Albedos for a cloud bar array over a reflecting surface

Abstract

The purpose of this study is to develop a model for the albedo of a cloud bar array over a reflecting surface. The model is based on the discrete-ordinates method for evaluation of radiant exchange between surfaces separated by a radiatively transparent medium. The model assumes that the clouds are opaque and accounts for the cloud geometry, the separation between the clouds, the height of the clouds above the ground, and the ground reflectance. The cloud bar array is irradiated by direct and diffuse components of solar energy. Cloud albedos are greater than the ground reflectance for ground surfaces with low reflectances and are less than the ground reflectance for highly reflecting ground surfaces but may be greater than the albedo for a plane layer cloud. In view of these findings, care must be exercised to account properly for the effects of cloud geometry and ground reflectance when cloud albedos are determined. One of the difficultiesinvolved with radiative transfer analysis between surfaces separated by a radiatively nonparticipating medium is the evaluation of geometric factors, commonly referred to as view factors. For a nonreflecting ground, evaluation of the view factors is manageable. However, for a reflecting ground, evaluation of view factors between an area on the ground and an area on the side of a cloud becomes tedious because the ground may see many sides in the cloud bar array and partial obstruction due to blockages occurs. In an attempt to circumvent the problems of finding view factors for complex geometries, Stlnchez and Smith [1992] developed a radiant exchange model using the discrete-ordinates method (DOM). The model was shown to produce accurate heat fluxes for geometries involving shadowing and obstruction. For application to the cloud bar array, the model must be extended to account for a collimated radiant energy source. Ol LIIIb lb LU albedo for a cloud bar a•ay over a reflecting surface. The model uses the discrete-ordinates method to determine radiant exchange between surfaces. Emphasis is placed on examining the effect of the cloud bar geomet• and ground reflectance on the cloud alb•o. The cloud bar system, governing radiative transfer equations, and the numerical solution of these equations using the DOM •e presented in the next two sections. To veri• the accuracy of the model based on the DOM, a second model based on the radiosity/i•adiation method (RIM) is also developed. Results for the cloud albedo as a function of the cloud geometric parameters, ground reflectance, and direction of incident sol• energy are then examined. Conclusions follow the results section.