Radiation modeling of $CO_2$ 4.3㎛ band is carried out for the temperature inversion in combustion gases. For this purpose, a prerequisite work is made to build an approximate $CO_2$ 4.3㎛ database by following the procedure of HITELOR(Scutaru et al., 1992) database. Hot bands of $CO_2$ are missing in HITRAN(Rothman et al., 1992), where the spectroscopic parameters of cold bands for eight most abundant $CO_2$ isotopes are complied. A new database includes molecular constants associated with excited vibrational levels, band centers and intensities of hot bands, and the absorption coefficient at $0.03 cm^{-1}$ resolution. This database is suitable for applications where temperatures up to 2500 K may exist. As the second work, two narrow band models are proposed to improve the accuracy of the rediative properites; one is CK-based WNB (WSGGM-based Narrow Band) with seven gray gases, the other is CKFG-based WNB with three fictitious gases for each of which three gray gases are taken. The spectral intensities at each narrow band are calculated for temperature profiles of parabolic and boundary layer types. Comparison with LBL calculation shows better agreement for the two WNB models than for the popular SNB model (Soufiani et al., 1997). Finally, temperature inversion techniques are scrutinized. The error analysis is performed in various measurement conditions varying the number and combination of sensing narrow bands, path lengths, and the shape, level and gradient of temperature. Temperature inversion is carried out by using LBL, SNB and CK-based WNB models. Here, measurement intensities are substituted by the LBL calculations at the given temperature profiles. It thus focuses only on the error of inversion caused by the approximate spectral modeling and the employed narrow bands. Results indicate that the errors of spectral intensities at some narrow bands amplify the error of the obtained temperature, and that CK-based WNB model gives more accurate result in the inversion than SNB model. Also, it is found that cold gas temperature beyond hot gas near the sensor, if any, has great error in the inversion, especially when the optical depth is large.
