Radiative transfer in the O2 A-band - a fast and accurate forward model based on the ℓ-distribution approach

•Application of the L-distribution method for radiative transfer in the O2 A-band is considered.•The L-distribution method is described and two path-reordering strategies, based on statistical concepts, are compared.•Applications representative of actual space sounding missions involving clouds are treated.•Results are assessed against reference Line-By-Line calculations.•The L-distribution method based on the so-called Kendall’s reordering strategy is shown to provide a higher accuracy than k-distributions at a smaller computational cost.