Not yet reviewed by Pith; the record is open.

The calculation of internal atmospheric (longwave) fluxes is a key component of any model of exoplanet atmospheres that requires radiative-transfer (RT) calculations. For atmospheres containing a strong scattering component such as cloud particles, most 1D multiple-scattering RT methods typically involve numerically expensive matrix inversions. This computational bottleneck is exacerbated when multitudes of RT calculations are required, such as in general circulation models (GCMs) and retrieval methods. In an effort to increase the speed of RT calculations without sacrificing too much accuracy, we investigate the applicability of approximate longwave scattering methods developed for the Earth science community to hot Jupiter atmospheres. We test the absorption approximation (AA) and variational iteration method (VIM) applied to typical cloudy hot Jupiter scenarios, using 64 stream DISORT calculations as reference solutions. We find the four-stream VIM variant is a highly promising method to explore using for hot Jupiter GCM and retrieval modelling, showing excellent speed characteristics, with typical errors $\sim$1\% for outgoing fluxes and within $\sim$50\%, but with larger errors in the deep cloud layer test case, for vertical heating rates. Other methods explored in this study were found to typically produce similar error characteristics in vertical heating rates.