Elements of Radiative-Transfer Theory Used in the Monte Carlo Methods

Marchuk, G. I.; Mikhailov, Gennadi A.; Nazaraliev, Magamedshafi A.; Darbinjan, Radzmik A.; Kargin, B. A.; Elepov, Boris S.

doi:10.1007/978-3-540-35237-2_2

Cited by 4 publications

(6 citation statements)

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“…The technique of maximum cross‐section (Marchuk et al, ), or NCAs as referred to in this paper, is an unbiased technique (no approximation is introduced; Coleman, ) that has been known since the origin of MC in all fields of particle transport physics but which has essentially been considered as a trick to avoid the heavy coding of crossing elementary volumes one after the other. It is only very recently that these algorithms were theoretically analyzed as a way to bypass the difficulties associated with the nonlinearity of Beer's extinction and to integrate the heterogeneities of k along the path as part of the MC integration itself (Galtier et al, ).…”

Section: Acceleration Grids For Large Surface and Volume Data Setsmentioning

confidence: 99%

“…A solution consists in adding virtual collisionners where true collisionners are scarce so that the total extinction coefficient is uniform throughout the whole field (Woodcock et al, 1965;Marchuk, Mikhailov, Nazaraliev, et al, 1980). This transforms the standard algorithms into new Monte Carlo algorithms, still unbiased (no approximation is introduced, Coleman (1968)), where there is no integral inside the exponential any more.…”

Section: Null-collision Algorithms and Their Integral Formulation Cou...mentioning

confidence: 99%

“…Such null-collision algorithms have been known since the origin of Monte Carlo in all fields of particle transport physics (under the name Maximum Cross-section in atmospheric radiation (Marchuk, Mikhailov, Nazaraliev, et al, 1980)), but they have essentially been considered as a trick to avoid the heavy coding of crossing elementary volumes one after the other. It is only very recently that they were theoretically analysed as a way to bypass the difficulties associated to the nonlinearity of Beer's extinction and to integrate the heterogeneities of k along the path as part of the Monte Carlo integration itself.…”

Section: The Expected Features Of Acceleration Grids For Path-tracing...mentioning

confidence: 99%

“…These 3D models can be divided into two categories: those using deterministic approaches (e.g. the Spherical Harmonics Discrete Ordinate Method Evans (1998)) and those using statistical approaches: Monte Carlo (MC) methods (Marchuk, Mikhailov, Nazaraliev, et al, 1980).…”

Section: Introductionmentioning

confidence: 99%

“…A path-tracing Monte Carlo library for 3-D radiative transfer in highly resolved cloudy atmospheres.group of cloud-radiation scientists who, over the past 40 years, have been developing and using reference 3-D radiative transfer models to analyze and document cloud-radiation 3-D interactions (see Davis & Marshak, 2010;Marshak & Davis, 2005, and references therein). These 3-D models can be divided into two categories: those using deterministic approaches (e.g., the Spherical Harmonics Discrete Ordinate Method; Evans, 1998) and those using statistical approaches, that is, Monte Carlo (MC) methods (Marchuk et al, 1980a). Our proposal builds upon one of the major strengths of MC models: that the computing time is only weakly sensitive to the size of the geometrical and spectral data set.…”

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confidence: 99%

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

Villefranque

Fournier

Couvreux

et al. 2019

J Adv Model Earth Syst

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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 broad range of issues related to these interactions, and to three‐dimensional interactions in particular, has 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. Building on this community effort, we present here an open‐source library for general use in Monte Carlo algorithms. This library is devoted to the acceleration of ray tracing in complex data, typically high‐resolution large‐domain grounds and clouds. The main algorithmic advances embedded in the library are 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 sensitive to the refinement of the volumetric data. The library is tested with a rendering algorithm that produces synthetic images of cloud radiances. Other examples of implementation are provided to demonstrate potential uses of the library in the context of 3‐D radiation studies and parameterization development, evaluation, and tuning.

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Section: Acceleration Grids For Large Surface and Volume Data Setsmentioning

confidence: 99%

Section: Null-collision Algorithms and Their Integral Formulation Cou...mentioning

confidence: 99%

Section: The Expected Features Of Acceleration Grids For Path-tracing...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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

Villefranque

Fournier

Couvreux

et al. 2019

J Adv Model Earth Syst

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A Monte Carlo-Based Strategy to Assess Complex Kinetics: Application of the Null-Reaction Method to DAEM

et al. 2023

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The distributed activation energy model (DAEM) is widely used in chemical kinetics to statistically describe the occurrence of numerous independent parallel reactions. In this article, we suggest a rethink in the context of a Monte Carlo integral formulation to compute the conversion rate at any time without approximation. After the basics of the DAEM are introduced, the considered equations (under isothermal and dynamic conditions) are respectively expressed into expected values, which in turn are transcribed into Monte Carlo algorithms. To describe the temperature dependence of reactions under dynamic conditions, a new concept of null reaction, inspired from null-event Monte Carlo algorithms, has been introduced. However, only the first-order case is addressed for the dynamic mode due to strong nonlinearities. This strategy is then applied to both analytical and experimental density distribution functions of the activation energy. We show that the Monte Carlo integral formulation is efficient in solving the DAEM without approximation and that it is well-adapted due to the possibility of using any experimental distribution function and any temperature profile. Furthermore, this work is motivated by the need for coupling chemical kinetics and heat transfer in a single Monte Carlo algorithm.

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A Functionalized Monte Carlo 3D Radiative Transfer Model: Radiative Effects of Clouds Over Reflecting Surfaces

Barker

Cole

2023

J Adv Model Earth Syst

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Cloud-radiation interactions are both complicated and central to several fields of the atmospheric sciences ranging from satellite remote sensing to numerical weather and climate prediction. Monte Carlo (MC) methods are unbiased statistical integration methods (Cahalan et al., 2005;Mayer, 2009;Pincus & Evans, 2009) that are able to solve the full radiative transfer (RT) equation for arbitrarily complex 3D fields. They have not been directly used in operational contexts yet because of their potentially substantial computational cost, which is mostly attributable to tracking large numbers N of virtual photon paths throughout cloudy atmospheres. They have, however, been used often to study complex interactions between 3D clouds and radiation (e.g., Veerman et al. (2022)) and consequently to evaluate and improve fast approximate RT models (

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Elements of Radiative-Transfer Theory Used in the Monte Carlo Methods

Cited by 4 publications

References 0 publications

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

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

A Monte Carlo-Based Strategy to Assess Complex Kinetics: Application of the Null-Reaction Method to DAEM

A Functionalized Monte Carlo 3D Radiative Transfer Model: Radiative Effects of Clouds Over Reflecting Surfaces

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