It is unlikely that all scales of geometric variability relevant to the radiative transfer will ever be resolved in atmospheric circulation models. Similarly, it is unlikely that observational data such as those collected from aircraft will ever sample all relevant scales. Although we are only now beginning to understand the nature of the effect of spatial variation of radiative transfer, we expect that radiative transfer, through multiple scattering, filters much of the finer scale structures. The basic questions are how much structure information is needed to represent the radiative transfer on some other gross scale, what is the relevant form of this structure information and how should this information ultimately be incorporated into radiative transfer? Determinisitic studies such as those discussed above all grope with these issues.
An approach that directly addresses these questions is to treat radiative transfer as a stochastic process in which only broad statistical properties (about clouds, say) are assumed to be known and then used to calculate the ensemble averaged radiative properties. This is a relatively new approach in radiative transfer and is beginning to find its application in topics of atmospheric radiation [ Stephens et al., 1991; Evans, 1993b; Malgavi et al., 1993; Peltoniemi, 1993; and Su and Pomeraning, 1994]. The attraction is that the method offers a foundation for the parameterization of the effects of structure on radiative processes in a way that is both consistent with available knowledge and able to be incorporated into schemes presently used in climate models [e.g. Gabriel and Evans, 1994]. Some of the techniques developed use arbitrary statistics whereas others depend on the form of statistic assumed. In all, these studies suffer from a lack of statistical knowledge about the cloud variability and a viable area of research is to develop this knowledge using data from available field programs and remote sensors alike.