Harnessing machine learning for accurate treatment of overlapping opacity species in GCMs

To understand high precision observations of exoplanets and brown dwarfs, we
need detailed and complex general circulation models (GCMs) that incorporate
hydrodynamics, chemistry, and radiation. In this study, we specifically examine
the coupling between chemistry and radiation in GCMs and compare different
methods for mixing opacities of different chemical species in the correlated-k
assumption, when equilibrium chemistry cannot be assumed. We propose a fast
machine learning method based on DeepSets (DS), which effectively combines
individual correlated-k opacities (k-tables). We evaluate the DS method
alongside other published methods like adaptive equivalent extinction (AEE) and
random overlap with rebinning and resorting (RORR). We integrate these mixing
methods into our GCM (expeRT/MITgcm) and assess their accuracy and performance
for the example of the hot Jupiter HD~209458 b. Our findings indicate that the
DS method is both accurate and efficient for GCM usage, whereas RORR is too
slow. Additionally, we observe that the accuracy of AEE depends on its specific
implementation and may introduce numerical issues in achieving radiative
transfer solution convergence. We then apply the DS mixing method in a
simplified chemical disequilibrium situation, where we model the rainout of TiO
and VO, and confirm that the rainout of TiO and VO would hinder the formation
of a stratosphere. To further expedite the development of consistent
disequilibrium chemistry calculations in GCMs, we provide documentation and
code for coupling the DS mixing method with correlated-k radiative transfer
solvers. The DS method has been extensively tested to be accurate enough for
GCMs, however, other methods might be needed for accelerating atmospheric
retrievals.