Cloudy sky zenith radiance time-series covering spatial scales a few meters up to 200--400 km measured by a ground-based photometer at 753 nm are investigated with 2nd-order structure functions, and compared to broad-band short-wave column transmittance. A previously reported scale break occurs at scales on the order of the vertical cloud extension due to radiative smoothing (i.e., lateral photon transport by diffusion in optically thick clouds). We use simulated radiance and flux fields for 3D clouds to explain why optical depths can be extracted with reasonable accuracy from surface fluxes by using 1D radiative transfer theory at large-enough scales. We also show clear evidence of a transition from nonstationary to stationary behavior, i.e., a scale break, occurring at spatial scales of a few tens of kilometers. We argue that this qualitative change in the correlations of remotely observed radiation fields is likely to carry over to the most highly variable inherent cloud property, namely optical depth.