The Effects of Line-Wing Cutoff in LBL Integration on Radiation Calculations

There are three basic methods in radiative transfer calculations, i.e., line-by-line (LBL) integration, correlated k-distribution method, and band model. The LBL integration is the most accurate of all, in which, there are two quadrature algorithms named in this paper as integration by lines and by sampling "points when calculating atmospheric transmittance in the considered wavenumber region. Because the LBL integration is the most expensive of all, it is necessary and important to save calculation time but increase calculation speed when it is put into use in the daily operation in atmospheric remote sensing and atmospheric sounding. A simplified LBL method is given in this paper on the basis of integration by lines, which increases computational speed greatly with keeping the same accuracy. Then, we discuss the effects of different cutoff schemes on atmospheric absorption coefficient, transmittance, and cooling rate under both of accurate and simplified LBL methods in detail. There are four cutoff schemes described in this paper, i.e., CUTOFFs 1, 2, 3, and 4. It is shown by this numerical study that the way to cut off spectral line-wing has a great effect on the accuracy and speed of radiative calculations. The relative errors of the calculated absorption coefficients for CUTOFF 2 are the largest under different pressures, while for CUTOFF 1, they are less than 2% at most of sampling points and for CUTOFFs 3 or 4, they are ahnost less than 5% in the calculated spectral region, however, the calculation time is reduced greatly. We find in this study that the transmittance in the lower atmosphere is not sensitive to different LBL methods and different cutoff schemes. Whereas for the higher atmosphere, the differences of transmittance results between CUTOFF 2 and each of other three cutoff schemes are the biggest of all no matter for the accurate LBL or for the simplified LBL integrations. By comparison, the best and optimized cutoff scheme is given in this paper finally.