Adaptation of a matrix parameterization of the middle atmospheric radiative cooling for an arbitrary vertical coordinate grid

Matrices corresponding to a revised vertical grid are shown to be derived from the original grid by integrating the radiative cooling rate over model layers. The method is applied to temperature profiles that represent average or extreme atmospheric conditions and a range of vertical resolutions. The example makes use of the 15-micron CO2 band parameterization proposed by Akmaev and Shved (1982) for the LTE region of the middle atmosphere. Cooling rate errors provided by the present method are not more than 0.11 K/day for a vertical grid spacing of less than 5 km. The matrix transformation method is shown to be valuable for adapting effective matrix parameterizations of middle atmosphere cooling to atmospheric models with arbitrary vertical resolutions.