Exact and Approximate Solutions for Multiple Scattering by Cloudy and Hazy Planetary Atmospheres

Abstract

Abstract Solutions are obtained for the problem of multiple scattering by a plane parallel atmosphere with anisotropic phase functions typical of cloud and haze particles. The resulting albedos, angular distributions of intensities, and planetary magnitudes are compared to solutions obtained with approximate analytic phase functions and, in the case of the cloud phase function, to the solution obtained with the forward diffraction peak omitted from the phase function. It is shown that the cloud phase function with the truncated peak yields results practically identical to those obtained with the complete cloud phase function, not only for albedos and magnitudes, but also for the angular distribution; the approximation introduces errors of several per cent in the angular distribution for direct backscattering (the region of the glory), for emergent angles near grazing regardless of the incident angle, and, of course, a larger error occurs for total scattering angles near 0°. However, the errors are unimpor...