title: Simple model for the calculation of the flux of solar radiation through the atmosphere.
abstract: The flux of solar radiation through a model atmosphere composed of n homogeneous layers and a ground surface is represented by 2(n + 1) linear simultaneous equations. The system is solved explicitly for the albedo and for the radiation reaching the ground as a function of the vertically incident radiation and known or assumed reflection and transmission coefficients for each of the n layers and ground surface. Inasmuch as the only distinction among any of the layers resides in the transmission and reflection coefficients assigned to each, the model may be used for any combination of cloud and cloud-free layers. Sample calculations are made for the case of n = 7 for a wide variety of cloud states in order to illustrate the properties of the system. The principal virtue of the model lies in its simplicity and in the fact that explicit solutions are obtained for the total radiation reaching the ground and reflected to space. Since direct observations of both of these parameters are now available on a routi e ba is, the model offers the opportunity of determining the transmission and reflection statistics of any individual cloud type by a suitable least-squares procedure.
authors.forename: R
authors.initials: R
authors.lastname: Shapiro