Approximation to the Lorentzian coefficient for efficient calculation of transmittance profiles

A major problem in the calculation of line-by-line profiles of atmospheric transmittance lies in the excessive computational times associated with the evaluation of the Lorentzian coefficient for every gas, wavenumber, line, temperature, and pressure along the path. An approach to the solution of this problem is presented, whereby use is made of an approximating function that allows for the quantities involving temperature and pressure to be factored out of the wavenumber-dependent terms. Although the approximating function is restricted to wavenumbers farther than about a line halfwidth at STP from the line center, a numerical procedure is presented for dealing with the remaining few cases. This approach results in a significant reduction in the number of arithmetic operations from the use of the exact coefficient and generally yields a transmittance with a numerical accuracy of four significant figures or better. An application is made to five Nimbus 6 center-filter frequencies in the 4.3-mum CO(2) band for H(2)O, CO(2), N(2)O, and CO in a 33-level atmosphere with average computational times reduced by a factor of over 9.