In a planetary atmosphere the J value is determined by the angular-averaged radiance, or the average density of photons in an element of volume. The average density may be enhanced by multiple scattering of photons in a conservative, or near-conservative scattering atmosphere. We show that in a conservative semi-infinite medium this enhancement will be a factor of 5, for optical depths greater than about 20 for coherent scattering. We investigate the modification of the J values owing to multiple scattering in an optically thick medium of various optical depths, various single-scattering albedos of the scattering medium, and a range of surface albedos. We have applied the results to the calculation of J values in clouds in the terrestrial atmosphere and in the Rayleigh-scattering atmosphere of Uranus. We note that J values in a realistic atmosphere may be enhanced by as much as a factor of 5 throughout a large fraction of the atmosphere over those calculated without multiple scattering and surface reflection.
Time‐Dependent One‐Speed Albedo Problem for a Semi‐Infinite Medium
