The%20Greenhouse%20Effect

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The Greenhouse Effect
Solar Radiation, Earth's Atmosphere, and the
Greenhouse Effect. Martin Visbeck DEES,
Lamont-Doherty Earth Observatory visbeck_at_ldeo.colu
mbia.edu
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Elements of the Climate system
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Outline

• Review of radiation lecture
• Black body radiation
• Wien's Law
• Stefan Bolzmann Law
• The effective temperature of a planet
• The greenhouse effect

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Black Body Emission
T(sun) 5780 K
T(earth) 288 K
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Black Body Emission

• Wien's law states that
• lmax a / T
• where lmaxis given in mm, T is in units of K, and
  a is a constant equal 2897 mm K.
• The Stefan-Boltzman law states that
• I s T4
• where I is in units of W/m2, T is in units of K,
  and s (the Greek letter sigma) is a constant
  equal to 5.67 x 10-8 with units of W m-2 K-4.

Area Energy (integrate over log of wavelength)
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Temperature Scales

• Always use K (Kelvin)in Radiation
  calculations
• 0 K -273 C

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Solar Constant
I I0 (at the source) r(source)2 / r2

I2
I1
I0
r0
r1
r2
I2 I1 ( r22 / r12 )
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Solar Constant

• I I0 (at the source) r(source)2 / r2
• I0 s T4 (Stephan-Boltzmann Law) I0
  6.3 107 W/m2
• (Sun T5780K)
• I(at Earth) I0 rsun2 / r2
• 1367 W/m2
• (rsun 6.9 108 m)

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Three Aspects of Radiationinteracting with matter
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Interaction of Energy from the Sun with Earths
Atmosphere
The energy that drives the climate system comes
from the Sun. When the Sun energy reaches the
Earth it is partially absorbed in different parts
of the climate system. The absorbed energy is
converted back to heat which causes the Earth to
warm up and makes it habitable.
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The Earth Radiation Budget
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Emission Temperature of a Planet
Conservation of Energy Solar radiation absorbed
planetary radiation emitted
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Emission Temperature of a Planet
Solar radiation absorbed

• Iin S (1-A) p R2 S Solar flux (W/m2) A
  albedo of the planet R radius of the
  planet

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Emission Temperature of a Planet
Planetary radiation emitted

• Iout sT4 4p R2 s Steph.-Boltz.
  Const. T Temperature of
  planet R radius of the planet

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Emission Temperature of a Planet
Solar radiation absorbed planetary radiation
emitted Iin Iout S (1-A) p R2 sT4
4p R2
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Emission Temperature of a Planet
Solar radiation absorbed planetary radiation
emitted Iin Iout S (1-A) p R2 sT4
4p R2 gt S (1-A) 4 sT4 T4 S
(1-A) / (4s)
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Emission Temperature of a Planet
Solar radiation absorbed planetary radiation
emitted Iin Iout S (1-A) p R2 sT4
4p R2 gt S (1-A) 4 sT4 T4 S
(1-A) / (4s) We can now compute the emission
temperature for each planet. Lets do the Earth
here...
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Emission Temperature of a Planet
Solar radiation absorbed planetary radiation
emitted Iin Iout S (1-A) p R2 sT4
4p R2 T4 S (1-A) / (4s) T 255 K
-18 C is that an reasonable
answer?using A 0.3 S 1370 W/m2 s
5.67 10-8 W/m2/K4
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The Greenhouse EffectComposition of the
Atmosphere

• Here is how the greenhouse effect works The
  Earth's atmosphere contains many trace (or minor)
  components

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Greenhouse Effect
The Earth's atmosphere contains many trace (or
minor) components. While the major atmospheric
components (Nitrogen and Oxygen) absorb little or
no radiation, some of the minor components are
effective absorbers. Particularly effective is
water vapor, which absorb effectively in the IR
wavelength range.
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Greenhouse Effectabsorption by trace gases
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Absorption by trace gases influences the
atmospheres temperature
O2 ultraviolet light O O
O O2 O3
O3 ultraviolet light O2 O
Emission Temperature
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Greenhouse Effect
How big is the greenhouse effect on our planet
? Lets do a simple calculation...
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Greenhouse Effect
The simple model has one layer of greenhouse
gases that are transparent to short wave
radiation but absorb all long wave radiation. The
temperature of the absorbing layer is Ta The
temperature at the surface is Te
Ta
Te
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Greenhouse Effect
Solar radiation absorbed planetary radiation
emitted Top of the atmosphere balance
Energy conservation !
Ta
Te
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Greenhouse Effect
Solar radiation absorbed planetary radiation
emitted S (1-A) p R2 sTa4 4p R2 Ta4
S (1-A) / (4s) (S(1-A) H)
Energy conservation !
Ta
Te
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Greenhouse Effect
Earth radiation absorbed layer radiation
emitted S (1-A) p R2 sTa4 4p R2 Ta4
S (1-A) / (4s) (S(1-A) H)
Energy conservation !
Ta
IR absorbing layer
Te
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Greenhouse Effect
Short wave radiation absorbed layer radiation
emitted Earth radiation emitted S (1-A) p
R2 sTa4 4p R2 Ta4 S (1-A) / (4s)
(S(1-A) H)
2 s Ta4 s Te4 (H H G)
Ta
Earth Surface budget
Te
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Greenhouse Effect
S (1-A) p R2 sTa4 4p R2 Ta4 S
(1-A) / (4s) (S(1-A) H)
2 s Ta4 s Te4 (H H G)
Ta
S (1-A)/4 sTa4 sTe4 Te 2(1/4)
Ta (S(1-A)H G)
Te
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Greenhouse Effect
Bottom line Te 2(1/4) Ta
1.19 Ta Substituting previous
results
Ta
Te
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Emission Temperature of a Planet
Solar radiation absorbed planetary radiation
emitted Ta4 S (1-A) / (4s) Ta 255 K
-18 Cusing A 0.3 S 1370 W/m2 s
5.67 10-8 W/m2/K4
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Greenhouse Effect
Bottom line Te 2(1/4) Ta 1.19
Ta Substituting previous results Ta4 S
(1-A) / (4s) using A 0.3 S 1370 W/m2
Ta 255 K -18 C
Te 1.2Ta 303 K 30 C very warm
Earth !
Ta
Te
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Greenhouse Effect

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Atmospheric Dynamic Processes