On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres

Abstract The correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres is discussed in terms of the physical and mathematical conditions under which this method is valid. Two correlated conditions are necessary and sufficient for the exact transformation of the wavenumber integration to an integration over the cumulative probability (g), a monotonically increasing and smooth function in the absorption coefficient space. These conditions involve the use of a reference condition to define the absorption coefficient and an assumption concerning the ordering of the absorption coefficient. The correlated conditions are exact in the context of a single line, periodic lines, and the strong- and weak-line limits. In realistic atmospheres, these assumptions are best for adjacent levels but produce increasing blurring or deviations for distant levels. We investigate the blurring of the correlated assumptions on the computations of fluxes and heating rates based on “exact” line-by-line re...