A symbolic approach for the identification of radiative properties

Abstract

A new Symbolic Monte Carlo (SMC) based on null-collision algorithms, allows 1/ overcoming the usually required knowledge of the optical thickness in SMC, and 2/ expressing radiative quantities as simple polynomials of the absorption and scattering coefficients. The proposed method can be applied to complex systems such as heterogeneous absorbing and scattering media in complex geometry. It opens new outlooks for the analysis and the identification of radiative properties in a wide range of radiative transfer applications in participating media.

A Path‐Tracing Monte Carlo Library for 3‐D Radiative Transfer in Highly Resolved Cloudy Atmospheres

“…This explicit framework opened doors to new families of MC algorithms, with potential for solving various problems that were before then considered impossible: nonlinear models (Dauchet et al, 2018), coupled radiation-convection-conduction in a single MC algorithm , energetic state transitions sampled from spectroscopy instead of approximate spectral models (Galtier et al, 2016), symbolic MC in scattering media (Galtier et al, 2017), etc. Some of these methods are transposable to atmospheric radiative transfer with large benefits for our community, for example, conductoradiative MC models to investigate atmosphere-cities interactions, or line-sampling methods for benchmark spectral integration, to develop, tune and test spectral models.…”

Symbolic Monte Carlo method applied to the identification of radiative properties of a heterogeneous material

“…However, the identification of absorption and scattering coefficients was impossible in [10,11] as the analysis required the knowledge of the optical thickness. Galtier et al [12] circumvented this difficulty by the use of null-collisions method [13] to express a radiative quantity as a polynomial of absorption and scattering coefficients.…”

“…In this work, SMC algorithms presented in [12] are developed within the frame of inverse radiative transfer. A complete SMC framework for the identification of absorption and scattering coefficients of heterogeneous semitransparent materials from measurements of directional-hemispherical transmittance and reflectance is proposed.…”

Convergence issues in derivatives of Monte Carlo null-collision integral formulations: A solution

“…Then the choice is made to select a true-collision or a virtual-collision as function of their local respective-amounts and this is how the spatial information is recovered. But several other benefits were recently foreseen in [1] and practically tested in [5,6,7,8,9,10,11,12,13,14,15,16], mainly for radiative-transfer applications. The main idea is that null-collision algorithms transform the non-linearity of Beer-extinction into a linear-recursive problem that Monte Carlo handles without approximation [14].…”

“…This was for instance used in [5] to deal with absorption-spectra of molecular gases combining very numerous transitions: the summation over all transitions could be treated by the Monte Carlo algorithm itself, which was previously assumed impossible because this summation was inside the exponential of Beer-extinction. Similarly, the vanishing of the exponential allowed the extension of implicit Monte Carlo algorithms for inversion of absorption and scattering coefficients from intensity measurements [6]. Outside radiative transfer, a very similar idea was used to solve Electromagnetic Maxwell equations for energy propagation in particle-ensembles of statistically-distributed shapes despite of the nonlinearity associated to the square of the electric field [13].…”