Linearization of a longwave radiation scheme for intermediate tropical atmospheric models

A Green's function method is presented for linearizing longwave radiation schemes commonly used in general circulation models in order to produce simpler schemes suitable for use in intermediate complexity atmospheric models. Nonlocal dependence of radiative fluxes on vertical distributions of temperature, moisture, cloud fraction, and cloud top are retained, consistent with the nonlinear scheme. Treatment of several cloud cover types is used in linearizing cloud fraction. A weakly nonlinear scheme is also presented. The method is most useful if linearization about a single tropical reference profile has a sufficient range of validity. Tests are carried out using European Centre for Medium-Range Weather Forecosts (ECMWF) analysis fields, International Satellite Cloud Climatology Project (ISCCP), Comprehensive Ocean-Atmosphere Data Set (GOADS) and outgoing longwave radiation (OLR) data, and the Harshvardhan scheme as the nonlinear scheme. The linear scheme is found to reproduce the nonlinear results with surprising accuracy in simulation of longwave radiative fluxes associated with interannual variability, seasonal variations, and even tropical climatology as a departure from its spatial average. The spatial patterns and relative magnitudes associated with various contributions are discussed to help inform and provide a target for intermediate model simulations.