RADIATIVE-TRANSFER IN STOCHASTIC MEDIA

We review some basic concepts arising in the study of radiative transf er in a stochastic atmosphere and consider their application to realis tic atmospheric models. In particular, we examine the theory of Lindse y and Jefferies which deals with multicomponent atmospheres whose stoc hastic nature is entailed in the morphology of a network of boundaries separating different atmospheric components. This theory is based on the Markov assumption, that the probability, per unit path length alon g a ray, for transition into another component is independent of the d istance already traveled in the current component. We examine the appl icability of the theory to models that are non-Markovian, paying parti cular attention to the assignment of transition rates of such atmosphe res. We consider in detail transition probabilities for spherical, tub ular, conical, and other fluted structures, and show how the effects o f overlap are to be incorporated for the case of a two-component atmos phere. Comparisons of results obtained from the theory of Lindsey and Jefferies with those found from Monte Carlo calculations, for models b ased on identical structures randomly embedded into an ambient medium, show that the Markov assumption promises to be a good approximation f or the determination of the statistics of radiative transfer in a wide variety of stochastic atmospheres, even when they are markedly non-Ma rkovian.