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Mid‐Term Review
22 OCTOBER 2012
MET 5016 Physics of Atmospheres
Earth’s Equilibrium Black‐
Body Temperature
At the Earth’s equilibrium temperature what goes out equals what comes in.
Equate the solar heating to the infrared cooling globally
πA2S0(1 – α) = 4πA2σT BB4
Or , TBB4 = S0(1 – α)/4σ
This expression works out to TBB = 256 K for the Earth.
The average emitted (or absorbed) radiation is 239 W m‐2
But TBB is much cooler than the Earth’s average observed temperature 288 K
Why? 1
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The Greenhouse Effect
• Atmosphere transmits Solar radiation, but
• Absorbs all IR (ie BB)
• May be grey, ie. ε < 1.
• Upward emission from an ε
Upward emission from an ε = =
1 atmosphere is equal to the solar heating
• Which means that net surface and back radiation must also = solar heating
• So Tsfc > TBB
Intensity or Radiance

a
r2
• Radiance is the total a mount of energy per steradian propagating in a particular direction = Iυ(υ)
• Solid angle (in steradians) g (
)
dω = da/r2= sin θ dθ dφ
• Spectral radiance is per steradian per unit wavelength and also has a definite direction • I.e. a laser pointer beam
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Flux or Irradiance
• Integrate all the radiances over a hemisphere above or below the surface.
Fv 

I v ( ,  ) cos  d , and
hemisphere
F   Fv d
• Irradiance is more useful
• Can be spectral
Plank’s Law
Peak emission at
λmax (μm) = 2897/T
B (T ) 
2hc 2

5
1
e
hc /  kT
1
Total emission
(area under the curve)
E = σT4
One‐Layer Black Atmosphere
• Atmosphere is transparent to visible light and opaque to IR
• Same surface Albedo and Solar Irradiance as before
Surface heat balance:
FSOL   T04   T14
Atmosphere heat balance
0   T04  2 T14
The only radiation emitted from
the planet as a whole is that from
the top of the atmosphere, so
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FSOL   TBB
  T14
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Calculating the Surface Temperature
• From the last relation, it is clear that the atmosphere must be at TBB = 255K, the blackbody temperature of the Earth‐Atmosphere system
• It radiates the same amount of IR upward and downward. • From the energy balance for the Atmosphere:  T04  2 T14 , or T0  4 2TBB  1.19255 K
 305 K  31 C
• Which is also consistent with the Surface energy balance.
Vertical Profiles of Upwelling and Downwelling Radiation and of Blackbody Radiation in a Grey Atmosphere
Black and Grey Bodies
FBB   T 4
FG   T 4
Emissivity = ε = ratio of actual to blackbody < 1
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Static Stability
How the Sounding Lets Us Predict Convective Clouds
Global Radiative Balance
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Annual Mean Solar, IR & NET Radiation as a Function of Latitude
Jeans Escape
• H comes from photodissociation of H2O and CH4
• H2O vapor pressure at the tropopause is limited by cold temperatures
• This COLD TRAP limits the Thi COLD TRAP li i h
whole process
• CH4 is a minor constituent
• Upward eddy, then molecular diffusion
• Final escape in Exosphere where mean free path > H
• But only for atomic hydrogen on the tail of the Boltzmann Distribution
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I k ( z ) I k 0e  z / H I


,
z
cos 
cos 
Chapman Layer
Integrating
I
k H  0e  z / H
ln I 
 const.,
cos 
ρ
As altitude approaches
pp
infinity,
y, I  I0
I - dI
ln I 0  const.
Eliminating the constant of integration and exponentiating
 k H  0e  z / H 
I  I 0 exp 

cos 


Sidney Chapman 
Chapman layers are also good
models for spectral beam
absorption in the ionosphere
Beam essentially
y constant,, absorption
p
increasing as density does
z = H ln (kαHρ0)/cos θ
Beam attenuation
Ozone Photochemistry
• Total Ozone measured in Dobson Units – 0.01 mm of gas at STP
• Oxygen photodissociation: – O2 + hν  2O (J2, λ < 0.246 μ m)
• Ozone formation: – O2 + O + M  O3 + M
( k2)
• Atomic Oxygen recombination: Atomic Oxygen recombination:
G.M.B. Dobson
– O + O + M  O2 + M ( k1, SLOW)
• Ozone recombination:
– O3 + O  2O2
(k3)
• Ozone photodissociation: – O3 + hν  O2 + O
(J3, λ < 0.310, 1.140 μ m)
• Red equations recycle Odd Oxygen, blue equations convert it to molecular oxygen
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Brewer‐Dobson Circulation
Strongest in winter
hemisphere
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