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Faint Young Sun Paradox
Part I
September 9, 2008
Katye Altieri
History of earth Systems
Sun
 Middle sized, middle aged, normal star
 Solar heating determines energy balance of Earth
 Core produces energy through nuclear reactions
 4 H atoms fuse  1 He atom
 Energy is transferred by electromagnetic radiation
 Earth ~150 million km from the sun = perfect distance
 Not too hot, not too cold, but why is that??
Habitable planets
Radiation
 Electromagnetic waves move through space at a constant
speed
 c = ~ 3x108 m s-1
 Sunlight, microwaves, heat from a fire, radio waves, ultraviolet
rays, x rays gamma rays
Radiation cont.
 The different types of radiation are distinguished by their
wavelength λ
 a = long wavelength less Energy
 b = short wavelength more Energy
Electromagnetic spectrum
Blackbody radiation
 Monochromatic emissive power (or irradiance) of radiation
emitted by a blackbody is related to temperature (T) and
wavelength (λ)
2c h
FB ( )  ch / kT
e
1
2
 k = Boltzmann constant
 h = Planck’s constant
 c = speed of light in a vacuum
5
Blackbody radiation cont.
 Integrate over all wavelengths and the total emissive power
(FB in W m-2) of a blackbody is

FB   FB ( )d  T
4
0
  = 5.671x10-8 W m-2 K-4, the Stefan-Boltzmann constant
Blackbody radiation cont.
 E=total amount of radiation emitted by an object per square
meter (Watts m-2)
  is a constant
 T is the temperature of the object in K
 Simple relationship!
E  T
4
Sun emits E as a blackbody at ~6000K
Total Energy
output of Sun
3.8x1026 Watts
Earth receives
1370 W m-2
S0 Solar
constant
Albedo
 Earth receives both short and longwave radiation from the Sun
 Some radiation is reflected back to space
 Albedo-global mean planetary reflectance
 Clouds, air molecules, particles, surface reflection
 Earth’s albedo  ~ 0.3
 30% of the incoming solar flux is
reflected back to space
At equilibrium, In=Out
 Incoming solar energy at the surface of the Earth Fs
 S0 ~1368 Wm-2
S0
FS  (1   )
4
 Earth as a blackbody emits longwave radiation FL
FL  T
4
Earth
 (1   ) S 0 
TEarth  

 4 
1/ 4
Greenhouse Effect
 Solve for no atmosphere
 TEarth = 255 K (-18°C)
 Actual surface emission gives:
 TEarth = 288 K (15°C)
Greenhouse Effect =  ~ 33°C
Earth’s Atmosphere
 Nitrogen
78%
 Oxygen
21%
 Argon
1%
 Carbon Dioxide 0.037%
Greenhouse Gases in ppm
H2O 0.1-40,000
CO2 380
CH4 1.7
N2O 0.3
O3 0.01
Greenhouse gases
Faint Young Sun Paradox
Early Earth Atmosphere
 Methane and ammonia are even better GHG than carbon
dioxide
 There could be early volcanic sources of methane and
ammonia, but modern volcanic gases are primarily CO2 and
N2
 Without volcanic methane and ammonia, you are left with
“weakly reduced” atmosphere that leads to a warm Earth
Methane vs. Carbon dioxide
CH4
 Currently, very short atmospheric lifetime ~ 10 years
 With O2 present, methane is oxidized to CO2
 In the absence of O2, CH4 lifetime can reach ~50,000 years
 No obvious large sources of methane pre-life
CO2
 Negative feedback: changes in the rate of consumption by
silicate weathering
Summary
 During Earth’s history somehow the amount of greenhouse
gases adjusted relative to the amount of change in the
radiative forcing. As the sun has warmed, the amount of the
greenhouse effect has declined so that Earth’s water didn’t
evaporate.
 Are there other possibilities? Change in albedo perhaps?
 Methane story isn’t over…
 Zahnle, et al., Geobiology (2006), 4, pp271-283