Path-tracing Monte Carlo Library for 3D Radiative Transfer in Highly Resolved Cloudy Atmospheres

Interactions between clouds and radiation are at the root of many difficulties in numerically predicting future weather and climate and in retrieving the state of the atmosphere from remote sensing observations. The large range of issues related to these interactions, and in particular to three-dimensional interactions, motivated the development of accurate radiative tools able to compute all types of radiative metrics, from monochromatic, local and directional observables, to integrated energetic quantities. In the continuity of this community effort, we propose here an open-source library for general use in Monte Carlo algorithms. This library is devoted to the acceleration of path-tracing in complex data, typically high-resolution large-domain grounds and clouds. The main algorithmic advances embedded in the library are those related to the construction and traversal of hierarchical grids accelerating the tracing of paths through heterogeneous fields in null-collision (maximum cross-section) algorithms. We show that with these hierarchical grids, the computing time is only weakly sensitivive to the refinement of the volumetric data. The library is tested with a rendering algorithm that produces synthetic images of cloud radiances. Two other examples are given as illustrations, that are respectively used to analyse the transmission of solar radiation under a cloud together with its sensitivity to an optical parameter, and to assess a parametrization of 3D radiative effects of clouds.Comment: Submitted to JAMES, revised and submitted again (this is v2

Thermique non-linéaire et Monte-Carlo

The work presented adresses the numerical simulation of coupled-heat transfer problems in the presence of four standard non-linear sources: temperature at power 4 in radiation and conductivity, heat capacity and convective exchange coefficient, all of the three functions of temperature. Our specificity is the use of a Monte Carlo method that preserves a set of strong points in the algorithms used for linearization, most notably for the ability to compute probes in complex geometry. We begin with a synthesis of the statistical reformulation of the justifying models, within the linear framework, with a randomized reading of the conducto-convecto-radiative coupling which will be the starting point of our proposal. We then group our 4 non-linear questions in the same formal framework, built on transportation physics, in order to exploit the results of a recent revisiting of zero-collision algorithms. The resulting branch algorithms face computational difficulties: the number of branches increases very strongly at low Knudsen numbers. We then propose a workaround strategy that ensures a limitation of the number of branches via a hierarchical rewriting inspired by Picard’s method.Les travaux présentés concernent la simulation numérique de problèmes couplés en transfert thermique en présence de quatre sources de non-linéarité tout-à-fait standard~: la température à la puissance quatre en rayonnement et la conductivité, la capacité calorifique et le coefficient d'échange convectif tous trois fonctions de la température. Notre spécificité est l'utilisation d'une méthode de Monte Carlo qui préserve un ensemble de points forts des algorithmes utilisés pour le linéaire, notamment la capacité au calcul sonde en géométrie complexe. Nous commençons par une synthèse des travaux de reformulation statistique des modèles justifiant, dans le cadre linéaire, une lecture en marche aléatoire du couplage conducto-convecto-radiatif qui sera le point de départ de notre proposition. Nous regroupons ensuite nos quatre questions non-linéaires dans un même cadre formel, construit sur la physique du transport, de façon à exploiter les résultats d'une revisite récente des algorithmes à collisions nulles. Les algorithmes branchants qui en résultent se heurtent à des difficultés calculatoires : le nombre de branches augmente très fortement aux faibles nombres de Knudsen. Nous proposons alors une stratégie de contournement qui assure une limitation du nombre de branches via une ré-écriture hiérarchique inspirée de la méthode de Picard

Timing the spinal cord development with neural progenitor cells losing their proliferative capacity: a theoretical analysis

International audienceIn the developing neural tube in chicken and mammals, neural stem cells proliferate and differentiate according to a stereotyped spatiotemporal pattern. Several actors have been identified in the control of this process, from tissue-scale morphogens patterning to intrinsic determinants in neural progenitor cells. In a previous study (Bonnet et al. eLife 7, 2018), we have shown that the CDC25B phosphatase promotes the transition from proliferation to differentiation by stimulating neurogenic divisions, suggesting that it acts as a maturating factor for neural progenitors. In this previous study, we set up a mathematical model linking fixed progenitor modes of division to the dynamics of progenitors and differentiated populations. Here, we extend this model over time to propose a complete dynamical picture of this process. We start from the standard paradigm that progenitors are homogeneous and can perform any type of divisions (proliferative division yielding two progenitors, asymmetric neurogenic divisions yielding one progenitor and one neuron, and terminal symmetric divisions yielding two neurons). We calibrate this model using data published by Saade et al. (Cell Reports 4, 2013) about mode of divisions and population dynamics of progenitors/neurons at different developmental stages. Next, we explore the scenarios in which the progenitor population is actually split into two different pools, one of which is composed of cells that have lost the capacity to perform proliferative divisions. The scenario in which asymmetric neurogenic division would induce such a loss of proliferative capacity appears very relevant

Three viewpoints on null-collision Monte Carlo algorithms

International audienceIn 2013, Galtier et al. [1] have revisited theoretically a numerical trick that had been used since the very beginning of linear-transport Monte-Carlo simulation: introducing virtual absorbers or scatterers into a heterogeneous field to make it "look" homogeneous. Webriefly describe some reported and ongoing researches that were initiated by this theoretical work and we try to classify them by proposing three alternative viewpoints on the very same null-collision concept

Path-tracing Monte Carlo Libraries for 3D Radiative Transfer in Cloudy Atmospheres

Interactions between clouds and radiation are at the root of many difficulties in numeri-cally predicting future weather and climate and in retrieving the state of the atmospherefrom remote sensing observations. The large range of issues related to these interactions,and in particular to three-dimensional interactions, motivated the development of accurateradiative tools able to compute all types of radiative metrics, from monochromatic, localand directional observables, to integrated energetic quantities. In the continuity of thiscommunity effort, we propose here an open-source library for general use in Monte Carloalgorithms. This library is devoted to the acceleration of path-tracing in complex data,typically high-resolution large-domain grounds and clouds. The main algorithmic advancesembedded in the library are those related to the construction and traversal of hierarchicalgrids accelerating the tracing of paths through heterogeneous fields in null-collision (maxi-mum cross-section) algorithms. We show that with these hierarchical grids, the computingtime is only weakly sensitivive to the refinement of the volumetric data. The library is testedwith a rendering algorithm that produces synthetic images of cloud radiances. Two otherexamples are given as illustrations, that are respectively used to analyse the transmissionof solar radiation under a cloud together with its sensitivity to an optical parameter, andto assess a parametrization of 3D radiative effects of clouds

Rayonnement 3d sw et lw dans les nuages de couche limite : Monte carlo et calcul de sensibilité

National audienc

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

International audienceWhen a Monte Carlo algorithm is used to evaluate a physical observable A, it is possible to slightly modify thealgorithm so that it evaluates simultaneously A and the derivatives ∂ς A of A with respect to each problem-parameter ς. The principle is the following: Monte Carlo considers A as the expectation of a random variable, this expectation is an integral, this integral can be derivated as function of the problem-parameter to give a new integral, and this new integral can in turn be evaluated using Monte Carlo. The two Monte Carlo computations (of A and ∂ς A) are simultaneous when they make use of the same random samples, i.e. when the two integrals have the exact samestructure. It was proven theoretically that this was always possible, but nothing ensures that the two estimators have the same convergence properties: even when a large enough sample-size is used so that A is evaluated very accurately,the evaluation of ∂ς A using the same sample can remain inaccurate. We discuss here such a pathological example:null-collision algorithms are very successful when dealing with radiative transfer in heterogeneous media, but they are sources of convergence difficulties as soon as sensitivity-evaluations are considered. We analyse theoreticallythese convergence difficulties and propose an alternative solution

Three viewpoints on null-collision Monte Carlo algorithms

International audienceIn 2013, Galtier et al. [1] theoretically revisited a numerical trick that had been used since the very beginning of linear-transport Monte-Carlo simulation: introducing “null” scatterers into a heterogeneous field to make it virtually homogeneous.The rigorous connection between null-collision algorithms and integral formulations of the radiative transfer equation led to null-collision algorithms being used in distinct contexts, from atmospheric or combustion sciences to computer graphics, addressing questions that may strongly depart from the initial objective of handling heterogeneous fields (handling large spectroscopic databases, non-linearly coupling radiation with other physics).We briefly describe here some of this research and we classify it by proposing three alternative viewpoints on the very same null-collision concept: an intuitive, physical point of view, called similitude; a viewpoint built on the probability theory, where the null-collision method is seen as rejection sampling; and a more formal writing where the nonlinear exponential function is expanded into an infinite sum of linear terms.By formulating the null-collision concept under three distinct formalisms, our intention is to increase the reader’s awareness of its flexibility.The idea defended and illustrated in this paper is that the ability to explore null-collision algorithms under their different forms has often led to a broadening of the solution space when facing difficult problems, including ones where the Monte Carlo method was consensually considered inapplicable

Transient conducto-radiative heat transfer in a singlemonte-carlo algorithm : Handling the nonlinearity

International audienc

Combined conductive-convective-radiative heat transfer in complex geometry using the Monte Carlo method: application to solar receivers

International audienceDeterministic methods are commonly used to solve coupled conductive-convective-radiative systems in threedimensional geometries (3D). With the increasing amount and accuracy of data available, and growing complexity of systems studied, these methods have to deal with endless increases in computation times. This article presents a stochastic method for the simulation of the heat balance equation in solids and fluids with known velocity fields, as well as coupled surface to surface radiative transfers. The construction of the corresponding algorithm is comprehensively detailed and results are compared to deterministic simulations. The presented method uses a Monte Carlo approach and is shown to preserve short computation times for complex geometries