Two- and four- stream combination approximations for computation of diffuse actinic fluxes

The delta two-and four-stream combination approximations, which use a source function from the two-stream approximations and evaluate intensities in the four-stream directions, are formulated for the calculation of diffuse actinic fluxes. The accuracy and efficiency of the three computational techniques, i.e., the delta two-stream approximations, the delta two- and four-stream combination approximations based on various two-stream approaches, and the delta four-stream approximation, have been investigated. The diffuse actinic fluxes are examined by considering molecular, aerosol, haze and cloud scattering over a wide range of solar zenith angles, optical depths, and surface albedos. In view of the overall accuracy and computational efficiency, the delta two- and four-stream combination method based on the quadrature scheme appears to be well-suited to radiative transfer calculations involving photodissociation processes.