Generalized Radiative Transfer Theory for Scattering by Particles in an Absorbing Gas: Addressing Both Spatial and Spectral Integration in Multi-angle Remote Sensing of Optically Thin Aerosol Layers

We demonstrate the computational advantage gained by introducing non8 exponential transmission laws into radiative transfer theory for two specific sit9 uations. One is the problem of spatial integration over a large domain where 10 the scattering particles cluster randomly in a medium uniformly filled with an 11 absorbing gas, and only a probabilistic description of the variability is available. 12 The increasingly important application here is passive atmospheric profiling using 13 oxygen absorption in the visible/near-IR spectrum. The other scenario is spec14 tral integration over a region where the absorption cross-section of a spatially 15 uniform gas varies rapidly and widely and, moreover, there are scattering parti16 cles embedded in the gas that are distributed uniformly, or not. This comes up 17 in many applications, O2 A-band profiling being just one instance. We bring a 18 common framework to solve these problems both efficiently and accurately that 19 is grounded in the recently developed theory of Generalized Radiative Transfer 20 (GRT). In GRT, the classic exponential law of transmission is replaced by one with 21 a slower power-law decay that accounts for the unresolved spectral or spatial vari22 ability. Analytical results are derived in the single-scattering limit that applies to 23 optically thin aerosol layers. In spectral integration, a modest gain in accuracy is 24 obtained. As for spatial integration of near-monochromatic radiance, we find that, 25 although both continuum and in-band radiances are affected by moderate levels of 26 sub-pixel variability, only extreme variability will affect in-band/continuum ratios.