Vertical photon transport in cloud remote sensing problems

Photon transport in plane-parallel, vertically inhomogeneous clouds is inve stigated and applied to cloud remote sensing techniques that use solar refl ectance or transmittance measurements for retrieving droplet effective radi us. Transport is couched in terms of weighting functions which approximate the relative contribution of individual layers to the overall retrieval. Tw o vertical weightings are investigated, including one based on the average number of scatterings encountered by reflected and transmitted photons in a ny given layer. A simpler vertical weighting, based on the maximum penetrat ion of reflected photons, proves useful for solar reflectance measurements. These weighting functions are highly dependent on droplet absorption and s olar/viewing geometry. A superposition technique, using adding/doubling rad iative transfer procedures, is used to accurately determine both weightings , avoiding time-consuming Monte Carlo methods. Effective radius retrievals from modeled vertically structured liquid water clouds are then made using the standard near-infrared bands and compared with size estimates based on the proposed weighting functions. Agreement between the two methods is gene rally within several tenths of a micrometer, much better than expected retr ieval accuracy. Though the emphasis is on photon transport in clouds, the d erived weightings can be applied to any multiple-scattering plane-parallel radiative transfer problem, including arbitrary combinations of cloud, aero sol, and gas layers.