Over the past decade or so, the utility of multiple scattering Green functions has been demonstrated in a number of applications in cloud remote sensing. In view of (i) the large optical thicknesses observed for several important types of cloud, and (ii) the predominance of scattering over absorption by cloud droplets throughout most of the solar spectrum, the diffusion or "P1" limit of radiative transfer theory proves to be a productive framework for computing Green functions, as needed, in space and/or time. This is largely because the diffusion approximation leads to analytical expressions in Fourier-Laplace variables that return space-time radiation characteristics in the form of moments or of probability distributions (i.e., normalized Green functions). These characteristics are in turn shown to be quite accurate in comparison with Monte Carlo solutions of the full 3D radiative transfer equation. Moreover, physical insights into non-trivial multiple scattering processes are gained because diffusion has an analog in particle random walk theory that predicts qualitatively correct behavior of remote sensing observables as cloud parameters are varied.
In this review, we cover many aspects of the diffusion-theoretical approach to the calculation of radiation transport Green functions for internal as well as boundary sources, and for in situ detectors as well as remote cloud observations. Homogeneous, stratified and moderately variable stratiform cloud models are examined. Solar as well as pulsed laser sources are considered and closed-form expressions for responses in reflection as well as transmission are computed and validated. Last but not least, we discuss applications to current and futuristic cloud remote sensing technologies from ground-level, airborne and space-based platforms. Both active (lidar) and passive (especially, oxygen A-band spectroscopic) modalities are described. As it turns out, they share a surprising amount of common theoretical background that is best described in terms of multiple scattering Green functions.