GW 4.1 One-Layer Model: Derivation

What does the One-Layer model show?

• Sunlight that is not absorbed or reflected by the atmosphere, but partially reflected by the surface

• Infrared radiation that is emitted and absorbed by the atmosphere and the surface

Why is sunlight also called shortwave radiation?

The sun emits shorter wavelength than the Earth

Why does the factor of ¼ appear in front of the solar radiation flux in the one-layer model?

• The factor of ¼ represents the incoming sunlight or insolation measured in W m^-2

• Where does this come from?

  • Refer to attached image!

What is albedo?

• For the One-Layer Model, we assume that sunlight passes directly through the atmosphere

• When it hits Earth’s surface, some fraction is absorbed and some fraction is reflected

• The fraction reflected is called the albedo (α)

What is the solar energy flux absorbed by the surface?

¼ (1-α)S

What is the solar energy flux reflected back to space?

¼αS

What do we assume to be the emissivity of the surface?

• 1 b/c solids and liquids have emissivities close to 1

• This means that the surface will absorb all of the downward infrared radiation that the atmosphere emits toward it

Does the surface also emit its own radiation upward?

• Yes!

• Stefan-Boltzmann Law

  • It will emit a radiative flux of σT_s⁴ where T_s is the surface temperature

What factors impact atmospheric emissivity (ε)?

• CO₂ concentration

• H₂O concentration

• The amount and type of clouds

What is the atmosphere’s emitted radiative flux both upward and downward? And why?

• εσT_a⁴ where T_a is the atmospheric temperature

• Why is this?

  • Stefan-Boltzmann law tells us how much energy a blackbody will radiate per area per time

  • A layer of atmosphere has area that can emit both on its top and its bottom

According to Kirchoff’s Law, the atmosphere has to also do what?

• The atmosphere also has to absorb a fraction of ε of the infrared radiation that hits it

• In this case, the emission from the surface is what hits it

• It absorbs a radiative flux of εσT_s⁴ from the surface passes through the atmosphere and up into space

What is the effect of CO₂ in the one-layer model?

• By increasing CO₂:

  • (1) the atmosphere better absorbs long-wave radiation emitted by the Earth

  • (2) the Earth re-emits that radiation back to the surface, leading to the warming of the surface

• Things to notice here:

  • (1) The atmosphere absorbs and re-emits the long-wave radiation, it does not reflect it

  • (2) Changing the CO₂ does not affect the amount of solar radiation absorbed by the atmosphere in the one-layer model

  • (3) This is a good approximation of the effect of CO₂ in the real world

    • (3a) Increasing CO₂ leads to surface warming by increasing the amount of surface long-wave radiation absorbed by the atmosphere then re-emitted back down to the surface