Terrestrial and atmospheric radiation

Earth’s surface radiation

As well as any other body with temperature T>0K, the Earth radiates energy. Since the Earth’s temperature is rather low

(T=288K), it radiates energy in				part of the spectrum.
Neither Earth, nor its atmosphere, is not absolutely black
0,85...0,99		body. Therefore			B0	T04			0,95
B0 BSun	however		B0 and	I!	are of the same order
					of magnitude.
T°C	-40	-20	0	20		40
B kW/m²	0,17	0,24	0,32	0,43		0,55

1

Radiation of the atmosphere

It is of more complex character. As 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.

2

Carbon dioxide

Volume index of absorption by CO2 is presented below

,	2,6 – 2,8	4,1 – 4,4	9,1 – 10,9
, m 1 0,025		0,33
			2 10 5

12,9 – 17,1

0,83

		This is the most
Carbon dioxide absorbs		important
IR radiation very lightly		absorption band
in the atmospheric		of the carbon
window		dioxide

3

Ozone

Ozone has several absorption bands in the IR part of 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.

P Qw.v. ,Qc.d. P1 Qw.v. P2 Qw.v. P3 Qc.d.

Mass of water vapor Qw.v.

Mass of carbon dioxide Qc.d.

1 m²	1 m²

4

	3				3
P Qw.v. i exp i Qw.v.				P Qc.d. i exp i Qc.d.
	i 1				i 1
Functions	P1 Qw.v. 10	P1 Qw.v. 10 100			P	P
1					2	3
	0,19		0,19		0,05	0,32
2	0,21		0,26		0,19	0,40
3	0,35		0,29		--	0,28
1	47,0		43,0		0,29	0,056
2	1,1		1,0		0,023	0,0012
3	0,03		0,015		--	0

Cloud free atmosphere allows for passage of 17…35% of IR 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.	5

The IR radiation transmission function P for cloudiness depends on the mass of water droplets containing in the vertical air column of a unit section (cloud water storage).

Qδ kg/m²	0,01	0,03	0,07
P	0,144	0,013	0,0004

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.

6

Equation of the terrestrial radiation transfer in the atmosphere

The basis 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
I J	I J
			A′	θ
Energy brightness coming
from the upper hemisphere	J
				A
Energy brightness coming	J
from the lower hemisphere

Z+dz

Z

At the point A	J		The change of the
At the point A’	J	dJ	brightness is dJ
			7

Reasons for the change

Absorption	J adl		dl AA'		a is density of
					absorbing gases
					E is the brightness of
Radiation of the layer dz		E adl
					BB radiation

Diffusion of the radiant energy

On one hand it is	On the other hand it
extinction of the	results in increasing
radiation	of the brightness

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

8

dJ

J

E adl

dl

dz

dJ

J E a

dz

cos

dz

cos

Dividing by

cos

dJ

equations of heat (IR

dz

cos E J a

These are differential

From the similar

radiation) transfer.

To obtain equations for

reasoning

upward (Uλ) and

dJ

cos J

E a

downward (Gλ)

homogeneous fluxes,

these equations must be

dz

integrated with respect

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

9

							As result we get
	U	a B				U				G	a G B
	z									z
		B		C 5			and		1,66
					1
Here
					C2	1
				exp
					T

Fluxes Uλ and Gλ satisfy to the following boundary conditions:

G 0

at

Z

U

B 1 r G

at

Z 0

For practical purposes

T

1 Ф

U U d

G G d

z

t

cp

Some practical interest is related to vertical gradients of the quantities U, G, and Ф (effective flux ).

10

	Levels			P=P0	200 hPa	100 hPa
G	kW	m	2	0,327	0,084	0,06
	kW
Ф		m	2	0,016	0,103	0,119
U	kW	m2		0,343	0,187	0,185
hPa
	G		Ф		U
10
0
20
0
P=P0
			0, 1		0, 2	0, 3	11