The k distribution method is applied to band overlap and pressure as well as temperature dependence of absorption coefficients. The overlap of spectral absorption coefficients of H2O, CO2, O3, N2O, and CH4 is considered by a multivariate frequency distribution of absorption coefficients for a given pressure and temperature. In a first approach the vertical inhomogeneity is taken into account by the separation into the absorption coefficient at a reference state, the temperature dependence of the line strengths, and the dependence of the line profiles on pressure and temperature. If at distinct spectral positions absorption coefficients are changing from line wing absorption in the lower atmosphere to line centerlike absorption in the stratosphere, this is considered by a rough approximation. The known far wing scaling approximation is included, modified as special case. Comparison of infrared radiation flux densities in a standard atmosphere from this k distribution method with those from a line-by-line model leads to a difference about -1.8 W/m2 for the upward radiation flux density at the top of the atmosphere and -0.25 W/m2 for the downward directed at the surface. Cooling rate differences remain smaller than \0.1\ K/d for the entire troposphere, but reach an intolerable 5 K/d at 50-km height. In a second approach an extended version of the k distribution model is obtained by separating the spectral absorption coefficients into central and wing contributions. A multivariate frequency distribution which considers both strongly increases accuracy to less than 0.2% relative error for flux densities at all heights. And for cooling rates, a relative error of at most +/-15% is found in the upper stratosphere.
