Practical inclusion of CO 2 line mixing effects in a line-by-line atmospheric retrieval system

Abstract

A practical operational method is devised for computing air-broadened CO 2 line-coupling effects for least-squares estimation of the atmospheric state from IR spectra. Prior to operational data processing, a set of coefficients is derived that fully captures the line coupling effects within the impact approximation and a relaxation model. These coefficients are tabulated at reference temperature/pressure pairs, where they are computed from line pair relaxation rates, estimated using an exponential power energy-gap (PEG) law, the HITRAN values of line widths, and a parity-biased sum rule. The operational line-by-line retrieval software interpolates these tables to each atmospheric layer, and computes frequency-dependent absorption for the cluster of lines using the complex Voigt function. The time for computing the effects of coupling clusters of lines is thereby comparable to standard line-by-line processing on a per-line basis; no significant compute-time penalty is incurred, despite the fact that lines in clusters are fully coupled. The temperature and pressure dependence of the line coupling effects is shown to be acceptably accurate for several CO 2 Q-branches observed under conditions typical at the earth's surface and above, and is more rigorous and accurate than the first-order-in-pressure perturbation methods that have been reported elsewhere. Fully consistent partials of observed fluxes with respect to atmospheric parameters are computed and used successfully for least-square atmospheric retrievals.