Principles of the Twilight Theory

Abstract

Sunlight is both attenuated and scattered as it makes its way through the earth’s atmosphere. In the final analysis, it is the relation between these two acts that governs the whole complex of optical phenomena observed whenever the sky is bright, including the twilight period. We could, in principle, derive the full sweep of twilight phenomena just by solving the equation of radiative transfer, Eq. (II.2, 40), under the appropriate boundary conditions. But a general method of solution has yet to be developed for three-dimensional problems of the type applicable to twilight conditions. Even then we could only work out the behavior of the twilight sky if we knew the optical structure of the atmosphere in advance. But it is precisely the converse problem which is of greatest interest: to derive the structure of the atmosphere from the behavior of the twilight sky. Indeed a prime aim of twilight theory, in its present state at any rate, is to discover the basic laws of the phenomenon, and to distinguish the most important factors governing its progress. Clearly we can succeed only by adopting a simplified model for the phenomenon, later refining it by correcting for various side effects. It is not enough for our model to be a good representation of reality in a general way. Our analysis must in addition remain within the scope of the equation of transfer, and eventually lead to its solution. We have already pointed out that one way to proceed is by following the successive fortunes of each light beam through all the vicissitudes it encounters as it travels through the atmosphere.