It was recently shown that radiation, conduction and convection can be combined within a single Monte Carlo algorithm and that such an algorithm immediately benefits from state-of-the-art computer-graphics advances when dealing with complex geometries. The theoretical foundations that make this coupling possible are fully exposed for the first time, supporting the intuitive pictures of continuous thermal paths that run through the different physics at work. First, the theoretical frameworks of propagators and Green’s functions are used to demonstrate that a coupled model involving different physical phenomena can be probabilized. Second, they are extended and made operational using the Feynman-Kac theory and stochastic processes. Finally, the theoretical framework is supported by a new proposal for an approximation of coupled Brownian trajectories compatible with the algorithmic design required by ray-tracing acceleration techniques in highly refined geometry.
One aspect of climate change analysis is the quantification of radiative forcings, i.e., the change of top-of-atmosphere (TOA) net radiative flux induced by an isolated, instantaneous change in surface or atmospheric constitution. In this paper, we discuss recent advances in pathintegral formulations for producing reference estimates of radiative forcings, in the form of partial derivatives we call "sensitivities". We present the theoretical framework and highlight the role of computer science acceleration techniques in making the computational cost insensitive to the system's multidimensional and multiphysics complexity. The approach is demonstrated by estimating the flux sensitivity to the concentration of two greenhouse gases.
Nous souhaitons estimer le flux radiatif quittant la Terre intégré sur l'infrarouge thermique, sur toute la surface du globe et sur une période climatique de longue durée. Ce calcul est réputé très difficile à réaliser si on ne fait pas de simplifications de la description fréquentielle, spatiale ou temporelle (e.g. passer d'un modèle raie-par-raie à un modèle de bande, utiliser une discrétisation temporelle plus grossière, etc). Nous montrons que la méthode de Monte-Carlo permet d'éviter ces simplifications si on associe les deux idées suivantes : introduire des collisionneurs fictifs pour permettre le suivi de rayon sans connaissance du champ de coefficient d'extinction et échantillonner statistiquement les raies spectrales. Nous montrons qu'il n'est pas plus coûteux de réaliser cette intégration sur un jour ou un mois, sur une colonne atmosphérique ou sur toute la Terre, ou finalement sur une bande étroite fréquentielle ou sur tout le spectre infrarouge. ABSTRACT. We want to estimate the outgoing Earth's radiative flux integrated over the thermal infrared, over the entire surface of the globe and over a long climatic period. This calculation is known to be very difficult to achieve without simplifications of the frequency, spatial or temporal description (e.g. switching from a line-by-line model to a band model, using a coarser temporal discretization, etc). We show that the Monte-Carlo method can avoid these simplifications if we combine the following two ideas : introduce fictitious colliders to allow ray tracing without knowledge of the extinction coefficient field and statistically sample the spectral lines. We show that it is not more expensive to perform this integration over a day or a month, over an atmospheric column or over the whole Earth, or finally over a narrow frequency band or over the whole infrared spectrum.
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