50
October 2016
4.1 Optical thickness calculation
Beer-Lambert law applied to the atmosphere
I
=
I
0
⋅
exp
−
m
a
g
NO2
w
O3
r
[1]
I
0
: sunlight intensity outside the atmosphere
I : Light received on the ground
λ
is the wavelength of light
τ
a : aerosols transparency coefficient
τ
g
: gaz (CO
2
et O
2
) transparency coefficient
τ
NO2
: Nitrogen dioxide transparency coefficient (pollution)
τ
w
: water vapor transparency coefficient
τ
O3
: Ozone transparency coefficient
τ
r
: Rayleigh scattering coefficient
m : Air mass coefficient through which light (optical path)
m
=
1
sin
θ
is position angle of the Sun with the horizon
In the case of aerosols measures, the equation will be simplified by considering
that the atmospheric optical total thickness depends only on the dissipation of the
light by the molecules (Rayleigh) by ozone molecules (O
3
) and aerosol . We
distinguish the "natural" contribution (molecular) and "contaminating" (ae
others).
Contributions due to ozone (and perhaps other absorbing gases under certain
conditions) and aerosols can be separated after the measurement or using climate
data and average values of ozone depending on latitude eg , or by using the total
of air column with the time and place of collection of the actual measurement data.
Satellite mounted instruments such as the Total Ozone Mapping Spectrometer
(4)
(TOMS) provide such data.
(4)
http://ozoneaq.gsfc.nasa.gov
Equation [1] becomes :
I
(λ)=
I
0
(λ)⋅
exp
(−
m
( τ
a
+ τ
r
+ τ
O3
))
We search to determine
τ
a
.
τ
r
coefficient is proportional to the ratio of atmospheric pressure measured at the
observation point by pressure measured by the level of the surface of the sea
(p/p0) and therefore :
τ
r
=
a
R
⋅
p
p
0
τ
o
3
,
coefficient is supply by LOA for green and red light length. In the blue light,
this coefficient is null.
Summary of Contents for CALITOO
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