It is convenient to divide the effect of horizontal cloud variability on solar radiative fluxes into two parts. The first is due to optical depth variability and may be computed with the independent pixel approximation (IPA). The second part is due to horizontal photon transport and must be computed using a three-dimensional radiative transfer model. Many studies of Monte Carlo radiative transfer calculations in finite clouds have shown that this horizontal transport or "three-dimensional radiative" effect depends strongly on the cloud aspect ratio, cloud fraction, and solar zenith angle. However, the key parameters governing the 3D radiative effect in realistic fair weather cumulus cloud fields are still unknown. In this work we attempt to determine the characteristics of boundary layer cumulus cloud fields that are needed for correct simulation of the 3D radiative effect, focussing on the relationship between cloud thickness and optical depth.

The approach taken here is to compute the domain average solar flux in cloud fields derived from numerous large eddy simulation (LES) cumulus fields. Liquid water content fields for boundary layer cumulus clouds forced by surface fluxes are produced by an LES model with a 6.7x6.7 km^2 domain (100x100 point grid). The 3D radiative effect is computed with a broadband Monte Carlo model as the difference between 3D and IPA calculations of domain averaged reflected or absorbed solar flux. The 3D radiative effect of the original LES fields is compared with that of a series of approximate fields derived deterministically and stochastically from the LES cloud fields. Deterministic approximate fields are 1) the original optical depth and cloud top height for each column, but with a flat cloud base and adiabatic LWC, 2) the original optical depth in each column, but with cloud thickness from a power law function of optical depth, and 3) the original optical depths with a fixed mean cloud thickness. Stochastic approximate fields are generated with an 8 parameter Fourier power law filtering stochastic cloud model that outputs optical depth and cloud thickness fields. The stochastic optical depth and thickness field parameters are tuned to match the cloud fraction, mean, variance, and power spectral slope of the original fields. The correlation between the optical depth and cloud thickness fields can be varied from 0% through the correct value to 100%. We will determine how well the simple stochastic model represents the 3D radiative effect of the original cumulus fields.