Transcript Week 5 - Earth & Planetary Sciences

EART160 Planetary Sciences
Francis Nimmo
Last Week
• Planetary mass and radius give us bulk density
• Bulk density depends on both composition and size
• Larger planets have greater bulk densities because
materials get denser at high pressures
• The increase in density of a material is controlled by
its bulk modulus
• Planets start out hot (due to accretion) and cool
• Cooling is accomplished (usually) by either
conduction or convection
• Vigour of convection is controlled by the Rayleigh
number, and increases as viscosity decreases
• Viscosity is temperature-dependent, so planetary
temperatures tend to be self-regulating
Talk tomorrow
• 4pm in NS101
• Matija Cuk, The lunar cataclysm
This Week - Atmospheres
• What determines the surface temperature of a planet?
• What determines the temperature and pressure
structure of planetary atmospheres?
• What are the atmospheres made of, and where do
they come from?
• What determines the wind strengths?
• How do planetary atmospheres evolve?
Surface Temperature (1)
• What determines a planet’s surface temperature?
Incident
energy
Reflected
energy
Energy re-radiated
from warm surface
Absorbed energy
warms surface
 
rE 2
E r
Ein  (1  A)R F
2
R
Sun
Erad  4 R  T
2
4
A is albedo, FE is solar flux at Earth’s surface, rE is distance of Earth to Sun, r is
distance of planet to Sun,  is emissivity,  is Stefan’s constant (5.67x10-8 Wm-2K-4)
• Balancing energy in and energy out gives:
1/ 4
  rE  FE (1  A) 

Teq    
 r 

4



2
a
Surface Temperature (2)
•
•
•
•
Solar constant FE=1300 Wm-2
1/ 4
2
  rE  FE (1  A) 

Earth (Bond) albedo A=0.29, =0.9 Teq    
 r 

4



Equilibrium temperature = 263 K
 is Stefan’s constant
How reasonable is this value?
5.67x10 in SI units
-8
Body
Mercury
Venus Earth
Mars
A
0.12
0.75
0.29
0.16
Teq
446
238
263
216
Actual T
100-725
733
288
222
• How to explain the discrepancies?
• Has the Sun’s energy stayed constant with time?
Greenhouse effect
• Atmosphere is more or less transparent to radiation
(photons) depending on wavelength – opacity
• Opacity is low at visible wavelengths, high at infra-red
wavelengths due to absorbers like water vapour, CO2
• Incoming light (visible) passes through atmosphere
with little absorption
• Outgoing light is infra-red (surface temperature is
lower) and is absorbed by atmosphere
• So atmosphere heats up
• Venus suffered from a runaway greenhouse effect –
surface temperature got so high that carbonates in the
crust dissociated to CO2 . . .
Albedo effects
• Fraction of energy reflected (not absorbed) by surface
is given by the albedo A (0<A<1)
• Coal dust has a low albedo, ice a high one
• The albedo can have an important effect on surface
temperature
• E.g. ice caps grow, albedo increases, more heat is
reflected, surface temperature drops, ice caps grow
further . . . runaway effect!
• This mechanism is thought to have led to the
Proterozoic Snowball Earth
• How did the Snowball disappear?
• How did life survive?
• How might clouds affect planetary albedo?
Atmospheric Structure (1)
• Atmosphere is hydrostatic:
• Gas law gives us: P  RT
dP
dz
  ( z) g ( z)

• Combining these two (and neglecting latent heat):
dP
g
a
 P
dz
RT
Here R is the gas constant,  is the mass of one mole, and
RT/g is the scale height of the (isothermal) atmosphere (~10
km) which tells you how rapidly pressure increases with depth
• Result is that pressure decreases exponentially as a
function of height (if the temperature stays constant)
Scale Heights
• The scale height tells you how far upwards the
atmosphere extends
• Scale height H = RT/g. Does this make physical sense?
• Total column mass (per unit area) = 0H=P0/g (where’s
this from?)
• It turns out that most planets have similar scale heights:
Venus Earth
Mars
Jupiter Saturn Uranus Neptune
Tsurf (K) 733
288
215
165*
135*
76*
72*
Albedo
0.75
0.29
0.16
0.34
0.34
0.29
0.31
H (km)
16
8.5
18
18
35
20
19
* Temperature measured at 1bar pressure
Atmospheric Structure (2)
• Of course, temperature actually does vary with height
• If a packet of gas rises rapidly (adiabatic), then it will
expand and, as a result, cool
• Work done in expanding = work done in cooling

VdP  dP

 is the mass of one mole,  is
the density of the gas
Cp dT
Cp is the specific heat capacity
of the gas at constant pressure
• Combining these two equations with hydrostatic
equilibrium, we get the dry adiabatic lapse rate:
g
dT
a

dz
Cp
• On Earth, the lapse rate is about 10 K/km
• What happens if the air is wet?
Atmospheric Structure (3)
• Lower atmosphere (opaque) is dominantly heated from below
and will be conductive or convective (adiabatic)
• Upper atmosphere intercepts solar radiation and re-radiates it
• There will be a temperature minimum where radiative cooling is
most efficient (the tropopause)
mesosphere
radiation
Temperature
(schematic)
stratosphere
tropopause
clouds
troposphere
Lapse rate
appx. 1.6 K/km – why?
adiabat
Measured Martian temperature profiles
Giant planet atmospheric structure
• Note position and order of cloud decks
Atmospheric dynamics
• Coriolis effect – objects moving on a
rotating planet get deflected (e.g. cyclones)
• Why? Angular momentum – as an object
moves further away from the pole, r
increases, so to conserve angular
momentum w decreases (it moves
Deflection to right
in N hemisphere
backwards relative to the rotation rate)
• Coriolis acceleration = 2 w v sin(q) q is latitude
• How important is the Coriolis effect?
2 Lw sin q
v
is a measure of its importance (Rossby
number)
e.g. Jupiter v~100 m/s, L~10,000km we get ~30 so important
Hadley Cells
• Coriolis effect is complicated by fact that parcels of
atmosphere rise and fall due to buoyancy (equator is
hotter than the poles)
High altitude winds
Surface winds
• The result is that the atmosphere is
broken up into several Hadley
cells (see diagram)
• How many cells depends on the
Rossby number (i.e. rotation rate)
Slow rotator e.g. Venus
Medium rotator e.g. Earth
Ro~0.02
(assumes v=100 m/s)
Ro~4
Fast rotator e.g. Jupiter
Ro~30
Zonal Winds
• The reason Jupiter, Saturn, Uranus and Neptune have
bands is because of rapid rotations (periods ~ 10 hrs)
• The winds in each band can be measured by
following individual objects (e.g. clouds)
• Winds alternate between prograde (eastwards) and
retrograde (westwards)
Geostrophic balance
• In some situations, the only significant forces acting are
due to the Coriolis effect and due to pressure gradients
1 P
• The acceleration due to pressure gradients is
 x
• The Coriolis acceleration is 2 w v sinq
Why?
(Which direction?)
1
P
• In steady-state these balance, giving: v 
2 w sin q x
L
L
wind
Does this make sense?
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?
Where do planetary atmospheres come
from?
• Three primary sources
– Primordial (solar nebula)
– Outgassing (trapped gases)
– Later delivery (mostly comets)
• How can we distinguish these?
– Solar nebula composition well known
– Noble gases are useful because they don’t react
– Isotopic ratios are useful because they may
indicate gas loss or source regions (e.g. D/H)
– 40Ar (40K decay product) is a tracer of outgassing
Atmospheric Compositions
Earth
Venus
Mars
Pressure
1 bar
92 bar
0.006 bar
Titan
1.5 bar
N2
O2
H2O
Ar
CO2
CH4
40Ar
H/D
14N/15N
77%
21%
1%
0.93%
0.035%
1.7ppm
6.6x1016 kg
3000
272
3.5%
0.01%
0.007%
96%
1.4x1016 kg
63
273
2.7%
0.006%
1.6%
95%
?
4.5x1014 kg
1100
170
98.4%
0.004%
~1ppb
1.6%
3.5x1014 kg
3600
183
Isotopes are useful for inferring outgassing and atmos. loss
Not primordial!
• Terrestrial planet atmospheres are not primordial
(How do we know?)
• Why not?
– Gas loss (due to impacts, rock reactions or Jeans escape)
– Chemical processing (e.g. photolysis, rock reactions)
– Later additions (e.g. comets, asteroids)
• Giant planet atmospheres are close to primordial:
Solar
Jupiter
Saturn
Uranus
Neptune
H2
84
86.4
97
83
79
He
16
13.6
3
15
18
CH4
0.07
0.2
0.2
2
3
Why is the H/He ratio not constant?
Values
are by
number of
molecules
Atmospheric Loss
• Atmospheres can lose atoms from stratosphere,
especially low-mass ones, because they exceed the
escape velocity (Jeans escape)
• Escape velocity ve= (2 g R)1/2 (where’s this from?)
• Mean molecular velocity vm= (2kT/m)1/2
• Boltzmann distribution – negligible numbers of atoms
with velocities > 3 x vm
• Molecular hydrogen, 900 K, 3 x vm= 11.8 km/s
• Jupiter ve=60 km/s, Earth ve=11 km/s
• H cannot escape gas giants like Jupiter, but is easily
lost from lower-mass bodies like Earth or Mars
• A consequence of Jeans escape is isotopic
fractionation – heavier isotopes will be preferentially
enriched
Atmospheric Evolution
• Earth atmosphere originally CO2-rich, oxygen-free
• How do we know?
• CO2 was progressively transferred into rocks by the
Urey reaction (takes place in presence of water):
MgSiO3  CO2  MgCO3  SiO2
• Rise of oxygen began ~2 Gyr ago (photosynthesis &
photodissociation)
• Venus never underwent similar evolution because no
free water present (greenhouse effect, too hot)
• Venus and Earth have ~ same total CO2 abundance
• Urey reaction may have occurred on Mars (water
present early on), but very little carbonate detected
Summary
• Surface temperature depends on solar distance,
albedo, atmosphere (greenhouse effect)
• Scale height and lapse rate are controlled by bulk
properties of atmosphere (and gravity)
• Terrestrial planetary atmospheres are not primordial –
affected by loss and outgassing
• Coriolis effect organizes circulation into “cells” and
is responsible for bands seen on giant planets
• Isotopic fractionation is a good signal of atmospheric
loss due to Jeans escape
• Significant volatile quantities may be present in the
interiors of terrestrial planets
Key Concepts
•
•
•
•
•
•
•
•
•
•
•
•
Albedo and opacity
Greenhouse effect
Snowball Earth
Scale height H = RT/g
Lapse rate
Tropopause
Coriolis effect 2 w v sin(q)
Hadley cell
Geostrophic balance
Jeans escape
Urey reaction
Outgassing
Thermal tides
• These are winds which can blow from the hot (sunlit)
to the cold (shadowed) side of a planet
Solar energy added =
FE
R (1  A) 2 t
r
2
t=rotation period, R=planet radius, r=distance (AU)
Atmospheric heat capacity = 4R2CpP/g
Where’s this from?
Extrasolar planet (“hot Jupiter”)
So the temp. change relative to background temperature
T
gFE
 (1  A)
t
2
T
4PTCp r
Small for Venus (0.4%), large for Mars (38%)