Historically (before c.1995), three-dimensional atmospheric radiative transfer studies consisted generically in numerical model development, validation on a few test cases, and some important discussion of the relevance of the effort to programmatic activity (usually either as GCM radiation parameterization or remote sensing operations). With the availability of cheaper/faster/better computer hardware, we have entered a phase of extensive numerical experimentation in 3D radiative transfer where robust Monte Carlo methods compete with flexible pre-validated code such as Evans’ spherical-harmonic/discrete-ordinate method (SHDOM). A problem area is defined, numbers are crunched, plausible explanations of the findings are articulated. The procedure is essentially empirical. The Independent Pixel(Column) Approximation and its numerous deteministic and probabilistic variations have become the first line-of-attack in the applications because computer time/resources are still a concern and detailed information on 3D cloud structure may not be available anyway. In short, 3D radiative transfer has its tools and its goals; it is at cruising altitude.

What 3D radiative transfer seems to be currently lacking is a clear conceptual framework. It is not unusual now to see practitioners use 3D concepts without stating it. For instance, when radiances or fluxes are used to determine cloud properties in a plane-parallel model that “fit the data,” these properties are the “effective” properties that account for the internal variability. This is not proof that 3D effects are negligible until independent estimates are provided for the inherent cloud properties and it is shown that they predict the same internal/boundary radiation field as observed, preferably across wavelengths.

Geophysical fluid dynamics developed the opposite way. Powerful concepts such as circulation, convection, turbulence, waves, instabilities, fronts, blocking, and so on, were defined even before the advent of computers and are still useful. Non-dimensional numbers can be estimated and used to predict what type of flow will occur. Radiative transferists are also dealing with flow, indeed that a rather strange fluid: a photon gas interacting with a complex optical medium. I will revisit our existing non-dimensional numbers (based on optical properties means) and propose a few more (based on their gradients). The classic example is optical depth and its utility as a demarcation between regimes dominated by photon streaming versus photon diffusion. As further illustration, I will use these numbers to predict

* when IP(C)A effects are maximal,

* when strong deviations from the IP(C)A --photon “channeling”-- can be expected,

* when photon diffusion goes from standard to anomalous.

The last item is in fact a statement about the fundamental transport kernel (when can it be assumed exponential, as in plane-parallel theory? and when is it effectively power-law?). In the two last entries, spatial correlations in the cloud- and extinction-fields are critically important. In all three diagnostics, the nonlinear (multiplicative) nature of matter-radiation interaction plays a key role.