Modeling of gas absorption cross sections by use of principal-component-analysis model parameters

Monitoring the amount of gaseous species in the atmosphere and exhaust gases by remote infrared spectroscopic methods calls for the use of a compilation of spectral data, which can be used to match spectra measured in a practical application. Model spectra are based on time-consuming line-by-line calculations of absorption cross sections in databases by use of temperature as input combined with path length and partial and total pressure. It is demonstrated that principal component analysis (PCA) can be used to compress the spectrum of absorption cross sections, which depend strongly on temperature, into a reduced representation of score values and loading vectors. The temperature range from 300 to 1000 K is studied. This range is divided into two subranges (300-650 K and 650-1000K), and separate PCA models are constructed for each. The relationship between the scores and the temperature values is highly nonlinear. It is shown, however, that because the score-temperature relationships are smooth and continuous, they can be modeled by polynomials of varying degrees. The accuracy of the data compression method is validated with line-by-line-calculated absorption data of carbon monoxide and water vapor. Relative deviations between the absorption cross sections reconstructed from the PCA model parameters and the line-by-line-calculated values are found to be smaller than 0.15% for cross sections exceeding 1.27 x 10(-21) cm(-1) atm(-1) (CO) and 0.20% for cross sections exceeding 4.03 x 10(-21) cm(-1) atm(-1) (H2O). The computing time is reduced by a factor of 10(4).