Simple Radiative Transfer Methods for Calculating Domain-Averaged Solar Fluxes in Inhomogeneous Clouds

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Abstract
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 study addresses some issues pertaining to the use of cloud fraction by performing radiative transfer in inhomogeneous two-dimensional media. Two approximation techniques are developed to solve the equation of transfer for the spatial averages of diffuse flux. The first is based on a first-order closure technique that leads to a one-dimensional equation of transfer with a modified source term. The computational speed of this technique is equivalent to the plane-parallel method. The second method of approximation performs a full two-dimensional computation of the direct solar beam that is used as the pseudo-source in an independent pixel diffuse radiative transfer calculation. Both methods require a knowledge of the spatial distribution of the direct solar transmission, rather than cloud fraction, for their specification. Tests are performed comparing the accuracy of these two new methods, as well as the plane-parallel and independent pixel methods, with the complete solution using the spherical harmonic spatial grid method. The media have horizontal variations in extinction that are sinusoidal but truncated according to the cloud fraction. The 2D direct-beam independent pixel method is generally the most accurate approximation, especially for forward-scattering phase functions. The source closure method is substantially more accurate than the independent pixel or cloud-fraction weighted plane-parallel methods.

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