Application of Prony's Method to the Modeling of Spectral-Band Transmittance

Abstract

An application of the well-known Prony's method is made in the representation of the mean molecular transmittance over a spectral band in the infrared region, with a summation of exponential terms. The method was found to be reliable, direct, and accurate when it was used with computer-simulated transmittance spectra, for six temperature-retrieval channels of the Nimbus-5 spectrometer in the 15 µm CO₂ band. The results indicate that for typical atmospheric absorber concentrations, only two, five, and six terms are generally needed for modeling O₃, CO₂, and H₂O vapor with a transmittance accuracy of one in the fourth decimal place. This accuracy is compatible with the limitations imposed by uncertainties in the present knowledge of line parameters and is of the order obtained with polynomial-type band models having a much higher number of terms.