Colorado State University
Fort Collins, CO 80523
The use of cloud fraction as a means of incorporating horizontal cloud inhomogeneity in radiative transfer calculations is widespread in the atmospheric science community. This research attempts to bypass the use of cloud fraction in radiative transfer modeling for two- dimensional media. Gabriel describes two approximation techniques useful in calculating the domain averaged bulk radiative properties such as albedo, flux divergence and mean radiance that dispense with the need to use cloud fraction as a specifier of cloud inhomogeneity.
The first approximation method is based on a first order closure technique (C1) (see Figure 4.1) which is formulated by exploiting the translational invariance of the equation of transfer, thus leading to a one-dimensional equation of transfer with a modified source term. This approach allows computational speeds that exceed that of the independent pixel approximation (IPA) and also yields a large improvement in accuracy over the IPA as determined by numerical solutions of the two-dimensional equation of transfer. The method is accurate for clouds that do not exhibit a strong forward peak in the phase function. For clouds exhibiting a large asymmetry factor, the closure method provides usable accuracy for optical depths of order 10. In the linear regime, where optical depths are of order unity or less, the closure has been found to be accurate regardless of the asymmetry factor, because of the linearity of the radiative transfer.
The second method of approximation is similar to the IPA, in that it considers horizontal variations in the optical depth, but performs a full three- dimensional computation of the direct beam that is used as the pseudo-source in an independent pixel diffuse radiative transfer calculation. This method is generally more accurate than the closure method but cannot be used to give local net fluxes at cloud boundaries, because, for example, the computed albedos can exceed unity. The reason for this behavior is that energy can stream only up or down, not laterally. The results suggest that the variability of the medium can largely be accounted for through the pseudo-source term. This conclusion offers hope of parameterizing the equation of transfer in terms of the statistical properties of the medium.
