Treatment of overlapping gaseous absorption with the correlated-k method in hot Jupiter and brown dwarf atmosphere models

The correlated-k method is frequently used to speed up radiation calculations in both one-dimensional and three-dimensional atmosphere models. An inherent difficulty with this method is how to treat overlapping absorption, I.e. absorption by more than one gas in a given spectral region. We have evaluated the applicability of three different methods in hot Jupiter and brown dwarf atmosphere models, all of which have been previously applied within models in the literature: (I) random overlap, both with and without resorting and rebinning, (II) equivalent extinction and (III) pre-mixing of opacities, where (I) and (II) combine k-coefficients for different gases to obtain k-coefficients for a mixture of gases, while (III) calculates k-coefficients for a given mixture from the corresponding mixed line-by-line opacities. We find that the random overlap method is the most accurate and flexible of these treatments, and is fast enough to be used in one-dimensional models with resorting and rebinning. In three-dimensional models such as global circulation models (GCMs) it is too slow, however, and equivalent extinction can provide a speed-up of at least a factor of three with only a minor loss of accuracy while at the same time retaining the flexibility gained by combining k-coefficients computed for each gas individually. Pre-mixed opacities are significantly less flexible, and we also find that particular care must be taken when using this method in order to to adequately resolve steep variations in composition at important chemical equilibrium boundaries. We use the random overlap method with resorting and rebinning in our one-dimensional atmosphere model and equivalent extinction in our GCM, which allows us to e.g. consistently treat the feedback of non-equilibrium chemistry on the total opacity and therefore the calculated P-T profiles in our models.