Radiative transfer in the [formula omitted] A-band - a fast and accurate forward model based on the [formula omitted]-distribution approach

Abstract

An efficient method based on accurate transmissivity calculations to account for gaseous absorption in Monte Carlo / quasi-Monte Carlo radiative transfer codes is presented. The modeling approach is based on an improved non-uniform transmission formulation, called the ℓ-distribution method. The technique is founded on two components: 1/ an original uniform method to tabulate band averaged transmissivities of gaseous paths and 2/ its extension to non-uniform paths, based on the Godson-Weinreb-Neuendorffer’s (GWN) approximation that consists of the definition of effective scaling factors to relate gaseous spectra in distinct states. As the GWN method is known to provide results dependent on the ordering of the gas layers, two path reordering strategies are introduced and compared. One of them is founded on results from statistical theory and requires the introduction of a new coefficient (Kendall’s Ke). This coefficient together with its role on the path reordering strategy is introduced, detailed and analyzed. The two schemes are then assessed against Line-By-Line calculations in line-of-sight geometries. Two configurations representative of radiative transfer in the O2 A-band for scattering atmospheres are then studied: the first one only considers molecular (Rayleigh) scattering and the second one involves various cloud configurations (single or bi-layer clouds located at various altitudes). For these calculations, the ℓ-distribution methods based on the two path reordering schemes were implemented in the 3D Monte Carlo code 3DMCPOL. Results of the ℓ-distribution method are compared with solutions provided by the Correlated k-distribution method and assessed against Line-By-Line calculations. The ℓ-distribution approach combined with the Kendall’s reordering strategy is shown to provide results more accurate than k-distributions at smaller calculation costs. The ℓ-distribution method is shown to be a relevant candidate for radiative transfer in the atmosphere, both for remote sensing applications but also for weather forecasting or radiative budget studies, with or without scattering phenomena.