Atmosphere Consisting of Layers with Large Optical Thickness

The equations derived in Chap. 6 are valid for layers of arbitrary optical thickness. However, when τ _j (j = 1,2,…,n) increases (especially if it occurs simultaneously in all layers), it becomes more difficult to solve these equations. In order to describe the internal radiation field in detail, one needs to take an enormous number of equations and, consequently, to store a lot of information on computer. Therefore, it is important that one can derive simple asymptotic formulas for the quantities that describe the radiation field in an atmosphere consisting of layers with large optical thickness τ _j ≫ 1). Accuracy of these formulas grows with increasing τ _j . It turns out to be possible to express analytically these quantities in terms of functions describing the radiation field in the corresponding semi-infinite layers and intensities at interlayer boundaries. The present chapter deals with such asymptotic formulas.