TOWARDS A REFERENCE FRAMEWORK FOR RADIATIVE TRANSFER AND UNCERTAINTY PROPAGATION IN STOCHASTIC MEDIA

Accurate modeling of transport phenomena in stochastic media is a major challenge in fields such as atmospheric radiative transfer, neutron transport, and optical diagnostics in disordered materials. In atmospheric science, for instance, the statistical description of clouds—due to their fractal structures, broken fields, and turbulent dynamics—greatly affects photon transport. In such stochastic media, the usual representation of radiance as a deterministic scalar field is inaccurate. It must instead be treated as a random variable, with its distribution statistics, especially the mean (expectation) for forward modeling and variance for uncertainty propagation, being critical. This shift to statistical modeling of radiance requires new theoretical and computational tools for robustly computing these quantities. While previous studies have addressed this, most either rely on approximate models [1] or fail to provide the numerical precision for the propagated uncertainties [2, 3]. This work presents a reference framework for radiative transfer in stochastic media, where radiance statistics are expressed as path-integral quantities and solved using nonlinear branching Monte Carlo methods [4]. The benchmark configuration is a one-dimensional, purely absorbing layer with uncertainty introduced through a vertically varying absorption coefficient, modeled as an Ornstein– Uhlenbeck stochastic process, adding a layer of complexity to the model. Our approach allows for the accurate computation of the radiance distribution's moments and their numerical precision, even with large parametric uncertainties that lead to nonlinear regimes. Future developments will explore stochastic transport in scenarios involving more complexity, such as multiple scattering, polarization, spectroscopic uncertainties, and ultimately, in real-world stochastic media. In scenarios where this Monte Carlo framework may be too slow for operational calculations, it is expected to at least serve as a reference for analyzing and validating approximate models that are less computationally demanding.