The three dimensional Monte Carlo radiation transport model McArtim is extended to account for the simulation of the propagation of polarized radiation and the inelastic rotational Raman scattering which is the cause of the so called Ring effect. From the achieved and now sufficient precision of the calculated Ring effect new opportunities in optical absorption spectroscopy arise. In the calculation the method of importance sampling (IS) is applied. Thereby one obtains from an ensemble of Monte Carlo photon trajectories an intensity accounting for the elastic aerosol particle-, Cabannes- and the inelastic rotational Raman scattering (RRS) and simultaneously an intensity, for which Rayleigh scattering is treated as an elastic scattering process. By combining both intensities one obtains the so called filling-in (FI, which quantifies the filling-in of Fraunhofer lines) as a measure for the strength of the Ring effect with the same relative precision as the intensities. The validation of the polarized radiometric quantities and the Ring effect is made by comparison with partially published results of other radiation transport models. Furthermore the concept of discretisation of the optical domain into grid cells is extended by making grid cells arbitrarily joining into so called clusters, i.e. grid cell aggregates. Therewith the program is able to calculate derivatives of radiometrically or spectroscopically accessible quantities, namely the intensities at certain locations in the atmospheric radiation field and the light path integrals of trace gas concentrations associated thereto, i.e. the product of the DOAS (differential optical absorption spectroscopy) method, with respect to optical properties of aerosols and gases in connected spatial regions. The first and second order derivatives are validated through so called self-consistency tests. These derivatives allow the inversion of three dimensional tracegas and aerosol concentration profiles and pave the way down to 3D optical scattered light tomography. If such tomographic inversion scheme is based solely on spectral intensitites the available second order derivatives allows the consideration of the curvature in the cost function and therefore allows implementation of efficient optimisation algorithms. The influence of the instrument function on the spectra is analysed in order to mathematically assess the potential of DOAS to a sufficient degree. It turns out that the detailed knowledge of the instrument function is required for an advanced spectral analysis. Concludingly the mathematical separability of narrow band signatures of absorption and the Ring effect from the relatively broad band influence of the elastic scattering processes on the spectra is demonstrated which corresponds exactly to the DOAS principle. In that procedure the differential signal is obtained by approximately 4 orders of magnitude faster then by the separate modelling with and without narrow band structures. Thereby the fusion of the separated steps DOAS spectral analysis and subsequent radiation transport modeling becomes computationally feasible.

The theory of radiative transfer is applied to the problem of multiple wave scattering in a one-dimensional multilayer. A new mathematical model of a multilayer is presented in which both the refractive index and width of each layer are randomized. The layer widths are generated by a new probability distribution which allows for strong layer width disorder. An expression for the transport mean free path of the multilayer is derived based on its single-scattering properties. It will be shown that interference between the field reflected from adjacent layer interfaces remains significant even in the presence of strong layer width disorder. It will be proven that even when the scattering is weak, the field in a random multilayer localizes at certain frequencies. The effect of increasing layer width randomization on this form of localization is quantified. The radiative transfer model of time-harmonic scattering in multilayers is extended to narrow-band pulse propagation in weakly scattering media. The tendency of pulses to broaden in this medium is discussed. A radiative transport model of the system is developed and compared to numerical solutions of the wave equation. It is observed that pulse broadening is not described by simple transfer theory. The radiative transfer model is extended by the addition of a Laplacian term in an attempt to model the effect of ensemble average pulse broadening. Numerical simulation results in support of this proposal are given, and applications for the theory suggested. Finally, the problem of acoustic wave scattering by planar screens is considered. The study was motivated by the idea that multiple scattering experiments may prove possible in a medium composed of such scatterers. Successful multiple scattering in a medium of planar scatterers will depend on the scattering cross-section at angles away from normal incidence. The scattering cross-section is calculated for a circular disc using a new technique for solving the acoustic wave equation on planar surfaces. The method is validated by comparison with available analytic solutions and the geometric theory of diffraction.

The theory of radiative transfer is applied to the problem of multiple wave scattering in a one-dimensional multilayer. A new mathematical model of a multilayer is presented in which both the refractive index and width of each layer are randomized. The layer widths are generated by a new probability distribution which allows for strong layer width disorder. An expression for the transport mean free path of the multilayer is derived based on its single-scattering properties. It will be shown that interference between the field reflected from adjacent layer interfaces remains significant even in the presence of strong layer width disorder. It will be proven that even when the scattering is weak, the field in a random multilayer localizes at certain frequencies. The effect of increasing layer width randomization on this form of localization is quantified. The radiative transfer model of time-harmonic scattering in multilayers is extended to narrow-band pulse propagation in weakly scattering media. The tendency of pulses to broaden in this medium is discussed. A radiative transport model of the system is developed and compared to numerical solutions of the wave equation. It is observed that pulse broadening is not described by simple transfer theory. The radiative transfer model is extended by the addition of a Laplacian term in an attempt to model the effect of ensemble average pulse broadening. Numerical simulation results in support of this proposal are given, and applications for the theory suggested. Finally, the problem of acoustic wave scattering by planar screens is considered. The study was motivated by the idea that multiple scattering experiments may prove possible in a medium composed of such scatterers. Successful multiple scattering in a medium of planar scatterers will depend on the scattering cross-section at angles away from normal incidence. The scattering cross-section is calculated for a circular disc using a new technique for solving the acoustic wave equation on planar surfaces. The method is validated by comparison with available analytic solutions and the geometric theory of diffraction.

The theory of radiative transfer is applied to the problem of multiple wave scattering in a one-dimensional multilayer. A new mathematical model of a multilayer is presented in which both the refractive index and width of each layer are randomized. The layer widths are generated by a new probability distribution which allows for strong layer width disorder. An expression for the transport mean free path of the multilayer is derived based on its single-scattering properties. It will be shown that interference between the field reflected from adjacent layer interfaces remains significant even in the presence of strong layer width disorder. It will be proven that even when the scattering is weak, the field in a random multilayer localizes at certain frequencies. The effect of increasing layer width randomization on this form of localization is quantified. The radiative transfer model of time-harmonic scattering in multilayers is extended to narrow-band pulse propagation in weakly scattering media. The tendency of pulses to broaden in this medium is discussed. A radiative transport model of the system is developed and compared to numerical solutions of the wave equation. It is observed that pulse broadening is not described by simple transfer theory. The radiative transfer model is extended by the addition of a Laplacian term in an attempt to model the effect of ensemble average pulse broadening. Numerical simulation results in support of this proposal are given, and applications for the theory suggested. Finally, the problem of acoustic wave scattering by planar screens is considered. The study was motivated by the idea that multiple scattering experiments may prove possible in a medium composed of such scatterers. Successful multiple scattering in a medium of planar scatterers will depend on the scattering cross-section at angles away from normal incidence. The scattering cross-section is calculated for a circular disc using a new technique for solving the acoustic wave equation on planar surfaces. The method is validated by comparison with available analytic solutions and the geometric theory of diffraction.

The theory of radiative transfer is applied to the problem of multiple wave scattering in a one-dimensional multilayer. A new mathematical model of a multilayer is presented in which both the refractive index and width of each layer are randomized. The layer widths are generated by a new probability distribution which allows for strong layer width disorder. An expression for the transport mean free path of the multilayer is derived based on its single-scattering properties. It will be shown that interference between the field reflected from adjacent layer interfaces remains significant even in the presence of strong layer width disorder. It will be proven that even when the scattering is weak, the field in a random multilayer localizes at certain frequencies. The effect of increasing layer width randomization on this form of localization is quantified. The radiative transfer model of time-harmonic scattering in multilayers is extended to narrow-band pulse propagation in weakly scattering media. The tendency of pulses to broaden in this medium is discussed. A radiative transport model of the system is developed and compared to numerical solutions of the wave equation. It is observed that pulse broadening is not described by simple transfer theory. The radiative transfer model is extended by the addition of a Laplacian term in an attempt to model the effect of ensemble average pulse broadening. Numerical simulation results in support of this proposal are given, and applications for the theory suggested. Finally, the problem of acoustic wave scattering by planar screens is considered. The study was motivated by the idea that multiple scattering experiments may prove possible in a medium composed of such scatterers. Successful multiple scattering in a medium of planar scatterers will depend on the scattering cross-section at angles away from normal incidence. The scattering cross-section is calculated for a circular disc using a new technique for solving the acoustic wave equation on planar surfaces. The method is validated by comparison with available analytic solutions and the geometric theory of diffraction.

Esta pesquisa consiste na solução do problema inverso de transferência radiativa para um meio participante (emissor, absorvedor e/ou espalhador) homogêneo unidimensional em uma camada, usando-se a combinação de rede neural artificial (RNA) com técnicas de otimização. A saída da RNA, devidamente treinada, apresenta os valores das propriedades radiativas [ω, τ0, ρ1 e ρ2] que são otimizadas através das seguintes técnicas: Particle Collision Algorithm (PCA), Algoritmos Genéticos (AG), Greedy Randomized Adaptive Search Procedure (GRASP) e Busca Tabu (BT). Os dados usados no treinamento da RNA são sintéticos, gerados através do problema direto sem a introdução de ruído. Os resultados obtidos unicamente pela RNA, apresentam um erro médio percentual menor que 1,64%, seria satisfatório, todavia para o tratamento usando-se as quatro técnicas de otimização citadas anteriormente, os resultados tornaram-se ainda melhores com erros percentuais menores que 0,04%, especialmente quando a otimização é feita por AG. / This research consists in the solution of the inverse problem of radiative transfer for a participating media (emmiting, absorbing and/or scattering) homogeneous one-dimensional in one layer, using the combination of artificial neural network (ANN), with optimization techniques. The output of the ANN, properly trained presents the values of the radiative properties [w, to, p1 e p2] that are optimized through the following techniques: Particle Collision Algorithm (PCA), Genetic Algorithm (GA), Greedy Randomized Adaptive Search Procedure (GRASP) and Tabu Search (TS). The data used in the training are synthetics, generated through the direct problem without the introduction of noise. The results obtained by the (ANN) alone, presents an average percentage error minor than 1,64%, what it would be satisfying, however, for the treatment using the four techniques of optimization aforementioned, the results have become even better with percentage errors minor than 0,03%, especially when the optimization is made by the GA.

Suite à la signature du Protocole de Montréal en 1987, la concentration atmosphérique des substances destructrices d’ozone (ODS) est en baisse. La couche d’ozone montre des signes de récupération (Morgenstern et al. 2008a). Toutefois, l’émission des gaz à effet de serre (GHG) est en augmentation et devrait affecter au cours du 21ème siècle la distribution et les niveaux d’ozone dans l’atmosphère terrestre. En particulier, la modélisation du climat futur montre des signes d’accélération de la circulation de Brewer-Dobson transportant l’ozone de l’équateur vers les pôles. L’ozone est un constituant chimique important de l’atmosphère. Bien que nocif dans la troposphère, il est essentiel à la vie sur Terre grâce à sa capacité d’absorption d’une grande partie du rayonnement ultraviolet (UV) provenant du Soleil. Des modifications dans sa variabilité temporelle ou géographique impliqueraient des changements d’intensité du rayonnement UV à la surface de la Terre (Hegglin et al. (2009), Bais et al. (2011)). Le rayonnement UV à la surface affecte toute la biosphère. Les interactions entre rayonnement UV et écosystèmes terrestres et aquatiques sont nombreuses. Ces interactions ont des effets sur les cycles biogéochimiques et engendrent des rétroactions positives et négatives sur le climat (Erickson III et al., 2015a). La capture du CO2 atmosphérique par photosynthèse des plantes terrestres en est un exemple (Zepp et al., 2007a). Dans l’océan la pompe biologique du CO2 par la photosynthèse du phytoplancton est aussi directement affecté par la variabilité du rayonnement UV (Hader et al., 2007a). Pour l’homme le rayonnement UV est nécessaire car il participe à la photosynthèse de la vitamine D (Holick et al., 1980), mais une surexposition à des niveaux d’intensité élevés du rayonnement UV est la cause principale du développement de cancer de la peau (Matsumura and Ananthaswamy, 2004). L’objectif de ce travail de thèse est d’analyser l’évolution possible du rayonnement UV au cours du 21ème siècle, en particulier aux tropiques sud, dans le cadre des modifications climatiques attendues. Une première partie de ce travail consiste à modéliser le rayonnement UV en ciel clair dans les tropiques grâce au modèle TUV (Madronich et al., 1998) et à comparer les résultats aux mesures sols réalisées à la Réunion. Cette première partie permet l’utilisation future du modèle aux tropiques avec un bon niveau de confiance. La sensibilité du modèle de transfert radiatif en fonction de différents paramètres d’entrée est analysée (section efficace d’absorption de l’ozone,spectre extraterrestriel du soleil, ...). Les sorties du modèle sont ensuite validées à partir de mesures UV spectral au sol obtenues grâce à un spectromètre BENTHAM DM300n. Un filtrage ciel-clair des données au sol est opéré à partir de mesures de flux et de l’algorithme de Long and Ackerman (2000). Les projections climatiques des indices UV (Mc Kinlay and Diffey, 1987) sont réalisées par la suite. Pour cela, on utilise les sorties de plusieurs modèles de Chimie-Climat participant à l’exercice d’inter-comparaison CCMI (Chemistry Climate Model Initiative), couplées aux modèle TUV, validé en première partie dans les tropiques. L’exercice CCMI consiste à projeter le climat et la chimie Terrestre jusqu’en 2100 selon différents scénarios. Ces sorties décrivant la chimie et physique de l’atmosphère servent d’entrée au modèle de transfert radiatif, on obtient alors le rayonnement UV jusqu’en 2100 pour différents scénarios. Une première analyse comparative de l’UV obtenue pour quatre scénarios d’émissions (RCP2.6/4./6.0/8.5, Meinshausen et al., 2011) est effectuée. La fin du travail consiste à étudier l’impact des ODS, GHG et aérosols sur l’évolution du rayonnement UV au cours du 21ème siècle, avec un focus particulier sur les tropiques de l’hémisphère sud. / Following the 1987 Montreal Protocol, atmospheric concentrations of ozone-depleting substances are decreasing. The ozone layer shows signs of recovery. Nonetheless, greenhouse gases emissions (GHG) are rising et should affect the ozone distribution in the atmosphere. Ozone is an important due to his ability to absorb ultraviolet (UV) radiation. The goal of this work is to analyse the possible evolution of UV radiation through the 21st century, particularly in the tropics, for possible climate modification. The first part of this work is to UV in clear-sky in the tropics with the TUV (Madronich et al., 1998) model and to compare against ground-based observations made on Reunion Island. This validation allows the utilisation of TUV in the tropics with a good confidence level. The sensitivity of the model is analysed for multiple parameters. Modelling output is validated against spectral ground-based measurement. Climate Projection of UVI (Mc Kinlay and Diffey, 1987) are then realized with the use of output from model participating in the CCMI ( Model Initiative) exercise and the TUV model. CCMI output describes the chemistry and physics of the atmosphere through the 21st century for four climate scenarios (RCP2.6/4.5/6.0/8.5), they are used as input for the TUV model in order to obtain UV radiation. ODS, GHG and aerosols impact on UVI evolution is analysed.

L'ingénierie de la photosynthèse est une voie prometteuse en vue de produire à la fois des vecteurs énergétiques et des molécules plateformes pour palier la raréfaction des ressources fossiles. Le défi à relever est de taille car il faut réussir à mettre au point des procédés solaires de production de biomasse à constante de temps courte (quelques jours), là où une centaine de millions d'années a été nécessaire à la formation du pétrole. Cet objectif pourrait être atteint en cultivant des micro-organismes photosynthétiques dans des photobioréacteurs dont les performances cinétiques en surface et en volume seraient optimales. Une telle optimisation nécessite avant tout une analyse fine des transferts radiatifs au sein du procédé. L'analyse radiative des photobioréacteurs qui est ici proposée s'ouvre sur la détermination des propriétés d'absorption et de diffusion des suspensions de micro-organismes photosynthétiques, à partir de leurs caractéristiques morphologiques, métaboliques et structurales. Une chaîne de modélisation est construite, mise en oeuvre et validée expérimentalement pour des micro-organismes de formes simples ; à terme, la démarche développée pourra directement être étendue à des formes plus complexes. Puis, l'analyse du transfert radiatif en diffusion multiple est introduite et illustrée par différentes approximations qui apparaissent pertinentes pour une conceptualisation des photobioréacteurs, menant ainsi à la construction d'un intuitif nécessaire à leur optimisation. Enfin, la méthode de Monte Carlo est mise en oeuvre afin de résoudre rigoureusement la diffusion multiple en géométries complexes (géométries qui découlent d'une conception optimisée du procédé) et afin de calculer les performances cinétiques à l'échelle du photobioréacteur. Ce dernier calcul utilise une avancée méthodologique qui permet de traiter facilement le couplage non-linéaire du transfert radiatif à la cinétique locale de la photosynthèse (et qui laisse entrevoir de nombreuses autres applications dans d'autres domaines de la physique du transport). Ces outils de simulation mettent à profit les développements les plus récents autour de la méthode de Monte Carlo, tant sur le plan informatique (grâce à une implémentation dans l'environnement de développement EDStar) que sur le plan algorithmique : formulation intégrale, algorithmes à zéro-variance, calcul de sensibilités (le calcul des sensibilités aux paramètres géométriques est ici abordé d'une manière originale qui permet de simplifier significativement sa mise en oeuvre, pour un ensemble de configurations académiques testées). Les perspectives de ce travail seront d'utiliser les outils d'analyse développés durant cette thèse afin d'alimenter une réflexion sur l'intensification des photobioréacteurs, et d'étendre la démarche proposée à l'étude des systèmes photoréactifs dans leur ensemble. / Photosynthesis engineering is a promising mean to produce both energy carriers and fine chemicals in order to remedy the growing scarcity of fossil fuels. This is a challenging task since it implies to design process for solar biomass production associated with short time constant (few days), while oil formation took hundred million of years. This aim could be achieved by cultivating photosynthetic microorganisms in photobioreactors with optimal surface and volume kinetic performances. Above all, such an optimization necessitate a careful radiative study of the process. A radiative analysis of photobioreactors is here proposed that starts with the determination of the absorption and scattering properties of photosynthetic microorganisms suspensions, from the knowledge their morphological, metabolic and structural features. A model is constructed, implemented and validated for microorganisms with simple shapes ; the extension of this approach for the treatment of complex shapes will eventually be straightforward. Then, multiple scattering radiative transfer analysis is introduced and illustrated through different approximations that are relevant for the conceptualization of photobioreactors, leading to the construction of physical pictures that are necessary for the optimization of the process. Finally, the Monte Carlo method is implemented in order to rigorously solve multiple scattering in complex geometries (geometries that correspond to an optimized design of the process) and in order to calculate the kinetic performances of the reactor. In this trend, we develop a novel methodological development that simplies the treatment of the non-linear coupling between radiative transfer and the local kinetic of photosynthesis. These simulation tools also benefit from the most recent developments in the field of the Monte Carlo method : integral formulation, zero-variance algorithms, sensitivity evaluation (a specific approach for the evaluation of sensitivities to geometrical parameters is here developed and shown to correspond to a simple implementation in the case of a set of academic configurations that are tested). Perspectives of this work will be to take advantage of the developed analysis tools in order to stimulate the reflexion regarding photobioreactor intensification, and to extend the proposed approach to the study of photoreactive systems engineering in general.

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / A formulação explícita matricial desenvolvida nesta tese de doutorado foi proposta visando ser uma alternativa na solução de Problemas Inversos de estimativa de propriedades radiativas em meios participantes homogêneos unidimensionais usando a Equação de Transferência Radiativa para modelar a interação da radiação com o meio participante. A equação de transporte é formulada em forma matricial e o domínio angular é discretizado usando conceitos do método de ordenadas discretas e a expansão da função de fase do espalhamento anisotrópico em uma série de polinômios de Legendre. A formulação proposta consiste em uma formulação explícita para o problema inverso. Um arranjo apropriado das condições de contorno prescritas (fluxos incidentes) e dos fluxos emergentes nos contornos de uma placa permitem o cálculo direto do operador de transmissão, do operador albedo e do operador de colisão. A partir do operador de colisão calculado são obtidos os valores estimados dos coeficientes de extinção total e de espalhamento. São apresentadas as formulações para problemas em regime estacionário e em regime transiente, bem como os resultados para alguns casos-teste. / The explicit matrix formulation developed in the present thesis has been proposed as an alternative for the solution of Inverse Problems for radiative properties estimation in one-dimensional homogeneous participating media using Radiative transfer equation for the modeling of the radiation interaction with the participating medium. This transport equation is formulated in a matrix form and the angular domain is discretized using concepts of the discrete ordinates methods and the expansion of the function of phase function of anisotropic scattering in a series of Legendre polynomial. The formulation proposed consists on an explicit formulation for the inverse problem. An adequate assembly of the prescribed boundary conditions (incidents flux) and of the emerging flux at the boundaries of the slab allows the direct computation of the transmission, albedo and collision operators. From the computed collision operator estimated values for total extinction and scattering coefficients are obtained. The formulations for steady state and transient situations are presented, as well as test case results.

Nesta tese é proposta uma implementação para a solução do problema inverso com as estimativas das propriedades radiativas (o albedo de espalhamento simples, a espessura ótica do meio e as reflectividades difusas) a partir dos valores das intensidades de radiação que deixam o meio participante utilizando uma abordagem híbrida de sistemas neuro-fuzzy (SNF), o qual combina a utilização de sistemas de inferência fuzzy com as redes neurais artificiais. Busca-se com a utilização desse sistema híbrido integrar a habilidade dos sistemas fuzzy no tratamento de informações inexatas, imprecisas, e vagas, e a capacidade das redes neurais artificiais de tratar o aprendizado por experiência e a generalização do conhecimento. É proposta também uma metodologia de máquinas de comitês neuro-fuzzy na solução deste problema inverso em transferência radiativa. Foi observado paralelamente que a solução dos sistemas neuro-fuzzy e dos sistemas híbridos de máquinas de comitê neuro-fuzzy, apresentam baixa qualidade nos resultados quando são utilizados os dados experimentais com os menores coeficientes de sensibilidade para os parâmetros que serão estimados. Por outro lado, quando são utilizados dados com maior sensibilidade, são obtidos melhores resultados. Esta abordagem procura evitar a possibilidade da não convergência desses métodos. / In this thesis is proposed an implementation for solving the inverse problem with the estimates of radiative properties (the single scattering albedo, the optical thickness of the media and the diffuse reflectivities) by the values of the intensities of radiation that leaves the participant medium using a hybrid approach of neuro-fuzzy systems, which combines the use of fuzzy inference systems with artificial neural networks. The use of this hybrid system try to include the ability of fuzzy systems in the treatment of inaccurate, imprecise, and vague data, and the ability of artificial neural networks to deal with learning from experience and widespread knowledge. Also is proposed a methodology for machines committees in neuro-fuzzy solution of this inverse problem in radiative transfer. It was observed in parallel that the solution of neuro-fuzzy systems and hybrid systems neuro-fuzzy committee machines, have a poor quality results when using the experimental data with the lowest sensitivity coefficients for the parameters that will be estimated. Moreover, when data are used with greater sensitivity, better results are obtained. This approach seeks to avoid the possibility of non-convergence in such methods.