Chapter 4
Calculating Transmission Functions
with Modeling Absorption Bands
of Atmospheric Gases
Abstract Molecular absorption bands are modeled. Elsasser’s regular and statistic
(Goody’s) models are considered. The algorithm for calculation transmission
function is presented. The Practice for the transmission function is described.
4.1 The Individual Spectral Line
The ideal case of the atmosphere containing only one gas characterized by
only one spectral absorption line is considered. The contour of the line, which
generally might depend on many factors, is assumed here to be possessing Lorenz’s
shape. Then the absorption coefficient k n at the wave number n is possible to
express as:
k n ¼
S
p
a
ðn À n 0 Þ
2 þ a 2
¼ Sf n À n 0
ð
Þ;
(4.1)
where S is the intensity of the absorption line (depends on temperature);
n 0 is the frequency defining the spectral line position in spectrum; a is the halfwidth
depending on pressure and temperature; The function f(n – n 0 ) is the spectral
absorption line contour. With reasoning the homogeneous (over altitude) atmosphere and the constant absorption coefficient k n ¼ const, the expression for the
transmission function in the spectral interval Dn could be written as follows:
P n ðuÞ ¼
1
Dn
ð
D n
e
Àkn u dn ;
(4.2)
where u is the integral content of absorbing gas over the radiation path.
Thus, the presentation of the exponent is needed for integrating in the Eq. 4.2.
I. Melnikova et al., Remote Sensing of the Environment and Radiation Transfer,
DOI 10.1007/978-3-642-14899-6_4, # Springer-Verlag Berlin Heidelberg 2012
39