Effect of Specular Reflection at the Ground on Light Scattered from a Rayleigh Atmosphere

Abstract

The method of Chandrasekhar is used to compute the parameters that characterize the scattered light leaving the top of a Rayleigh atmosphere. The atmosphere of this model lies above a smooth water surface, which reflects light according to Fresnel’s law. The combined atmosphere and water is called the Fresnel model. The results for the Fresnel model are compared with corresponding results for a second model, which is called the Lambert model, since its ground reflects light according to Lambert’s law. The reflectance at the ground is less than 0.1, if either the solar zenith angle θ0 0.6. The relative difference between the outward fluxes from the tops of the atmospheres of the two models is less than 0.07 if θ0 0.5, but the difference becomes large at small τ1. The maximum degree of polarization and the neutral-point positions at the top of the atmosphere of the Fresnel model are quite different from those of the Lambert model, when the total optical thickness is less than 0.5. The neutral points for the Fresnel model appear outside of the vertical plane through the sun for restricted ranges of both the total normal optical thickness and the solar zenith angle.