Ku Y Sj wj499

The HITRAN data corresponds to reference temperature and pressure conditions (Tref = 296 K and Pref = 1 atm). This means that for different conditions, corrections to the line intensities and half-widths must be done, before the calculation of the absorption coefficient. In order to correct for temperature variations in the line strength, we need to know the temperature dependence of the statistical weight and level populations. Based on the condition of LTE, the Boltzmann distribution provides this information mHu exp (-cauiu/T), (4.100)

9un\

In the above, c2 = hc/k = 1.439 cm K, with k the Boltzmann constant and E1 the energy (cm-1) of the lower state that is also provided in the HITRAN database. Q(T) is the total partition function of the molecule that is given by the usual expression:

Substituting the above in the line strength equation we get

From the last result it is clear that the temperature dependence of the line intensity relative to the reference temperature will have the form, eqn (4.89),

<7 m - <? (T MT«*) exp(-c2JE1/T) [1 — exp(—C2^iu/T)] lu( j ~ lu( ref j Q(T) exp{-c2E,/Tret) [1 - exp(-c2^lu/Tref)]' ( j

In the last expression all parameters necessary for the calculations are directly provided from the database. Q(T) is calculated using the Gamache et al. (1990) parametrization that approximates the partition function as a third order polynomial of temperature

where the constants depend on the molecule/isotope under consideration. Typical values of the parameters for sample molecules are given in Table 4.3.

The effects of pressure and temperature on the half-width are described in the form

-f(p,T)pIef= i J [(p -_ps)7air(i>ref, Tref) + Ps'7self(i>ref, Tref)] • (4.106)

In the above, ps is the partial pressure of the absorbing molecule, 7se1f is the self-broadening half-width of the transition line and n is a constant. The last

Table 4.3 Partition function parameters for sample molecules for the temperature range 70-400 K. (From Gamache et al. 1990)

Molecule

Parameter

a

b

c

d

14N2

7.3548E-01

7.86628E-01

-1.82828E-

-06

6.8772E-

-09

12C16 O

-4.8544

3.4530E-01

5.4835E-

05

-6.0682E-

08

16O12C16O

-2.1995

9.67518E-01

-8.0827E-

04

2.80408E-

06

H12C14N

-9.7107E-01

2.9506

-1.6077E-

03

6.11488E-

06

14N14N16O

-9.5291

1.5719E+01

-1.20638E-

02

5.37818E-

05

H12C12CH

2.5863

1.1921

-7.9281E-

-04

4.62258E-

-06

two parameters are also included in the HITRAN database. A typical value for n is 1/2 which comes from collision theory. For most cases 7a;r ^ Yseif and if the molecule under consideration is a minor species then ps ^ p. Then the above expression takes the simpler form

Pref V T J

Finally, the position of the line centre for a specific transition can be affected by the pressure. The database provides this information also, in the form of a pressure-shift parameter, S (cm-1/atm)

4.7.1 Application to N2O

As an example of the above formulation, we present an application to N2 O. The HITRAN database contains 25 724 lines for the possible transitions of the N2O molecule and its isotopes, covering the spectrum between 523 and 5131 cm-1. An example of rotational line strengths is given in Fig. 4.17 for the region of the 7.8 pm band. Figure 4.18 presents the calculated cross-section for the above region at 298 K and 1 atm pressure for a Voigt line profile. In the calculation of the cross-section high resolution must be considered in between the line positions in order to have a correct description of the variation in absorption with wave number.

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