An optimal approach to overlapping bands with correlated k distribution method and its application to radiative calculations

[1] It is found that the possibly achieved higher accuracy cannot be obtained for all overlapping bands if only one scheme is used to treat them in atmospheric absorption calculations. The commonly used multiplication transmittance scheme is not acceptable when correlation existing in the practical absorption spectra becomes strong. Therefore an optimized scheme to obtain k distribution parameters for overlapping bands is developed in this paper based on the completely uncorrelated, perfectly correlated, and partly correlated schemes. Two partial correlation formulae are given in the paper. Calculations of radiative flux and atmospheric heating (or cooling) rate are validated in detail using a line-by-line model described in the paper for six model atmospheres. The optimized scheme developed here has an accuracy in longwave clear skies of 0.07 K d−1 in the entire troposphere and 0.35 K d−1 above the tropopause; the accuracy of upward, downward, and net fluxes is 0.76 W m−2 at all altitudes. In shortwave region, the absolute errors of the heating rate are less than 0.05 K d−1 in the troposphere and less than 0.25 K d−1 above the tropopause; net flux errors are less than 0.9 W m−2 at all altitudes. For an ensemble of 42 diverse atmospheres, the new scheme guarantees an average maximum error of longwave heating rate of 0.068 K d−1 in troposphere, 0.22 K d−1 above tropopause, and an accuracy of 1.1 W m−2 of radiative net flux for all the levels. For a case of doubled CO2 concentration, radiative forcing calculations have an accuracy of 0.04 W m−2.