Calculation of the shortwave radiation field at the boundaries of a cloudless atmosphere

A numerical solution was obtained for equations governing the Ambartsumian functions for homogeneous and inhomogeneous models of the atmosphere. A finite number, N, of expansion terms in the Legendre polynomials was used to represent the light scattering indicatrix. The values of the Ambartsumian functions were used to calculate the underlying surface illumination, the atmospheric albedo, and the radiative flux divergence. An analysis was performed of the influence of atmospheric inhomogeneity and of N on the result of the calculation, and approximate formulas were obtained for the above values. An assessment of the error arising from the application of the formulas was made on the basis of exact solutions.