Radiative transport theory, at least in its present form, began early this century. Since then the field has been greatly advanced, with many excellent treatises on the subject now available including works by Chandrasekhar (1960), Mihalas (1978) and van de Hulst (1981). Over the years it has been applied to many types of problems in engineering and the physical sciences including solar atmospheres, terrestrial atmospheres, underwater radiation fields, reflective properties of many types of surfaces, biophysical studies such as scattering and reflection by blood cells and tissue, and in the study of high-temperature machinery (Flatau and Stephens, 1988) to name a few. Examples of other applications can be found in the Journal of Quantitative Spectroscopy and Radiative Transfer, 36(1), 1986.
The transfer of solar radiation in terrestrial atmospheres is governed by a single equation: the radiative transfer equation. Its solution results in a description of the radiation field at each point in the atmosphere. Much of the progress over recent years deals with how this equation can be solved in an efficient and accurate manner. As a result many different solution techniques exist, each with its own advantages and disadvantages. Among the more common are the doubling and adding method (e.g.: Plass et al., 1973), the discrete ordinates method (e.g.: Stamnes and Conklin, 1984), spherical harmonic method (e.g.: Karp et al., 1980), Monte-Carlo solutions (e.g.: Collins et al., 1972), invariant imbedding (e.g.: Bellman et al., 1963), the method of X and Y functions (e.g.: Chandrasekhar, 1960), and finally the successive orders of scattering method (e.g.: Irvine, 1975). It is the last method that will be used in this study.
This chapter first presents the underlying physics describing how solar radiation interacts with atmospheric matter. Following this is a detailed outline to the solution of the radiative transfer equation and the assumptions made in arriving at it.