Reflection and Transmission Functions for Finite Isotropically Scattering Atmospheres with Specular Reflectors.

Derivation of invariant imbedding equations for the diffusely reflected and transmitted radiation of an isotropically scattering and absorbing planetary atmosphere bounded below by a smooth, mirrorlike reflecting surface and illuminated by parallel rays of sunlight. First the integral equation for the source function is given and from it are derived the invariant imbedding equations. These are solved numerically by gaussian quadrature and the results are then used to produce the first known tables of the diffuse reflection function for a wide range of optical thicknesses and albedos for single scattering. Tables of the diffusely transmitted radiation, i.e., the radiation incident on the bottom specular reflector, are also given. This study provides a necessary first step toward the computational treatment of more realistic models of atmospheres involving anisotropic scattering, sphericity, frequency dependence, and other factors. It aids in the assessment of the role of a bottom specular reflector, e.g., a smooth sea-atmosphere interface. Subsequent studies will be devoted to the determination of the source function and to the solution of inverse problems. 51 pp. Refs. (MW)