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calculated per the altitude unit initially. After the differentiation of (5.1) we
obtained:
∂α P ( P i )
RT ( P i )
g ( P i )
∂α z ( P i ) =
.
(5.30)
µ
( P i ) P i
Owing to summarizing rules (1.24), analogous relations are also derived for
the volume coefficient of the aerosol scattering.
Now the final formulas are presented for the derivatives of the radiative
characteristics with respect to the desired parameters. The specifications, used
in Chapter 1 and in the previous section are kept.
Derivatives with respect to contents of the gases absorbing radiation (exclud-
ing the water vapor). Volume coefficient of the molecular absorption
κ m ( P i )
depends on these contents and the volume extinction coefficient in its turn
depends on the volume coefficient of the molecular absorption as per (1.24).
Then specify the concrete gas with subscript k and obtain:
∆τ ( P 1 , P 2 ))
=
∆τ ( P 1 , P 2 ))
∂α P ( P i )
∂α P ( P i )
∂α z ( P i )
∂κ m , k ( P i ) ∂κ m , k ( P i )
∂α z ( P i )
(
(
n k ( P i )
,
Q k ( P i )
n k ( P i )
Q k ( P i )
(5.31)
where:
∂α z ( P i )
∂κ m , k ( P i ) =
1
according to (1.23) and (1.24),
∂κ m , k ( P i )
=
C a , k
n k ( P i )
according to (1.22) and
P i
kT ( P i )
according to (5.18).
The cross-sections of the molecular absorption depending on wavelength
and (only for ozone) on temperature are computed by the linear interpolation
with (1.28) and (5.7). Certainly, the derivatives with respect to gases content
are not equal to zero within the spectral regions of these gases absorption only
(Table 5.1).
Derivative with respect to water vapor content . In addition to the volume
coefficient of themolecular absorption, the volume coefficient of themolecular
scattering also depends on H 2 O content as per (1.27). It yields the following
expression for the derivative of the free path:
n k ( P i )
Q k ( P i ) =
∆τ ( P 1 , P 2 ))
(
(5.32)
Q H 2 O ( P i )
=
∆τ ( P 1 , P 2 ))
∂α P ( P i )
∂α P ( P i )
∂α z ( P i )
∂κ m , k ( P i ) ∂κ m , k ( P i )
∂α z ( P i )
Q k ( P i ) + ∂σ z , m ( P i )
(
n k ( P i )
n k ( P i )
Q H 2 O ( P i )
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