Radiative Equilibrium

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Radiative Equilibrium
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R. E. in a Vacuum (Moon)

• Balance between Stefan-Boltzman and absorption
  (assume constant albedo)
• For radiative equilibrium

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Problem 6.13

• A0.10, e 1, S 1370 W m-2, s 5.67x10-8 W
  m-2K-4

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Simple spherical object

• For Earth orbit data T279 K

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Top of the Atmosphere

• For globally averaged values, absorbed radiation
  outgoing radiation for steady state
• Using the planetary albedo 30, the effective
  temperature is 255 K, observed is 288 K

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Simple one layer model

• Schematic diagram of radiative coupling

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F1S
F3(1-asw)F4 A(1-asw)2S
F7(1-aLW)F8 (1-aLW)sT4s
F5aLWsT4a
F2(1-asw)F1 (1-asw)S
F4AF2 A(1-asw)S
F6F5 aLWsT4a
F8 esT4ssT4s
1
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When the smoke clears

• If the as are 0, there is no atmosphere
• If the surface is black, A0 and as may be non
  zero, the system simplifies to
• If aLWgtaSW then the system will be warmer than
  would be the case if aLWaSW

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Greenhouse Effect

• Our atmosphere is relatively transparent to
  shortwave but pretty absorptive of longwave
  radiation
• For Earth we can approximate aSW 0.1 and aLW
  0.8, then the simple model gives a substantially
  warm atmosphere. Increasing aLW then warms the
  atmosphere further

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(Very) Simple Nigh time Radiative Cooling

• In simple two layer model, again assume global
  averages

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(Very) Simple Nigh time Radiative Cooling

• Ground gets cool rapidly
• Overestimation of cooling because of simplicity
  no clouds, variable water vapor content.
• But does show right direction!

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Radiative cooling of cloud tops

• Can produce dT/dt of -15 K/day 0.8 K/hr
• In some situations, such as long lived stratus
  the cooling is responsible for mixing between the
  cloud top and overlying warmer (q) drier air, and
  their roll or cellular forms

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IR Imaging from Space
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Microwave Imaging

• Used for monitoring
• Snow extent
• Sea Surface Temperature
• Some hope for measuring precipitation

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Next Transmission in the Atmosphere