Riccardo Rigon

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Solar Radiation Long wave radiation

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Or is used for photosynthesis

or other chemical reactions

Spectral response

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Earth “is” a gray body

Having a temperature emits radiation

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Long wave radiation

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Gray Bodies

• Plank’s Law for gray bodies:

• The Stefan-Boltzmann equation for gray bodies:

W� = ✏�2⇡c2h��5

ech

�KT � 1[Wcm�2µm�1]

W = ✏�T 4[Wcm�2]

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where ε is the average emissivity calculated over the entire electromagnetic

spectrum.

Long wave radiation

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Gray Bodies

The behavior of a real (gray) body is related to that of a black body by means of the quantity ελ, known as the emission coefficient or emissivity, which is defined as:

Kirchhoff (1860) demonstrated that a good “radiator” is also a good “absorber”, that is to say:

✏� =W�(real body)W�(black body)

↵ = ✏ ⇢ + ⌧ + ✏ = 1

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Long wave radiation

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Comparison of blackbody and gray body

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In reality emissivity depends, at least, on wavelength. Earth should be probably defined a selective radiator

Long wave radiation

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See the Earth as gray body

a n d g i v e n t h a t t h e

temperature of the Earth’s

surface is, on average,

about 288 K, it obviously

e m i t s a s p e c t r u m o f

radiation in the infrared

band.

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Long wave radiation

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Radiation emitted by the Sun and the Earth

Yochanan Kushnir

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Long wave radiation

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See the Earth as gray body

a n d g i v e n t h a t t h e

temperature of the Earth’s

surface is, on average,

about 288 K, it obviously

e m i t s a s p e c t r u m o f

radiation in the infrared

band.

A t m o s p h e r e i s n o t

anymore transparent to at

these wavelengths.

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Long wave radiation

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The atmosphere is warmed from below

Therefore the temperature is higher at ground level than it is at higher altitudes.

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Long wave radiation

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Greenhouse Effect

In the absence of atmospheric absorption the average temperature of the Earth’s surface would be about -170C.

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Long wave radiation

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Instead the average temperature is about 15 0C

Greenhouse Effect

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Long wave radiation

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Radiative heating

is completed by convective heat transfer, and by water vapor fluxes (latent and

sensible heat).

13But this you can see better on the energy budget slides.

Long wave radiation

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But now concentrate on the surroundings of a point

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Any point being at a certain temperature emits long wave radiation

which must be accounted for

Long wave radiation

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The atmosphere emits infrared itself

bacause of its temperature

Long wave radiation

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Long-wave radiation is given by the

balance of incident radiation from

the atmosphere and the radiation

emitted by the ground. Both values

are calculated with the Stefan-

Boltzmann law.

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All the contributions

Long wave radiation

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Longwave radiation coming from surrounding

Radiation losses

by the area under exam

Longwave radiation coming from sky

Longwave (infrared) radiation Topographic effects: angle of view

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Long wave radiation

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Long-wave radiation

The first component should be

calculated by integrating the formula

over the entire atmosphere, but,

given how complex this process is,

typically an empirical formula is

used that uses the value of air

temperature as measured near

ground level (2m) and a value of the

atmospheric emissivity based on

specific humidity, temperature, and

cloudiness. The second component,

on the other hand, is function of the

s u r f a c e t e m p e r a t u r e a n d i t s

emissivity.

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The real process:

The hydrological parameterisation:

Long-wave radiation

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Long wave radiation

Global emissivity of the atmosphere

Temperature at 2 m from ground

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The hydrological parameterisation:

€

εatm = εBrutsaert (1− N6) + 0.979N 4 Brutsaert (1975) + Pirazzini et al. (2000)

€

εatm = εBrutsaert (1+ 0.26N)

€

εatm = εIdso(1− N6) + 0.979N 4

€

εatm = εIdso,corr(1− N6) + 0.979N 4

Brutsaert (1975) + Jacobs (1978)

Idso (1981) + Pirazzini et al. (2000)

Hodges et al. (1983) + Pirazzini et al. (2000)

Parameterisation of Long-wave radiation

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Long wave radiation

where N is the fraction of sky covered by clouds

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Net Radiation

The sum of longwave and shortwave ratio

is called net radiation

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1Thank you for your attention !

G.U

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