Approximations for horizontal photon transport in cloud remote sensing problems

The effect of horizontal photon transport within real-world clouds can be o f consequence to remote sensing problems based on plane-parallel cloud mode ls. In this paper, analytic approximations for the root-mean-square horizon tal displacement of reflected and transmitted photons, relative to the inci dent cloud-top location, are derived for plane-parallel cloud layers. With anisotropic scattering, separate approximations are needed depending on the order of scattering. When sufficient numbers of photon scatterings occur, an approximation based on random walk theory (photon diffusion) is applicab le; when scattering numbers are relatively small, a modification to the dif fusion result is used. The resulting formulae are a function of the average number of photon scatterings, as well as particle asymmetry parameter and single scattering albedo. In turn, the average number of scatterings from p lane-parallel, vertically inhomogeneous cloud layers can be determined from efficient adding/doubling radiative transfer procedures. The transport app roximations are applied to liquid water clouds for typical remote sensing s olar spectral bands, involving both conservative and non-conservative scatt ering. Results compare well with Monte Carlo calculations. Though the empha sis is on horizontal photon transport in terrestrial clouds, the derived ap proximations are applicable to general anisotropic, multiple scattering, pl ane-parallel radiative transfer problems. Approximations useful for three-d imensional transport are also given. The complete horizontal transport prob ability distribution can be described with an analytic distribution specifi ed by the root-mean-square and average radial displacement values. However, it is shown empirically that the average displacement can be reasonably in ferred from the root-mean-square value. An estimate for the horizontal tran sport distribution can then be made from the root-mean-square photon displa cement alone. (C) 2000 Elsevier Science Ltd. All rights reserved.