Available Energy: Net Radiation and Soil Heat Flux - Transport in the Atmosphere-Vegetation-Soil Continuum - page 22

where τ λ v, i is the monochromatic transmissivity for a vertical beam. This shows that
τ λθ , i depends on the state and composition of the atmosphere (through τ λ v, i ) as well as
on the direction of the beam (through m r ).
The radiation entering the atmosphere will be attenuated by various processes,
each with a different extinction coeficient. Because all these processes are working
independently, we have (for n processes):

τ τ τ =⋅ ⋅ ⋅

= −+++

 τ

λ θ λ θ , 1 λ θ , 2 λ θ , n

(2.13)

( )

δδ δ
λ λ

 m

e

, 1 , 2 λ , n r

where τ λθ, i and δ λ , i are the transmissivity and optical thickness due to process i , respec-
tively. Those processes encompass various types of scattering and absorption. Note
that in Eq. ( 2.13 ) we have assumed the relative optical masses to be equal for all pro-
cesses.

Question 2.3: Consider radiation of a certain wavelength λ . For that wavelength, for
a substance i , the atmosphere has a transmissivity for a vertical beam ( τ λv ,, i ) of 0.8. The
vertical air mass m v is 10 000 kg m -2 and the speciic concentration of substance i is
0.003 kg kg -1 .
a) Verify that the value for the vertical air mass has a realistic order of magnitude.
b) What is the value of the extinction coeficient for substance i ?
c) If the solar zenith angle is 40 degrees, what is the transmissivity τ λθ , I ?
d) If the amount of radiation at the top of the atmosphere at wavelength λ is 1.5 W m -2
µm -1 , what is the amount of radiation arriving at Earth's surface for the situation
given under (b)?

Extinction: Scattering and Absorption
Extinction of short wave radiation is due both to scattering and to absorption. Owing
to the direction independence of Rayleigh scattering half of the scattered radiation is
scattered backward, thus reducing the light intensity. Mie scattering and geometric
optics scattering occur mainly in the forward direction, but there is also backward
scattering in some speciic directions (see Figure 2.1 ). Hence the net effect of all
types of scattering is that a part of the radiation is removed from the beam, either
backward or sideways.
Absorption of radiation in the shortwave part of the spectrum takes place in two
distinct wavelength regions. At the near-infrared part the most important absorbing
gas is water vapour (see Figure 2.2b ), which absorbs in a large number of bands.
Oxygen, carbon dioxide and methane play a smaller role, all at near-infrared wave-
lengths. On the other hand, absorption in the UV part of the spectrum is dominated
by ozone and oxygen. Ozone is active in a broad band of ultraviolet wavelengths
down to 0.2 μm, whereas oxygen absorbs - apart from the Herzberg band around
0.27 μm - at wavelengths below 0.2 μm. Absorption in the UV part of the spectrum