6 f-radiation-absorptions

Riccardo Rigon

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Solar Radiation Absorptions crossing the Atmosphere

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Atmosphere is a gray body

• The blackbody is an ideal object that absorb all the radiative energy it receives

• Real objects (bodies, “gray bodies”) are not capable of absorbing all radiation.

• To understand the difference between a blackbody and a gray body we need to

analyse the interactions between a surface and the electromagnetic radiation

incident onto it.

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Absorption and transmission of short wave radiation

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Atmospheric absorption

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Radiation passes quite freely through the Earth’s atmosphere and it warms

the surfaces of seas and oceans. A portion of between 45% and 50% of the

incident radiation onto the Earth reaches the ground


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Radiation transmitted

Radiation reflected

Shortwave Radiation budget

The solar radiation penetrates the

atmosphere, and it is transferred

towards the ground, after being

reflected and scattered.

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the incoming radiation equals

the reflected one plus

the absorbed plus

the transmitted

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S� It should not be forgot that

the radiation budget is an

energy budget, for which

Radiation

absorbed


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Energy absorbed by atmosphere

Transmitted

radiation

Corrected Solar constant

Solar radiation

reflected back to space

This budget can be apply to any slice of the atmosphere



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• is the reflection coefficient, said atmospheric reflectivity (albedo)

• is the transmission coefficient, said atmospheric transmissivity

• is the absorption coefficient, said atmospheric absorptivity

Coefficients

The following coefficients can also be defined

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Energy conservation:

Which is, indeed, valid for reflectivity, transmissivity and absorptivity of any other body

implies that reflectivity, transmissivity and absorptivity sum to one:

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R. Rigon

We just forget for a moment this. It will be splitted into two parts:

one depending on diffuse radiation and

another on cloud cover

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Atmosphere is pretty transparent: which means that we can, as a first approximation, neglect it (atmosphere is heated from below)

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In any case let’s concentrate on

the transmitted radiation

This can be decomposed into two parts:

direct and diffuse solar radiation

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Evidently, for simmetry

is also composed by reflected and diffuse solar radiation

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Diffuse radiation comes from scattering

Incident solar radiation strikes gas molecules, dust particles, and

pollutants, ice, cloud drops and the radiation is scattered. Scattering

causes diffused radiation.

Two types of light diffusion can be distinguished:

Mie scattering

Rayleigh scattering


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Rayleigh Scattering

•The impact of radiation with air molecules smaller than λ/π causes

scattering (Rayleigh scattering) the entity of which depends on the frequency of the incident wave according to a λ-4 type relation.

•In the atmosphere, the wavelengths corresponding to blue are scattered more readily than others.

incident radiation

diffuse radiation

transmitted radiation

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•When in the atmosphere there are particles with dimensions greater than 2 λ/π

(gases, smoke particles, aerosols, etc.) there is a scattering phenomenon that does not depend on the wavelength, λ, of the incident wave (Mie scattering).

•This phenomenon can be observed, for example, in the presence of clouds.

Mie Scattering

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incident radiation

diffuse radiation

transmitted radiation


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Diffused Light

Scattering selectively eliminates the shorter visible wavelengths, leaving the longer wavelengths to pass. When the Sun is on the horizon, the distance travelled by a ray within the atmosphere is five or six times greater than when the Sun is at the Zenith and the blue light has practically been completely eliminated.

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Tilt of the Earth’s axis and atmospheric effects

The tilt of the earth’s axis and atmospheric effects together affect the amount of radiation that reaches the ground.

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One way to take into account of absorption

Would be to run a full model of atmospheric transmission (e.g. Liou, 2002).

However hydrologists prefer to use parameterizations, and the

concept of atmospheric transmissivity.


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Solar radiation transmitted to the ground under clear sky conditions

Finally:

Fraction of direct solar radiation included between the considered

wavelengths

Transmittance of the atmosphere

Correction due to elevation of the site

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R. Rigon

We do not enter in the details of how

and

are determined. Please look, for instance, at Formetta et al., 2012

Solar radiation transmitted to the ground under clear sky conditions

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6 f-radiation-absorptions