Accurate computations of the radiance in the gaseous absorption bands typically require fine wavelength steps.
In this paper, we present a fast technique that allows us to compute a spectrum of the radiation reflected by the terrestrial atmosphere.
The technique is based on the $k$-correlation distribution model (where $k$ stands for the absorption coefficient). While the classical $k$-distribution model takes into account only the dependency of the radiance on $k$, the presented model takes as a predictor the direct transmittance and the scattering coefficient.
At selected spectral points, the full radiative transfer simulations are performed and the mathematical relation between a predictor and the radiance is established. Then, the radiance is restored on a fine wavelength grid. This approach can be used to enhance the accuracy of the convolved spectrum computations based on precomputed monochromatic lookup tables.
The numerical analysis shows that the method can be applied to cases with aerosol optical thickness not larger than 2.