Solar Radiation

Сентябрь 3, 2022

Содержание

2. Energy exchanges are derived from Kiehl & Trenberth (1997).
3. Energetic state of a body Any body the temperature of which is above 0 K radiates
4. Units and notions The unit of radiant energy is Joule (J) or kJ, mJ, hJ. The
5. Wave nature of the radiant flux Radiant energy spreads in form of waves of different length.
7. Absorption, reflection, transmission As a monochromatic flux of radiation falls on a body and passing through
8. Special properties of bodies Absolutely Black body (Bb) Absolutely White body (Wb) (In case of “geometric
9. Transmission function for the atmosphere The atmosphere is a transparent body. Meteorologists usually deal with some
10. Kirchhoff’s law There is a good relation between absorption and emittance of a body. The ratio
11. Gustav Robert Kirchhoff Wilhelm Wien 1824 –1887 Born Königsberg, Kingdom of Prussia He coined the term
12. Max Planck 1858 –1947 Planck was gifted when it came to musicPlanck was gifted when it
13. 1-st Wien’s law (Displacement law) Distribution of energy in an absolute Bb radiation spectrum is not
14. Practical application of the 1 Wien’s law?
15. Much of a person's energy is radiated away in the form of infrared light. Some materials
16. Temperatures of flames by appearance The temperature of flames with carbon particles emitting light can be
17. Some interesting results gained from the 1-st Wien’s law
18. The total flux and 2-nd Wien’s law The total flux of Bb radiation includes energy of
19. Grey body Since in the nature there are no absolutely black bodies, we may call all
20. Extinction and Bouguer’s law Notion of extinction The term extinction means weakening of the radiation energy
21. Extinction (Ex) is function of absorption (Ab) and diffusion (Df). However, Ab = Ab(λ), and Df
22. Sum up of the radiation laws Bouguer’s law 2 Wien’s laws Kirchhoff’s law Radiant energy brightness
23. Radiant energy brightness Spectral interval Radiant energy brightness is the amount of radiant energy passing in
24. This formula shows the relation between EMITTANCE (Fλ) and radiant energy BRIGHTNESS (Gλ)
25. Brightness - emittance relation in isotropic field of radiation In case the beam of rays spreading
26. Definitions Hour Angle of the Sun The Solar Hour Angle of the Sun for any local
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Energy exchanges are derived from Kiehl & Trenberth (1997).

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Energetic state of a body
Any body the temperature of which is

above 0 K radiates energy.
Equilibrium state
Non-equilibrium state

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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.
Units:

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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
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.

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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.
Absorption capability of the body (relative coefficient of absorption).
Reflection capability of the body (albedo).
Relative coefficient of transmission.
These coefficients depend on wavelength and properties of the body (Selectivity of the body)

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Special properties of bodies
Absolutely Black body (Bb)
Absolutely White body (Wb)
(In case

of “geometric reflection” – specular body)

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

If is large, is small (black soil). If is large, is small (Ice).
For a non-transparent body

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Transmission function for the atmosphere
The atmosphere is a transparent body.
Meteorologists usually

deal with some layers of it.
Monochromatic entering flux
Outgoing flux

Transmission function

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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.
For a Bb
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.
M. Plank’s formula

Emittance of a BLACK BODY

Radiation constants

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Gustav Robert Kirchhoff Wilhelm Wien
1824 –1887
Born Königsberg, Kingdom of Prussia
He coined the term "black

body" radiation in 1862

1864 –1928
born at Gaffken near Fischhausenborn at Gaffken near Fischhausen (Rybaki), Province of Prussia (now Primorsk, Russia)
In 1896 Wien empirically determined a distribution law of blackbody radiationIn 1896 Wien empirically determined a distribution law of blackbody radiation, later named after him: Wien's

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Max Planck
1858 –1947
Planck was gifted when it came to musicPlanck was gifted

when it came to music. He took singing lessons and played pianoPlanck was gifted when it came to music. He took singing lessons and played piano, organPlanck was gifted when it came to music. He took singing lessons and played piano, organ and celloPlanck was gifted when it came to music. He took singing lessons and played piano, organ and cello(Violoncello ), and composed songsPlanck was gifted when it came to music. He took singing lessons and played piano, organ and cello(Violoncello ), and composed songs and operasPlanck was gifted when it came to music. He took singing lessons and played piano, organ and cello(Violoncello ), and composed songs and operas. However, instead of music he chose to study physics.

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1-st Wien’s law (Displacement law)
Distribution of energy in an absolute Bb

radiation spectrum is not homogeneous. It depends on the body temperature. Suppose:
There is one wavelength (λm) where radiant energy is maximal.
The λm value depends on the body temperature. The lower the temperature, the larger the λm value.

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Practical application of the 1 Wien’s law?

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Much of a person's energy is radiated away in the form

of infrared light. Some materials are transparent in the infrared, while opaque to visible light, as is the plastic bag in this infrared image (bottom). Other materials are transparent to visible light, while opaque or reflective in the infrared, noticeable by darkness of the man's glasses.

http://en.wikipedia.org/wiki/Black_body

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Temperatures of flames by appearance
The temperature of flames with carbon particles

emitting light can be assessed by their color:
Red
Just visible: 525 °C (980 °F)
Dull: 700 °C (1,300 °F)
Cherry, dull: 800 °C (1,500 °F)
Cherry, full: 900 °C (1,700 °F)
Cherry, clear: 1,000 °C (1,800 °F)
Orange
Deep: 1,100 °C (2,000 °F)
Clear: 1,200 °C (2,200 °F)
White
Whitish: 1,300 °C (2,400 °F)
Bright: 1,400 °C (2,600 °F)
Dazzling: 1,500 °C (2,700 °F)
http://en.wikipedia.org/wiki/Fire#Typical_temperatures_of_fires_and_flames

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Some interesting results gained from the 1-st Wien’s law

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The total flux and 2-nd Wien’s law
The total flux of Bb

radiation includes energy of all wavelengths emitted by the body.
After integration
2-nd Wien’s law

Stephan-Boltzman constant

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Grey body
Since in the nature there are no absolutely black bodies,

we may call all of them grey bodies.
The grey body is a body the absorption capability of which is the same for every wavelength.
Radiation flux of any grey body can be presented as;

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Extinction and Bouguer’s law
Notion of extinction
The term extinction means weakening of

the radiation energy as its flux passing through a body (or atmospheric layer).
Extinction=absorption + diffusion
Bouguer’s law holds: the flux of radiation is extinguished proportionally to its intensity (Fλ), density of the medium it passes through (ρ), and the passing distance (dl).
is mass extinction index, its dimension is

Dimensionless

To make right hand part dimensionless
must be

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Extinction (Ex) is function of absorption (Ab) and diffusion (Df). However,

Ab = Ab(λ), and Df = Df(λ). Hence, the value of extinction index depends on λ too.
Volume extinction index (*)
Adopting
The volume extinction index is numerically equal to the relative value of the radiation flux extinction as the beam of rays passes through a unit distance.
As it follows from the formula (*), the value of the volume extinction index depends not only on the medium composition but also upon its density. Therefore, it can be applied in case of non-variable density.

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Sum up of the radiation laws
Bouguer’s law
2 Wien’s laws
Kirchhoff’s law
Radiant energy

brightness

Brightness - emittance relation in isotropic field of radiation

M. Plank’s formula

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Radiant energy brightness
Spectral interval
Radiant energy brightness is the amount of radiant

energy passing in a unit of time through a unit of area perpendicular to the rays, as the energy is placed in wavelength interval dλ (μ) and the solid angle ω (sr. or Steradian )

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This formula shows the relation between EMITTANCE (Fλ) and radiant energy

BRIGHTNESS (Gλ)

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Brightness - emittance relation in isotropic field of radiation
In case the

beam of rays spreading does not depend on the direction, the field of radiation is considered to be isotropic, i. e.

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Definitions
Hour Angle of the Sun
The Solar Hour Angle of the

Sun for any local location on the Earth is zero° when the sun is straight overhead, at the zenith, and negative before local solar noon and positive after solar noon. In one 24-hour period, the Solar Hour Angle changes by 360 degrees (i.e. one revolution).
Solar Noon (and Solar Time)
Solar Time is based on the motion of the sun around the Earth. The apparent sun's motion, and position in the sky, can vary due to a few things such as: the elliptical orbits of the Earth and Sun, the inclination of the axis of the Earth's rotation, the perturbations of the moon and other planets, and of course, your latitude and longitude of observation. Solar Noon is when the sun is at the highest in the sky, and is defined when the Hour Angle is 0°. Solar Noon is also the midpoint between Sunrise and Sunset.
Sun Declination
The Declination of the sun is how many degrees North (positive) or South (negative) of the equator that the sun is when viewed from the center of the earth. The range of the declination of the sun ranges from approximately +23.5° (North) in June to -23.5° (South) in December.

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Solar Radiation

Содержание

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

Energetic state of a bodyAny body the temperature of which is

Units and notionsThe unit of radiant energy is Joule (J) or

Wave nature of the radiant fluxRadiant energy spreads in form of

Absorption, reflection, transmissionAs a monochromatic flux of radiation falls on a

Special properties of bodies Absolutely Black body (Bb)Absolutely White body (Wb)(In case

Transmission function for the atmosphereThe atmosphere is a transparent body.Meteorologists usually

Kirchhoff’s lawThere is a good relation between absorption and emittance of

Gustav Robert Kirchhoff Wilhelm Wien 1824 –1887Born Königsberg, Kingdom of PrussiaHe coined the term "black

Max Planck1858 –1947Planck was gifted when it came to musicPlanck was gifted

1-st Wien’s law (Displacement law) Distribution of energy in an absolute Bb