Discrete-angle radiative transfer in a multifractal medium

摘要

Abstract: A simplified (discrete angle or DA) radiative transfer theory is presented as a computationally and conceptually advantageous alternative to standard (continuous angle) theory: its use is justified since these theories generally predict the same radiative scaling behavior whereas diffusion and independent pixel approximations do not. After briefly reviewing the basic ideas of random fractal geometry and multifractal cascade theory, we present some of our recent two-dimensional DA numerical simulations of transfer through a specific log-normal multifractal cloud model where the radiation fields are spatially resolved on a 1024 $MUL 1024 point grid. Using this database, we demonstrate how in inhomogeneous transfer problems horizontal fluxes work in quite subtle ways to create dramatic overall differences with homogeneous predictions for the same amount of scattering material, and how strongly multiple scattering can smooth extremely singular density fields. Furthermore, both of these effects are enhanced by increasing optical thickness which can be viewed as a measure of the strength of the nonlinear coupling between the density and radiance fields. Finally, we discuss some basic inequalities that arise between the various ways of computing overall (spatially averaged) response to illumination.!63