Tsunami is one of the most dangerous natural hazards in the coastal zone worldwide. Large tsunamis are relatively infrequent. Deposits are the only concrete evidence in the geological record with which we can determine both tsunami frequency and magnitude. Numerical modeling of sediment transport during a tsunami is important interdisciplinary research to estimate the frequency and magnitude of past events and quantitative prediction of future events. The goal of this dissertation is to develop robust, accurate, and computationally efficient models for sediment transport during a tsunami. There are two different modeling approaches (forward and inverse) to investigate sediment transport. A forward model consists of tsunami source, hydrodynamics, and sediment transport model. In this dissertation, we present one state-of-the-art forward model for Sediment TRansport In Coastal Hazard Events (STRICHE), which couples with GeoClaw and is referred to as GeoClaw-STRICHE. In an inverse model, deposit characteristics, such as grain-size distribution and thickness, are inputs to the model, and flow characteristics are outputs. We also depict one trial-and-error inverse model (TSUFLIND) and one data assimilation inverse model (TSUFLIND-EnKF) in this dissertation. All three models were validated and verified against several theoretical, experimental, and field cases. / Ph. D.

My research focuses on reconstructing past climate in southern Arizona using cave deposits called speleothems. However, this necessitates a broader perspective than simply a geochemical time series, and therefore, I also investigate modern cave systems using a combination of modeling and observational datasets. Finally, cave deposits are fundamentally non-renewable resources, and sampling for past climate reconstruction can be destructive, unlike other cave uses. My last investigation is focused on developing possible best practice recommendations for paleoclimate scientists and other cave stakeholders moving forward. We developed two new stalagmite records of past climate variability in southern Arizona over the past 7000 years. Past climate reconstruction from two caves (Cave of the Bells and Fort Huachuca Cave) highlights insolation control of southern Arizona hydroclimate from 7000-2000 years before present. Additionally, comparison between two stalagmites with different seasonal sensitivities uncovers a few eras of multi-decade long droughts in southern Arizona, which align with other regional reconstructions of past climates and elucidate forcings on Southwest paleoclimate as emergent from both external (insolation) and internal climate variability in the Pacific and Atlantic Ocean basins. Although the oxygen isotopic signal of cave calcite in speleothems is complex, agreement with these other records indicates that the speleothem records from these caves primarily record a climate signal.Modeling and monitoring of modern caves both helps us interpret paleoclimate records and enhances our understanding of cave systems in their own right. Modeling of Cave of the Bells dripwaters demonstrates the effect of storage and mixing on the dripwater oxygen isotope signal; non-climate processes can imprint on dripwater variability on multidecadal timescales. Monitoring shows that on very small spatial scales, every cave is different, and even sites within the same cave respond uniquely to surface climate. Most notably, calcite oxygen isotopic composition, used to reconstruct past climate, shows seasonal variability unrelated to dripwater and surface rainfall oxygen isotope variability. Substantial oxygen isotope disequilibrium is identified at numerous caves sites in southern Arizona, and this understanding aligns with a growing number of cave studies that demonstrate the long-held assumption of isotopic equilibrium in cave systems may not always be valid or that the way in which we define isotopic equilibrium insufficiently captures the variety of processes controlling the oxygen isotopic composition of speleothems. Overall, however, monitoring can identify stalagmites that are more sensitive to surface climate and less sensitive to these in-cave processes by identifying sites with dripwater variability responses to surface rainfall variability and sites that precipitate close to oxygen isotopic equilibrium. Finally, a major missing component in speleothem research is the fact that speleothems take thousands and sometimes hundreds of thousands of years to form. They are non-renewable resources on human timescales, and habitat for myriad microbes that have yet to be identified. Removal of speleothems for paleoclimate research is one of the only destructive uses of these deposits. With that in mind, I also analyze current methods of collecting speleothems and develop a framework based on two surveys of scientists and stakeholders to assist scientists and managers when evaluating potential methods of incorporating cave conservation into the speleothem sampling process. Thus, I approach caves from a variety of angles and timescales, from the past through the present to the future, illuminating caves as complex scientific and social systems.

No description available.

Muscle spindles are complex sensory organs that have been strongly implicated in the control and perception of movements. Human muscle spindles in relaxed muscles behave as stretch receptors, responding to the length and velocity of their parent muscles. However, it has been unclear how they discharge during active movements since their discharges are also affected by fusimotor activity and extrafusal contractions. The vast majority of neurophysiological recordings of muscle afferents have been obtained under passive conditions, or active but behaviourally restricted conditions. These restrictions prevent predictions of human muscle afferent activity during purposeful multi-joint movements, naturally occurring during tasks such as hand shaping, grasping or key-pressing. An experimental protocol was therefore developed which allowed recordings of muscle receptor afferent activity using microneurography during unrestrained wrist and digit movements. Along with single afferent discharges, recordings were obtained of electromyographic activity of major forearm muscles and the kinematics of the wrist and digits. This approach allowed investigations of the factors shaping afferent discharge during everyday manual tasks, i.e., block-grasping and pressing sequences of keys, and during active sinusoidal joint movements. The afferents’ ability to encode information concerning the state of the muscle and joint kinematics during these tasks was also assessed. The responses of spindle afferents from load-bearing muscles were approximatelly 90 degrees more phase-advanced than expected on the length of their parent muscles. That is, the discharges of primary muscle spindle afferents were significantly affected by both velocity and acceleration, the discharges of secondary afferents by velocity, and neither afferent type was particularly affected by static muscle length. Accordingly, these afferents failed to encode length, encoded velocity well and acceleration poorly. The representation of muscle length and velocity was, however, significantly improved when the discharge activity of Golgi tendon afferents was taken into consideration along with muscle spindle activity. The discharge of primary afferents during both key-pressing and block-grasping was best correlated to the muscle velocities observed ~100-160 ms in the future. This predictive ability went beyond what could be expected from the spindles’ simultaneous sensitivity to velocity and acceleration, and could thus only be explained by implicating the fusimotor drive. In addition, evidence is presented that the fusimotor control of spindles was contingent on entire movement sequences during the key-pressing task. It is proposed that the phase relationship between the discharge rate of spindle afferents and the length of their parent muscles is load dependent. Moreover, muscle spindles seem to act as forward sensory models of their parent muscle, which makes sensorial feedback control possible despite neural delays.

Conditioning geologic models to production data and assessment of uncertainty is generally done in a Bayesian framework. The current Bayesian approach suffers from three major limitations that make it impractical for field-scale applications. These are: first, the CPU time scaling behavior of the Bayesian inverse problem using the modified Gauss-Newton algorithm with full covariance as regularization behaves quadratically with increasing model size; second, the sensitivity calculation using finite difference as the forward model depends upon the number of model parameters or the number of data points; and third, the high CPU time and memory required for covariance matrix calculation. Different attempts were used to alleviate the third limitation by using analytically-derived stencil, but these are limited to the exponential models only. We propose a fast and robust adaptation of the Bayesian formulation for inverse modeling that overcomes many of the current limitations. First, we use a commercial finite difference simulator, ECLIPSE, as a forward model, which is general and can account for complex physical behavior that dominates most field applications. Second, the production data misfit is represented by a single generalized travel time misfit per well, thus effectively reducing the number of data points into one per well and ensuring the matching of the entire production history. Third, we use both the adjoint method and streamline-based sensitivity method for sensitivity calculations. The adjoint method depends on the number of wells integrated, and generally is of an order of magnitude less than the number of data points or the model parameters. The streamline method is more efficient and faster as it requires only one simulation run per iteration regardless of the number of model parameters or the data points. Fourth, for solving the inverse problem, we utilize an iterative sparse matrix solver, LSQR, along with an approximation of the square root of the inverse of the covariance calculated using a numerically-derived stencil, which is broadly applicable to a wide class of covariance models. Our proposed approach is computationally efficient and, more importantly, the CPU time scales linearly with respect to model size. This makes automatic history matching and uncertainty assessment using a Bayesian framework more feasible for large-scale applications. We demonstrate the power and utility of our approach using synthetic cases and a field example. The field example is from Goldsmith San Andres Unit in West Texas, where we matched 20 years of production history and generated multiple realizations using the Randomized Maximum Likelihood method for uncertainty assessment. Both the adjoint method and the streamline-based sensitivity method are used to illustrate the broad applicability of our approach.

L’objectif principal de la présente thèse était de déterminer les facteurs susceptibles d’influencer l’efficacité des processus de contrôle en ligne des mouvements d’atteinte manuelle. De nos jours, les mouvements d’atteinte manuelle réalisés dans un environnement virtuel (déplacer une souris d’ordinateur pour contrôler un curseur à l’écran, par exemple) sont devenus chose commune. Par comparaison aux mouvements réalisés en contexte naturel (appuyer sur le bouton de mise en marche de l’ordinateur), ceux réalisés en contexte virtuel imposent au système nerveux central des contraintes importantes parce que l’information visuelle et proprioceptive définissant la position de l’effecteur n’est pas parfaitement congruente. Par conséquent, la présente thèse s’articule autour des effets d’un contexte virtuel sur le contrôle des mouvements d’atteinte manuelle. Dans notre premier article, nous avons tenté de déterminer si des facteurs tels que (a) la quantité de pratique, (b) l’orientation du montage virtuel (aligné vs. non-aligné) ou encore (c) l’alternance d’un essai réalisé avec et sans la vision de l’effecteur pouvaient augmenter l’efficacité des processus de contrôle en ligne de mouvement réalisés en contexte virtuel. Ces facteurs n’ont pas influencé l’efficacité des processus de contrôle de mouvements réalisés en contexte virtuel, suggérant qu’il est difficile d’optimiser le contrôle des mouvements d’atteinte manuelle lorsque ceux-ci sont réalisés dans un contexte virtuel. L’un des résultats les plus surprenants de cette étude est que nous n’avons pas rapporté d’effet concernant l’orientation de l’écran sur la performance des participants, ce qui était en contradiction avec la littérature existante sur ce sujet. L’article 2 avait pour but de pousser plus en avant notre compréhension du contrôle du mouvement réalisé en contexte virtuel et naturel. Dans le deuxième article, nous avons mis en évidence les effets néfastes d’un contexte virtuel sur le contrôle en ligne des mouvements d’atteinte manuelle. Plus précisément, nous avons observé que l’utilisation d’un montage non-aligné (écran vertical/mouvement sur un plan horizontal) pour présenter l’information visuelle résultait en une importante diminution de la performance comparativement à un montage virtuel aligné et un montage naturel. Nous avons aussi observé une diminution de la performance lorsque les mouvements étaient réalisés dans un contexte virtuel aligné comparativement à un contexte naturel. La diminution de la performance notée dans les deux conditions virtuelles s’expliquait largement par une réduction de l’efficacité des processus de contrôle en ligne. Nous avons donc suggéré que l’utilisation d’une représentation virtuelle de la main introduisait de l’incertitude relative à sa position dans l’espace. Dans l’article 3, nous avons donc voulu déterminer l’origine de cette incertitude. Dans ce troisième article, deux hypothèses étaient à l’étude. La première suggérait que l’augmentation de l’incertitude rapportée dans le contexte virtuel de la précédente étude était due à une perte d’information visuelle relative à la configuration du bras. La seconde suggérait plutôt que l’incertitude provenait de l’information visuelle et proprioceptive qui n’est pas parfaitement congruente dans un contexte virtuel comparativement à un contexte naturel (le curseur n’est pas directement aligné avec le bout du doigt, par exemple). Les données n’ont pas supporté notre première hypothèse. Plutôt, il semble que l’incertitude soit causée par la dissociation de l’information visuelle et proprioceptive. Nous avons aussi démontré que l’information relative à la position de la main disponible sur la base de départ influence largement les processus de contrôle en ligne, même lorsque la vision de l’effecteur est disponible durant le mouvement. Ce résultat suggère que des boucles de feedback interne utilisent cette information afin de moduler le mouvement en cours d’exécution. / The main objective of this thesis was to identify factors that may influence the effectiveness of the online control processes of manual reaching movements. Nowadays, producing manual movements made in a virtual environment (moving a computer mouse to control a cursor on the screen, for example) have become commonplace. As compared to movements made in natural settings (pushing the start button on the computer), those made in virtual context pose serious challenges to the central nervous system because the proprioceptive and visual information defining the position of the effector is not perfectly congruent. This thesis focuses on the effects of a virtual environment on the control of manual reaching movements. In our first article, we examined whether such factors as (a) the amount of practice, (b) the orientation of the virtual display (aligned vs. non-aligned) or (c) the availability of the visual feedback on alternated trials could increase the efficiency of online control processes of movements made under virtual context. These factors did not influence the effectiveness of process control movements made in virtual context, suggesting that it is difficult to optimize the control of manual reaching movements when they are made under a virtual context. One of the most surprising results of this study is that we have not reported detrimental effects of screen orientation on the performance of participants, which was inconsistent with the existing literature on this subject. Section 2 was intended to push forward our understanding of online control processes of movements made in virtual and natural contexts. In the second article, we highlighted the adverse effects of a virtual environment on the online control of manual reaching movements. More specifically, we observed that the use of a non-aligned display to present visual information resulted in a significant decrease in performance as compared to an aligned or natural display. We also observed a decrease in performance when the movements were performed in a virtual aligned display as compared to a natural context. The decrease in performance observed in the two virtual conditions was largely due to a decrease of the effectiveness of online control processes. We therefore suggest that the use of a virtual representation of the hand introduced uncertainty as to its position in space, which in turn led to less efficient online control. In our third article, we wanted to determine the origin of this uncertainty and how it impacted on movement control. In the third article, two hypotheses were considered. The first suggested that the increase in uncertainty reported in the virtual context of the previous study was due to loss of visual information relative to the configuration of the arm. The second suggested instead that the uncertainty came from the proprioceptive and visual information that is not perfectly congruent in a virtual context as compared to a natural one (the cursor is not directly aligned with the finger for example). The data have not supported our first hypothesis. It rather appears that the uncertainty is caused by the dissociation of visual and proprioceptive information. We also demonstrated that the information on the starting base on the position of the hand greatly influences the control process online, even when vision is available during the effector movement. This result suggests that internal feedback loops use this information to modulate the ongoing movement.

L’objectif principal de la présente thèse était de déterminer les facteurs susceptibles d’influencer l’efficacité des processus de contrôle en ligne des mouvements d’atteinte manuelle. De nos jours, les mouvements d’atteinte manuelle réalisés dans un environnement virtuel (déplacer une souris d’ordinateur pour contrôler un curseur à l’écran, par exemple) sont devenus chose commune. Par comparaison aux mouvements réalisés en contexte naturel (appuyer sur le bouton de mise en marche de l’ordinateur), ceux réalisés en contexte virtuel imposent au système nerveux central des contraintes importantes parce que l’information visuelle et proprioceptive définissant la position de l’effecteur n’est pas parfaitement congruente. Par conséquent, la présente thèse s’articule autour des effets d’un contexte virtuel sur le contrôle des mouvements d’atteinte manuelle. Dans notre premier article, nous avons tenté de déterminer si des facteurs tels que (a) la quantité de pratique, (b) l’orientation du montage virtuel (aligné vs. non-aligné) ou encore (c) l’alternance d’un essai réalisé avec et sans la vision de l’effecteur pouvaient augmenter l’efficacité des processus de contrôle en ligne de mouvement réalisés en contexte virtuel. Ces facteurs n’ont pas influencé l’efficacité des processus de contrôle de mouvements réalisés en contexte virtuel, suggérant qu’il est difficile d’optimiser le contrôle des mouvements d’atteinte manuelle lorsque ceux-ci sont réalisés dans un contexte virtuel. L’un des résultats les plus surprenants de cette étude est que nous n’avons pas rapporté d’effet concernant l’orientation de l’écran sur la performance des participants, ce qui était en contradiction avec la littérature existante sur ce sujet. L’article 2 avait pour but de pousser plus en avant notre compréhension du contrôle du mouvement réalisé en contexte virtuel et naturel. Dans le deuxième article, nous avons mis en évidence les effets néfastes d’un contexte virtuel sur le contrôle en ligne des mouvements d’atteinte manuelle. Plus précisément, nous avons observé que l’utilisation d’un montage non-aligné (écran vertical/mouvement sur un plan horizontal) pour présenter l’information visuelle résultait en une importante diminution de la performance comparativement à un montage virtuel aligné et un montage naturel. Nous avons aussi observé une diminution de la performance lorsque les mouvements étaient réalisés dans un contexte virtuel aligné comparativement à un contexte naturel. La diminution de la performance notée dans les deux conditions virtuelles s’expliquait largement par une réduction de l’efficacité des processus de contrôle en ligne. Nous avons donc suggéré que l’utilisation d’une représentation virtuelle de la main introduisait de l’incertitude relative à sa position dans l’espace. Dans l’article 3, nous avons donc voulu déterminer l’origine de cette incertitude. Dans ce troisième article, deux hypothèses étaient à l’étude. La première suggérait que l’augmentation de l’incertitude rapportée dans le contexte virtuel de la précédente étude était due à une perte d’information visuelle relative à la configuration du bras. La seconde suggérait plutôt que l’incertitude provenait de l’information visuelle et proprioceptive qui n’est pas parfaitement congruente dans un contexte virtuel comparativement à un contexte naturel (le curseur n’est pas directement aligné avec le bout du doigt, par exemple). Les données n’ont pas supporté notre première hypothèse. Plutôt, il semble que l’incertitude soit causée par la dissociation de l’information visuelle et proprioceptive. Nous avons aussi démontré que l’information relative à la position de la main disponible sur la base de départ influence largement les processus de contrôle en ligne, même lorsque la vision de l’effecteur est disponible durant le mouvement. Ce résultat suggère que des boucles de feedback interne utilisent cette information afin de moduler le mouvement en cours d’exécution. / The main objective of this thesis was to identify factors that may influence the effectiveness of the online control processes of manual reaching movements. Nowadays, producing manual movements made in a virtual environment (moving a computer mouse to control a cursor on the screen, for example) have become commonplace. As compared to movements made in natural settings (pushing the start button on the computer), those made in virtual context pose serious challenges to the central nervous system because the proprioceptive and visual information defining the position of the effector is not perfectly congruent. This thesis focuses on the effects of a virtual environment on the control of manual reaching movements. In our first article, we examined whether such factors as (a) the amount of practice, (b) the orientation of the virtual display (aligned vs. non-aligned) or (c) the availability of the visual feedback on alternated trials could increase the efficiency of online control processes of movements made under virtual context. These factors did not influence the effectiveness of process control movements made in virtual context, suggesting that it is difficult to optimize the control of manual reaching movements when they are made under a virtual context. One of the most surprising results of this study is that we have not reported detrimental effects of screen orientation on the performance of participants, which was inconsistent with the existing literature on this subject. Section 2 was intended to push forward our understanding of online control processes of movements made in virtual and natural contexts. In the second article, we highlighted the adverse effects of a virtual environment on the online control of manual reaching movements. More specifically, we observed that the use of a non-aligned display to present visual information resulted in a significant decrease in performance as compared to an aligned or natural display. We also observed a decrease in performance when the movements were performed in a virtual aligned display as compared to a natural context. The decrease in performance observed in the two virtual conditions was largely due to a decrease of the effectiveness of online control processes. We therefore suggest that the use of a virtual representation of the hand introduced uncertainty as to its position in space, which in turn led to less efficient online control. In our third article, we wanted to determine the origin of this uncertainty and how it impacted on movement control. In the third article, two hypotheses were considered. The first suggested that the increase in uncertainty reported in the virtual context of the previous study was due to loss of visual information relative to the configuration of the arm. The second suggested instead that the uncertainty came from the proprioceptive and visual information that is not perfectly congruent in a virtual context as compared to a natural one (the cursor is not directly aligned with the finger for example). The data have not supported our first hypothesis. It rather appears that the uncertainty is caused by the dissociation of visual and proprioceptive information. We also demonstrated that the information on the starting base on the position of the hand greatly influences the control process online, even when vision is available during the effector movement. This result suggests that internal feedback loops use this information to modulate the ongoing movement.

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.

Cette thèse traite un problème inverse en astronomie. L’objectif est de reconstruire un objet 2D+λ, ayant une distribution spatiale et spectrale, à partir d’un ensemble de données multispectrales de basse résolution fournies par l’imageur MIRI (Mid-InfraRed Instrument), qui est à bord du prochain télescope spatial James Webb Space Telescope (JWST). Les données multispectrales observées souffrent d’un flou spatial qui dépend de la longueur d’onde. Cet effet est dû à la convolution par la réponse optique (PSF). De plus, les données multi-spectrales souffrent également d’une sévère dégradation spectrale en raison du filtrage spectral et de l’intégration par le détecteur sur de larges bandes. La reconstruction de l’objet original est un problème mal posé en raison du manque important d’informations spectrales dans l’ensemble de données multispectrales. La difficulté se pose alors dans le choix d’une représentation de l’objet permettant la reconstruction de l’information spectrale. Un modèle classique utilisé jusqu’à présent considère une PSF invariante spectralement par bande, ce qui néglige la variation spectrale de la PSF. Cependant, ce modèle simpliste convient que dans le cas d’instrument à une bande spectrale très étroite, ce qui n’est pas le cas pour l’imageur de MIRI. Notre approche consiste à développer une méthode pour l’inversion qui se résume en quatre étapes : (1) concevoir un modèle de l’instrument reproduisant les données multispectrales observées, (2) proposer un modèle adapté pour représenter l’objet à reconstruire, (3) exploiter conjointement l’ensemble des données multispectrales, et enfin (4) développer une méthode de reconstruction basée sur la régularisation en introduisant des priori à la solution. Les résultats de reconstruction d’objets spatio-spectral à partir de neuf images multispectrales simulées de l’imageur de MIRI montrent une augmentation significative des résolutions spatiale et spectrale de l’objet par rapport à des méthodes conventionnelles. L’objet reconstruit montre l’effet de débruitage et de déconvolution des données multispectrales. Nous avons obtenu une erreur relative n’excédant pas 5% à 30 dB et un temps d’exécution de 1 seconde pour l’algorithme de norm-l₂ et 20 secondes avec 50 itérations pour l’algorithme norm-l₂/l₁. C’est 10 fois plus rapide que la solution itérative calculée par l’algorithme de gradient conjugué. / This thesis deals with an inverse problem in astronomy. The objective is to reconstruct a spatio-spectral object, having spatial and spectral distributions, from a set of low-resolution multispectral data taken by the imager MIRI (Mid-InfraRed Instrument), which is on board the next space telescope James Webb Space Telescope (JWST). The observed multispectral data suffers from a spatial blur that varies according to the wavelength due to the spatial convolution with a shift-variant optical response (PSF). In addition the multispectral data also suffers from severe spectral degradations because of the spectral filtering and the integration by the detector over broad bands. The reconstruction of the original object is an ill-posed problem because of the severe lack of spectral information in the multispectral dataset. The difficulty then arises in choosing a representation of the object that allows the reconstruction of this spectral information. A common model used so far considers a spectral shift-invariant PSF per band, which neglects the spectral variation of the PSF. This simplistic model is only suitable for instruments with a narrow spectral band, which is not the case for the imager of MIRI. Our approach consists of developing an inverse problem framework that is summarized in four steps: (1) designing an instrument model that reproduces the observed multispectral data, (2) proposing an adapted model to represent the sought object, (3) exploiting all multispectral dataset jointly, and finally (4) developing a reconstruction method based on regularization methods by enforcing prior information to the solution. The overall reconstruction results obtained on simulated data of the JWST/MIRI imager show a significant increase of spatial and spectral resolutions of the reconstructed object compared to conventional methods. The reconstructed object shows a clear denoising and deconvolution of the multispectral data. We obtained a relative error below 5% at 30 dB, and an execution time of 1 second for the l₂-norm algorithm and 20 seconds (with 50 iterations) for the l₂/l₁-norm algorithm. This is 10 times faster than the iterative solution computed by conjugate gradients.

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.:1.1. Radiation Transport Modeling and Atmospheric State Inversion 1.2. Vector RTE Solution Methods 1.3. Scope of the Thesis 1.4. Outline of the Thesis 2.1. General Structure 2.1.1. Chemical Composition of the Gas Phase 2.1.2. The Troposphere, Temperature and Pressure Vertical Structure 2.1.3. The Stratosphere 2.2. Aerosols and Clouds 2.2.1. Classification and Morphology 2.2.2. Water Related Particle Growth and Shrinking Processes 2.2.3. Size Spectra and Modes 3.1. Electromagnetic Waves 3.1.1. Maxwell\''s Equations 3.1.2. Measurement of Electromagnetic Waves 3.1.3. Polarization State of EM Waves 3.1.4. Stokes Vectors 3.2. Scattering and Absorption of EM Waves by Molecules and Particles 3.2.1. General Description of Scattering and Coordinate Systems 3.2.2. Molecular Scattering 3.2.3. Molecular Absorption Processes and Electronic Molecular States 3.2.4. Scattering On Spherical Particles - Mie Theory 3.3. Mathematical Description of Radiation Transport 3.3.1. Radiance and Irradiance 3.3.2. Absorption, Scattering and Extinction Coefficients 3.3.3. Optical Thickness and Transmission 3.3.4. Scattering 3.3.5. Incident (Ir)Radiance 3.3.6. The Black Surface Single Scattering Approximation 3.3.7. Radiative Transfer Equations 4.1. General Monte Carlo Methods 4.1.1. Numerical Integration 4.1.2. Importance Sampling and Zero Variance Estimates 4.1.3. Optimal Sampling 4.1.4. Sampling from Arbitrary Distributions 4.2. Path Generation or Collision Density Estimation 4.2.1. Discretization of the Optical Domain into Cells and Clusters 4.2.2. RTE Integral Form 4.2.3. Formal Solution of the IRTE 4.2.4. Overview on Monte Carlo RTE Solution Algorithms 4.2.5. Crude Monte Carlo 4.2.6. Sequential Importance Sampling (SIS) or Path Generation 4.3. Importance Sampling in Monte Carlo SIS Radiative Transfer 4.3.1. Weights for Alternate Kernels 4.3.2. Weights in the Calculation of RTE Functional Estimates 4.3.3. Application of IS to Mie Phase Functions Scatter Angle Sampling 5.1. Radiances, Intensities and the Reciprocity Theorem 5.1.1. Scalar Radiance Estimates 5.1.2. Backward Monte Carlo Scalar Radiance 5.1.3. Vector Radiances 5.2. Radiance Derivatives 5.2.1. Variables for Radiance Derivatives 5.3. Validation of Functionals 5.3.1. Validation of Vector Radiances 5.3.2. Validation of Radiance Derivatives 6.1. A Simply Structured Instrument Forward Model 6.2. Pure Atmospheric Spectra and Absorption 6.2.1. Direct Light Spectra 6.2.2. Scattered Sun Light Spectra 6.3. (D)OAS from the Perspective of Radiative Transfer Modeling 6.3.1. (Rest) Signatures of Weakly Absorbing Gases 6.3.2. Spectroscopic Measurements and Standard DOAS 6.4. DOAS Analysis Summary 6.4.1. DSCD Retrieval 6.4.2. Inversion 7.1. RRS-Modified RTE 7.1.1. RRS Cross Sections for Scattering out and into a Wavelength 7.1.2. Modification of the RTE Loss and Source Terms 7.2. Intensity Estimates Considering Rotational Raman Scattering 7.2.1. RRS in the Path Sampling Procedure 7.2.2. Adjoint RRS Correction Weights 7.2.3. Local Estimates of Intensities with RRS 7.2.4. Intensity Estimates 7.3. Ring Spectra 7.3.1. Elastic Biasing of the Local Estimates 7.3.2. Cumulative Weights and Local Estimates 7.3.3. Test of the Elastic Biasing 7.4. Validation 7.4.1. Comparison to an Analytic Single Scattering Code 7.4.2. Single Scattering Model Including Rotational Raman Scattering 7.4.3. Multiple Scattering Model Comparison 7.4.4. Comparison with A Measurement 7.4.5. Validation of Approximate Methods For Ring Effect Modeling 7.5. Summary and Discussion 8.1. Status and Summary 8.1.1. Ring-Effect and Absorption Corrected Radiances 8.1.2. Derivatives of Radiometric Quantities Accessible Through Spectroscopy 8.1.3. Polarization 8.1.4. Time Integrated Sensitivities for 3D UV/vis/NIR Remote Sensing 8.2. Outlook A.1. Zero Variance Estimates A.2. Free Path Length Sampling in a Homogeneous Medium A.3. Cumulative Differential Scatter Cross Sections A.3.1. Cardanic formulas A.3.2. Rayleigh and Raman Phase Functions A.3.3. Henyey-Greenstein Model A.3.4. Legendre Polynomial Phase Function Model A.3.5. Table Methods A.4. Greens Function in the Derivation of the IRTE A.5. Source Code For Stokes Vector Transformation Plot B.1. 1st Order Derivatives B.2. 2nd Order Derivatives B.3. Hessian of Integrals Depending on Many Variables C.1. Slit Function f Derivatives C.2. Signal Sn Derivatives C.3. Chi Square Spline Fitting C.3.1. Constrained Non-Linear Least Square Problem C.3.2. Spline Fitting C.3.3. Jacobians and Hessian