The formula accounting for resonance absorption in the oxygen spectral line at the
wavelength l ¼ 2.53 mm and the contribution of oxygen molecule absorption lines
near l ¼ 5 mm for calculating the first component G o2 of absorption coefficient:
G O2 n i ; h j
À
Á ¼ 1:2305
n i
2 p h j
À Á
T h j
À Á
Â
Ã3 exp À
4:14
T h j
À Á
!
Â
4n i
2
Dn h j
À Á
n O2
2 À n i
2
ð
Þ
2 þ 4n O2
2 Dn O2 h j
À Á
Â
à 2 :
(3.17)
The central frequency of the line is n 0 ¼ 118.750343 GHz; p(h j ) is the atmospheric pressure (mmHg) at the altitude h j ; T(h j ) is the temperature (K) at the
altitude h j ; The dimensions of the value G O2 is [1/km].
The halfwidth value of oxygen absorption line at the wavelength l ¼ 2.53 mm
and at the altitude h j is defined as:
Dn O2 h j
À Á ¼ Dn p h j
À Á
Â
à 2 þ Dn D h j
À Á
Â
à 2
È
É 1
2 :
(3.18)
Where Dn p and Dn D are broadening by pressure and Doppler broadening:
Dn D h j
À Á ¼ 7:5210
À6
ffiffiffiffiffiffiffiffiffiffiffiffi ffi
T h j
À Á
q
;
(3.19)
Dn p h j
À Á ¼ ap h j
À Á
0:21 þ 0:78 b
½
Š
300
T h j
À Á
"
# C
:
(3.20)
The value a ¼ 2.131*10
À3
(GHz/mmHg) in the last equation is the coefficient of
broadening line by pressure, and the value b ¼ 0.75 is the coefficient of collisions
effectiveness for molecules N 2 and O 2 comparing with collisions between O 2 and
O 2 ; The parameter C ¼ 0.9 is the temperature coefficient.
The water vapor absorption G H2O n i ; h j
À
Á
might be calculated with the empirical
approximation that looks as:
G H2O n i ; h j
À
Á ¼ G R n i ; h j
À
Á þ G N n i ; h j
À
Á :
(3.21)
The resonance term G R n i ; h j
À
Á
and non-resonance term G N n i ; h j
À
Á
are defined by
the following expressions:
G R n i ; h j
À
Á ¼ 343
n
2
i D n h j
À Á
r H2O h j
À Á
T h j
À Á
Â
à 5
2
exp À
644
T h j
À Á
!
Â
1
n i À n H 2 O
ð
Þ
2 þ Dn H 2 O h j
À Á
Â
Ã
2
þ
1
n i þ n H 2 O
ð
Þ
2 þ Dn H 2 O h j
À Á
Â
Ã
2
"
#
;
(3.22)
34
3 The Direct Calculation of the Absorption Coefficient of Atmosphere Gases