Theoretical Reims-Tomsk Spectral data

Dependence on temperature and pressure

The values of some spectral line parameters depend on environmental temperature and pressure. The database contains the values of these parameters at T_ref and P_ref of corresponding data source.

Temperature dependence of the line intensity

To calculate the intensity S^j of jth spectral line at temperatures different from the reference temperature of the data source, one uses the following expression

S^j(T) = S^j(T_ref) · rQ · rB · rE , (1)

where S(T_ref) is the intensity of the line j at T_ref , rQ is the ratio of total internal partition functions at  T_ref and T

rQ = Q(T_ref)/Q(T) . (2)

The values of the partition functions Q(T) for isotopologues presented in HITRAN are calculated by Fortran program, TIPS.for in the temperature interval from 70 to 3000 K. The values of the partition functions Q(T) for isotopologues not presented in HITRAN are provided by authors of corresponding linelists.

rB accounts for the ratio of Boltzmann populations

rB = exp⁡(−c₂·E^j_l/T)/exp⁡(−c₂·E^j_l/T_ref) . (3)

rE accounts the effect of stimulated emission

rE = (1 - exp(-c₂·WN^j/T))/(1- exp(-c₂·WN^j/T_ref)) . (4)

In expessions (3) and (4) E^j_l is the lower-state energy of jth line, WN^j is the wavennumber of jth line and c₂ is the second radiation constant.

Temperature and pressure dependence of the line width

The half-width at half maximum (HWHM) of spectral lines used on simulation of spectrum functions for building of profile of spectral line (see Line profiles).

The Doppler half-width of the line j is independent of the pressure and calculated by the expression following the expression (2) in previous paragraph

D^j(T) = D^j(T_ref)·sqrt(T/T_ref) . (5)

The Lorentz half-width of the line j at temperature T, pressure P and partial pressure P_self  is calculated as

L^j(T,P) = (T_ref/T)^Nj_t · (L^j_env(T_ref,P_ref) · (P - P_self) + L^j_self · P_self) , (6)

where N^j_t -temperature-dependence exponent defined above.

Temperature and pressure dependence of the line position

The air pressure leads to a shift of the line position. This shift is given by expression

WN^j(P) = WN^j + P^j_shift · P/P_ref , (7)

where WN^j is the wavenumber of the line j, P^j_shift is the pressure shift of the line j at P_ref .
The pressure shift should also include a temperature dependence, but that effect is not considered now.