Multiple scattering of anisotropic radiation through a layer of clouds

A method by which the transport of anisotropic radiative multiple scattering can be predicted is developed in this paper. A one-dimensional integral intensity model and a three-dimensional diffusion intensity model are both constructed. The former provides a closed-form solution, while the latter involves successive approximation and Gauss's quadrature. On the basis of these methods, the reflection and transmission of solar radiation in a homogeneous cloud layer are computed. The results differ from those for isotropic and Rayleigh scattering assumptions and illustrate the effects on transmission and reflectivity of optical thickness, wavelength, incidence angle, and albedo of single scattering.Nomenclature D ⁺ transmitted diffusion radiation intensity W/cm² sr · m] - D ^– reflected diffusion radiation intensity W/cm² sr · m] - I pencil of radiation or specific intensity W/cm² sr · m] - I ₀ solar irradiance W/cm²] - K extinction cross-section or total cross-section, + - s (u, ), unit scattered radiation vector - s ₀ (u ₀, ₀), unit incident radiation vector - t optical thickness - u cosine of the viewing angle, , which is measured from the vertical - u ₀ cosine of the angle of incident, ₀, which is measured from the vertical - absorption cross-section - scattering function - absorption coefficient - scattering angle, s · s ₀ - scattering cross-section - scattered azimuthal angle - ₀ incident azimuthal angle - a sphere - a solid angle - ₀ albedo of single scattering,