  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 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.
