On the approximate model of scattering radiance for cloudless sky

Effect factors on sky radiance were analyzed based on the transfer theory of light in the random medium. In fact, these factors mainly include: 1) absorbed and scattered extinction of solar radiance by atmosphere; 2) single scattering process of solar radiance by atmosphere along viewing direction; 3) multiple scattering process of solar radiance by atmosphere along viewing direction; 4) thermal radiation of atmosphere. The latter three ones among these factors increase sky radiance. After this analysis, derivative process of the Radiative Transfer Equation was studied thoroughly from the law of conservation of energy and the transmission of solar radiance in the earth-atmosphere system, and some methods of dealing with the multiple scattering are analyzed and used in calculating sky radiation. Finally, an approximate model was developed for sky radiance of sunshiny and cloudless sky to make full use of the RTE, an analytical express of sky radiance is gave out for single scattering and quasi-multiple scattering effects. Sky spectral radiance was calculated for some representative case of clear sky, and results have been compared with those of MODTRAN. The results show that the present model is efficient under the sunny and cloudless condition.