Numerical Simulation of Polarized Light and Temperature in a Stratified Atmosphere with a Slowly Varying Refractive Index

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Autore principale:	Pironneau, Olivier
Natura:	Preprint
Pubblicazione:	2024
Soggetti:	Analysis of PDEs
Accesso online:	Acceder al recurso
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_version_	1866915065317294080
author	Pironneau, Olivier
author_facet	Pironneau, Olivier
contents	This article is an attempt to elucidate the effect of a slowly varying refractive index on the temperature in a stratified atmosphere, with a particular focus on greenhouse gases such as CO2. It validates an iterative method for the vector radiative transfer equations (VVRTE) called Iterations on the Source. As the system proposed by Chandrasekhar and Pomraning is not well posed for all rays directions when the refractive index varies, so instead we solve an integral representation of VRTE without the problematic rays. A mathematical proof is given showing monotonicity, convergence of the iterations and existence and uniqueness. Furthermore the convergence is geometric if the absorption is not too large. Some numerical tests are performed showing the effect of a layer of cloud with a refractive index greater than air, polarisation and scattering.
format	Preprint
id	arxiv_https___arxiv_org_abs_2412_11262
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Numerical Simulation of Polarized Light and Temperature in a Stratified Atmosphere with a Slowly Varying Refractive Index Pironneau, Olivier Analysis of PDEs This article is an attempt to elucidate the effect of a slowly varying refractive index on the temperature in a stratified atmosphere, with a particular focus on greenhouse gases such as CO2. It validates an iterative method for the vector radiative transfer equations (VVRTE) called Iterations on the Source. As the system proposed by Chandrasekhar and Pomraning is not well posed for all rays directions when the refractive index varies, so instead we solve an integral representation of VRTE without the problematic rays. A mathematical proof is given showing monotonicity, convergence of the iterations and existence and uniqueness. Furthermore the convergence is geometric if the absorption is not too large. Some numerical tests are performed showing the effect of a layer of cloud with a refractive index greater than air, polarisation and scattering.
title	Numerical Simulation of Polarized Light and Temperature in a Stratified Atmosphere with a Slowly Varying Refractive Index
topic	Analysis of PDEs
url	https://arxiv.org/abs/2412.11262

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