A superposition technique for deriving mean photon scattering statistics in plane-parallel cloudy atmospheres

Photon transport in a multiple scattering medium is critically dependent on scattering statistics, in particular the average number of scatterings. A superposition technique is derived to accurately determine the average numb er of scatterings encountered by reflected and transmitted photons within a rbitrary layers in plane-parallel, vertically inhomogeneous clouds. As expe cted, the resulting scattering number profiles are highly dependent on clou d particle absorption and solar/viewing geometry. The technique uses effici ent adding and doubling radiative transfer procedures, avoiding traditional time-intensive Monte Carlo methods. Derived superposition formulae are app lied to a variety of geometries and cloud models, and selected results are compared with Monte Carlo calculations. Cloud remote sensing techniques tha t use solar reflectance or transmittance measurements generally assume a ho mogeneous plane-parallel cloud structure. The scales over which this assump tion is relevant, in both the vertical and horizontal, can be obtained from the superposition calculations. Though the emphasis is on photon transport in clouds, the derived technique is applicable to any multiple scattering plane-parallel radiative transfer problem, including arbitrary combinations of cloud, aerosol, and gas layers in the atmosphere. (C) 2000 Elsevier Sci ence Ltd. All rights reserved.