Generalized Eddington analytical model for azimuthally dependent radiance simulation in stratified media

Abstract

A fast analytical radiative transfer model to account for propagation of unpolarized monochromatic radiation in random media with a plane-parallel geometry is presented. The model employs an Eddington-like approach combined with the delta phase-function transformation technique. The Eddington approximation is extended in a form that allows us to unfold the azimuthal dependence of the radiance field. A first-order scattering correction to the azimuth-dependent Eddington radiative model solution is also performed to improve the model accuracy for low-scattering media and flexibility with respect to use of explicit arbitrary phase functions. The first-order scattering-corrected solution, called the generalized Eddington radiative model (GERM), is systematically tested against a numerical multistream discrete ordinate model for backscattered radiance at the top of the medium. The typical mean accuracy of the GERM solution is generally better than 10% with a standard deviation of 20% for radiance calculations over a wide range of independent input optical parameters and observation angles. GERM errors are shown to be comparable with the errors due to an input parameter uncertainty of precise numerical models. The proposed model can be applied in a quite arbitrary random medium, and the results are appealing in all cases where speed, accuracy, and/or closed-form solutions are requested. Its potentials, limitations, and further extensions are discussed.

Hydrometeor scattering and stochastic modeling for free-space optical channel characterization

“…In the last decades several approximate analytical approaches have been proposed. Eddington approximation within the two-stream hypothesis [11] represents a common approach to solve numerically RTE in fast, but still fairly accurate way [12].…”

“…The same notation can used also in RTE context, if we intend T, and k e as apparent one due to not only singlescattering, but also to multiple scattering effects [12]. In this work we have adopted the Eddington model proposed by [11] to evaluate the effects of multiple scattering.…”

“…In this work we have adopted the Eddington model proposed by [11] to evaluate the effects of multiple scattering. The proposed model framework also implements other methods, in particular the hybrid Eddington one of [11] and the Tam-Zardecki approach for open detector receivers [12]. …”