Opacity of Atmosphere (no clouds)
Horel & Geisler Chapter 3
Fraction of radiation absorbed by entire atmosphere (mostly in the troposphere)
Notes:
As the temperature of a body increases, the radiation emitted from it not only becomes more intense, but also shifts to shorter wavelengths. Because the surface of the sun is about 25 times hotter (in oK) than that of Earth, radiant energy leaving the earth has wavelengths in the infra red, around 5-25 microns. These are about 25 time longer than those of visible light, where most of the solar energy resides, and the principal modes of interaction with the atmosphere are quite distinct. Because of this difference we can usefully consider separately two quite distinct classes: solar radiation that is transmitted or reflected, but not significantly absorbed in the atmosphere, and infra red radiation that is transmitted or absorbed, but not significantly reflected in the atmosphere.
This diagram shows the the fraction of radiation absorbed as light of various wavelengths passes from top to bottom of the atmosphere or vice versa, under cloud free conditions. The principal wavelengths coming from the sun are marked in YELLOW, whereas those emitted by the earth are in GREEN. Note that the atmosphere is mostly transparent (0% opaque) in the visible and bands, and mostly opaque in the infrared. We will idealize this as being completely transparent (no absorption) in the solar band, and uniformly absorbing (and emitting) throughout the earth emission band. Clouds reflect additional sunlight, but absorb infra red. Accurate calculations become very complicated, though feasible on modern computers. They support the qualitative conclusions from the highly simplified analysis presented here.