We describe an efficient computational scheme for downward surface flux computations in a vertically inhomogeneous grey planetary atmosphere for different values of solar zenith angle. We start with the basic equations of a recently developed discrete ordinates spectral nodal method, and we derive suitable bidirectional functions whose diffuse components do not depend on the solar zenith angle. We then make use of these bidirectional functions to construct an efficient scheme for computing the downward surface fluxes in a given model atmosphere for a number of solar zenith angles. We illustrate the merit of the computational scheme described here with downward surface flux computations in a three-layer grey model atmosphere for four values of solar zenith angle, and we conclude this article with general remarks and directions for future work.
atmospheric radiation; discrete ordinates; spectral nodal method; bidirectional functions; radiative flux; computational efficiency
