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