We are motivated here by the important problem of partitioning the absorption of solar radiation inside the atmosphere-surface system over vast (>100 km) domains, a basic step towards climate forecasting, in the presence of clouds. It is shown under very general conditions that the effective transport kernel is never exponential and always decays more slowly. However, for this strong statement about effective medium theory to have a significant impact, we need to be in a situation where the unresolved (and assumed
random) variability has spatial correlations that range at least to the actual mean-free-path which, incidentally, is always larger than predicted by the mean density and cross-section.
The cloudy atmosphere ranges from totally- to semi-opaque, so deviations from exponential decay in the transport kernel will
matter. The observed variability in a wide variety of cloud
scenarios leads to power-law kernels, hence to a "Levy-flight" or "anomalous diffusion" model for the multiple scattering. It will be shown that recent advances in differential absorption spectroscopy in oxygen lines agree with specific predictions of this unconventional model for bulk photon transport through the atmosphere. It is not clear that the anomalous diffusion model can be applied to the estimation of detailed layer-by-layer solar energy deposition. However, it can certainly help in conveying statistical meaning to the new observational diagnostics of absorption in the complex atmospheric medium, namely, photon pathlengths from oxygen line spectroscopy.
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