Parameterization of Reflectivity for Broken Cloud Fields

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Abstract
To parameterize the reflected fluxes from broken cloud fields, Monte Carlo calculations are performed for several cumulus cloud fields. The results with the effects of cloud-cloud interaction and enhanced illuminated area are analyzed. A general relationship between the reflectivity of an isolated cloud and that of finite cloud fields is developed using the above two effects. From this relationship, the effective cloud fraction is parameterized. The result shows that the effective cloud fraction is a nonlinear function of the square of that value and the enhanced illuminated area. This parameterization is examined for cuboidal cylindrical, capped cylindrical and hemispherical cloud geometries arranged in regular, random and checkerboard patterns. The results show that the parameterization gives reflected fluxes that are considerably more accurate than these obtained with the plane-parallel approximation.

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