Geoscience Reference
In-Depth Information
The value is written to the counter at every step of modeling the photon
scattering in the atmosphere according to (2.9):
1
x ( P ,
=
a ( x ( P ,
χ
W a :
W a +
)) .
(5.21)
χ
)
Finally,thefollowingvalueiswrittentothecounterofthederivativessimulta-
neously with writing weight
ψ
to the counter of irradiances as per to (2.18):
W a
( P , P )) ,
1
| µ |
ψ
∆τ
a (
where P is the coordinate of the counter.
The obtained algorithm is essentially simplified while taking into account
that the following sumis calculated simultaneously at the point of the scattering
modeling P =
P 2
( P )
ω 0 ( P )
)
1
1
1
x ( P ,
α
( P )) +
ω 0 ( P )) +
a ( x ( P ,
χ
a (
a (
)) .
(5.22)
α
χ
After substituting the expressions of the optical parameters through aerosol
and molecular components (1.24) and (1.25) with the elementary algebraic
manipulations, this sum is reduced to the following form:
σ m ( P ) x m (
χ
σ a ( P ) x a ( P ,
χ
a [
)+
)]
,
(5.23)
σ m ( P ) x m (
χ
σ a ( P ) x a ( P ,
χ
)+
)
σ a , x a are the volume coefficients and phase functions of the
molecular and aerosol scattering. In addition, remember that the phase func-
tion of the molecular scattering determined by (1.25) does not depend on
optical parameters. Finally, the only value is written to the counter in the
algorithm of the photon free path modeling:
σ m , x m ,
where
1
| µ |
∆τ ( P 1 , P 2 )) ,
=
W a :
W a
a (
(5.24)
and after modeling the scattering angle the only value is:
)
)
σ a ( P ) a x a ( P ,
χ
σ m ( P )+ x a ( P ,
χ
σ a ( P )+
χ
W a + x m (
)
=
a
a
W a :
.
σ m ( P ) x m (
χ
σ a ( P ) x a ( P ,
χ
)+
)
(5.25)
Theexplicitexpressionsoftheabove-mentionedderivativesthroughthede-
sired parameters of the inverse problem are presented further. The total set
of the retrieved parameters has been defined in the previous section. There
are the vertical profile of air temperature T ( P i ), profiles of contents of four
gases absorbing radiation Q H 2 O ( P i ), Q O 3 ( P i ), Q NO 2 ( P i ), Q NO 3 ( P i )(TheO 2 con-
tent is constant), volume coefficients of the aerosol absorption and scattering
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