ERRORS INDUCED BY THE NEGLECT OF POLARIZATION IN RADIANCE CALCULATIONS FOR RAYLEIGH-SCATTERING ATMOSPHERES

Although neglecting polarization and replacing the rigorous vector rad iative transfer equation by its approximate scalar counterpart has no physical background, it is a widely used simplification when the incid ent light is unpolarized and only the intensity of the reflected light is to be computed. In this paper we employ accurate vector and scalar multiple-scattering calculations to perform a systematic study of the errors induced by the neglect of polarization in radiance calculation s for a homogeneous, plane-parallel Rayleigh-scattering atmosphere (wi th and without depolarization) above a Lambertian surface. Specificall y, we calculate percent errors in the reflected intensity for various directions of light incidence and reflection, optical thicknesses of t he atmosphere, single-scattering albedos, depolarization factors, and surface albedos. The numerical data displayed can be used to decide wh ether or not the scalar approximation may be employed depending on the parameters of the problem. We show that the errors decrease with incr easing depolarization factor and/or increasing surface albedo. For con servative or nearly conservative scatter-ing and small surface albedos , the errors are maximum at optical thicknesses of about 1. The calcul ated errors may be too large for some practical applications, and, the refore, rigorous vector calculations should be employed whenever possi ble. However, if approximate scalar calculations are used, we recommen d to avoid geometries involving phase angles equal or close to 0-degre es and 90-degrees, where the errors are especially significant. We pro pose a theoretical explanation of the large vector/scalar differences in the case of Rayleigh scattering. According to this explanation, the differences are caused by the particular structure of the Rayleigh sc attering matrix and come from lower-order (except first-order) light s cattering paths involving right scattering angles and right-angle rota tions of the scattering plane.