從氣候模式之應用而言，二向法格式不僅普遍運用於短波輻射的計算，近來也逐漸在長波幅射的計算上被採用。然而，傳統二向法對長波輻射的計算卻有精確性不足的問題，Fu et al.依據Toon et al.之源函數技巧建構有二向法經濟性但能達到四向法精確性的二向/四向法格式，改進了這方面的問題。本研究的目的乃希望利用二向法為基礎系統性地建立一個解決部份雲量下輻射計算的方法。處理部份雲量的作法乃是沿續Geleyn and Hollingsworth 提出的概念，過去 Geleyn and Hollingsworth處理部份雲量的作法只建構在傳統二向法的應用範圍，在此我們進一步推導將其應用於具有源函數技巧內涵的二向法中，使二向/四向法格式能成功地結合此部份雲量條件下的計算架構。這使得無論短波或長波輻射模式，都可以使用二向運算結構與一致的雲疊合條件，以兼具效率且精確的方式處理部份雲量的計算問題。從氣候模式的應用而言，本研究所建立的方法是相當適用的。

　　　　　For the purpose of the application to climate models, the two-stream approximation has been not only widely used for the calculation of solar radiation, but also gradually employed for the calculation of infrared radiation. The traditional two-stream approximation, however, has the discrepancy of the accuracy in infrared radiation. Following the source function technique proposed by Toon el al., Fu et al. improve the accuracy problem in infrared radiative calculations by developing a two and four-stream approximation, which incorporates the speed of the two-stream scheme and the accuracy of the four-stream scheme. This study intends to provide a systematic development of a general solution for radiative calculations in partly cloudy conditions based on the two-stream approximation. The treatment of the cloud overlap follows the concept proposed by Geleyn and Hollingsworth, which was applied only to the traditional two-stream approximation before. In this study, we derive a solution to introduce the source function technique into the treatment of the cloud overlap. Consequently, the two and four-stream approximation can be readily used for cases of partly cloudy atmospheres to retain better accuracy. The methodology presented here should be suitable for the calculation of flux and heating rate in GCMs due to the fact that it possesses the features of accuracy and computational economy and accounts for cloud overlap of partly cloudy conditions in a consistent manner covering the whole spectrum calculation.