Terrestrial and atmospheric radiation

body with temperature T>0K, the Earth radiates energy. Since the

Earth’s temperature is rather low (T=288K), it radiates energy in IR part of the spectrum.
Neither Earth, nor its atmosphere, is not absolutely black body. Therefore

however

and

are of the same order of magnitude.

it follows from Kirchhoff’s law, the energy is emitted by

only those gases which absorb it.
H2O, CO2, O3 are the main absorbers. There are secondary absorbers (in IR area only): NO; N2O; N2O4; N2O5; C2H4; CH4.
Usually we neglect their activity in radiation process.
Water vapor
“WINDOW” of water vapor is 8,5…12 μ. For this wavelength interval the water vapor is most transparent (see table in the lecture note 5). This interval is often called window of minimal extinction.
The strongest water vapor absorption band fall on the spectrum interval 5,5..7,0 μ.

dioxide absorbs IR radiation very lightly in the atmospheric window
This

is the most important absorption band of the carbon dioxide

the spectrum. However, the only bands represents practical interest; that

is around 9,65 μ band. It is situated just in the “window”. All other absorption bands of ozone are override by absorption of water vapor and carbon dioxide.

Transmission function for IR radiation total flux

The function below accounts for water vapor and carbon dioxide only.

1 m²

Mass of water vapor Qw.v.

1 m²

Mass of carbon dioxide Qc.d.

terrestrial radiation. Cloudiness makes on appreciable contribution into absorption of

IR radiation. Mass absorption index of water droplets is 500 – 2000 cm²/g. That is much larger than for water vapor.

the mass of water droplets containing in the vertical air

column of a unit section (cloud water storage).

Cloudiness practically absorbs all infrared radiation at
Qδ >0,03. Real clouds always contain Qδ >0,03.
Due to strong absorption of the IR radiation by water vapor, carbon dioxide, and , particularly, by clouds, the significant part of the terrestrial radiation is absorbed by the atmosphere, while an appreciable part of the SR is allowed to pass through the atmosphere. Thus, the atmosphere provides for a strong warming effect of the Earth surface.

for the reasoning is the energy brightness.
Assuming isotropic field of

radiation, relation between
flux of radiation (I) and energy brightness (J) will be

Z

Energy brightness coming from the upper hemisphere

Energy brightness coming from the lower hemisphere

At the point A

At the point A’

The change of the
brightness is

gases
Radiation of the layer dz
is the brightness

of BB radiation

Diffusion of the radiant energy

On one hand it is extinction of the radiation

On the other hand it results in increasing of the brightness

The sum effect of the diffusion is very small and can be neglected.

(IR radiation) transfer.
To obtain equations for upward (Uλ) and downward

(Gλ) homogeneous fluxes, these equations must be integrated with respect

to θ from 0 to π/2 and with respect to azimuth from 0 to 2π

following boundary conditions:
For practical purposes
Some practical interest is related to

vertical gradients of the quantities U, G, and Ф (effective flux ).

over many locations and years are closely related with the

average temperature at the same levels where the fluxes were measured. An example of corresponding relations for the layer 1000 – 300 hPa are presented here.

The average value of the effective flux Ф is 0,016 kW/m² at the Earth surface. However it varies significantly in time and space. Fluctuation can reach 100%. At 200 hPa level it is 0,103 kW/m² and fluctuation is about 10%.

air cooling within all layers. The rate of cooling in

the troposphere is 0,7 – 1,0° C/24 hours.