl
• So ul ~( l)1/3 (very useful!)
• At what length does viscous
dissipation start to matter?
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
Re 
uL

ul ~( l)1/3
 NB
g   dT  g 
  

T   dz  C p 
2
l ~ uR / 
1/ 2
 dT
F ~ C p 
 dz
dT

dz
ad



3/ 2
1/ 2
g
 
T 
H2
F.Nimmo EART164 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
 S (1  A) 

Teq  
 4 
1/ 4
 3 
Ts  T 1  t s 
 4 
4
4
eq

Recall that t  a dz
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
P
t a
g
F.Nimmo EART164 Spring 11
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)
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)
F.Nimmo EART164 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 (CO2 and H2O)
• Snowball Earth
F.Nimmo EART164 Spring 11
Week 9 - Key equations
 S (1  A) 

Teq  
 4 
1/ 4
P
t a
g
MgSiO3  CO2  MgCO3  SiO2
 3 
Ts  T 1  t s 
 4 
4
4
eq
  nvth (1  l )e
l
2
Vi
2
M  2 pRi 0 H
Vesc
dma
p Rext Fext

dt
GM / R
2
F.Nimmo EART164 Spring 11