Solar Radiation

The energy emitted by the Sun is called

SOLAR RADIATION.

It is the only source of energy for the Earth. Other sources: Earth’s surface – 5000 times less, Stars – 30.000.000 times less.

When arriving to Earth, the larger part of the solar radiation (SR) transforms to heat energy, and a small portion of it to electric energy (upper atmosphere).

30 30 900km2 area receives annually

3,8 1015 kJ of energy

1

Energy exchanges are derived from Kiehl & Trenberth (1997).

2

Energetic state of a body

Any body the temperature of which is above 0 K radiates energy.

Eem		dEin	0				dT	0
		dt					dt

Eab dEdtin 0 dTdt 0

Eem Eab	Equilibrium state
Eem Eab	Non-equilibrium state	3

Units and notions

The unit of radiant energy is Joule (J) or kJ, mJ, hJ.

The basic characteristics of radiation is FLUX of RADIANT ENERGY.

Amount of energy emitted (or passing)

through the unit of area in a unit of time is termed

SURFACE DENSITY of RADIATION FLUX or RADIOSITY.

It is also called simply Radiant flux or Flux of

radiation.	dФ
	F ds
J m2s	Units:	W m2

4

Wave nature of the radiant flux

Radiant energy spreads in form of waves of different length. Distribution of energy in wavelength is very important characteristics.

Let’s take wavelength interval from λ to dλ i.e. dλ.

Amount of energy emitted trough the body surface ds is proportional to ds and dλ

dФ F dsd

F denotes monochromatic (homogeneous) flux of radiation. It

represents the quantity to characterize the wavelength around λ. It is also called spectral density of radiation flux or emitting capability of the body or simply emittance.

5

dФds F F d

0

Flux of radiant energy.

Surface density of the radiant flux.

Radiosity

Simply: radiant flux or flux of radiation.

J m2s		W m2

dФ F dsd

Spectral density of the radiant flux (спектральная плотность потока радиации).

Emitting capability of the body (излучательная способность).

Emittance

J m2s		W m2

6

Absorption, reflection, transmission

As a monochromatic flux of radiation falls on a body and passing through it, the flux is partly absorbed, partly reflected, and the remaining part is allowed for transmission.

F ''

F

F F ' F '' F '''

F

1

F '

F

F '''

F '

a

Absorption capability of the body (relative coefficient of

F

absorption).

F ''

r

Reflection capability of the body (albedo).

F

F

'''

d

Relative coefficient of transmission.

F

These coefficients depend on wavelength and properties

a r d

1

of the body (Selectivity of the body)

7

Special properties of bodies

a	1; F '	F
				Absolutely Black body (Bb)
r	d 0

r	1; F '' F
			Absolutely White body (Wb)
a d 0

(In case of “geometric reflection” – specular body)

There are no absolutely transparent bodies in the nature. Majority of solid bodies are not transparent.

d 0

a r 1

r

If a

is large,

r is small

(black soil). If

is large, a

is small (Ice).

For a non-transparent body

F '' 1 a F

F '

1 r F

F '

a F

F '' r F

8

Transmission function for the atmosphere

The atmosphere is a transparent body. Meteorologists usually deal with some layers of it.

F 0 Monochromatic entering flux

F m Outgoing flux

Transmission

function

		F 0 F m			F m
	A m		1						P m	F m
		F 0			F 0					F 0

A m P m 1

9

Kirchhoff’s law

There is a good relation between absorption and emittance of a body. The ratio Em/Ab does not depend on the nature of the body. It is the same function B(λ,T) for every of bodies.

That’s Kirchhoff’s law.

F		B ,T
					For a Bb a 1	F B ,T
a
		B ,T			Emittance of a BLACK BODY

In the nature there are no absolutely black bodies. Any real body emits and absorbs less energy of the same wavelength than Bb. However it emits and absorbs energy of the

same wavelength.	B ,T	C1 5						C 3,7418 10 16W / m2
M. Plank’s formula								1
			C2						2
								C2 1,438786 10		mK
		exp			1
			T
								Radiation constants		10