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Cette thèse est dédiée au développement d'outils mathématiques innovants améliorant la modélisation en électrophysiologie cardiaque.Une présentation du modèle bidomaine - un système réaction-diffusion - à domaine fixé est proposée en s'appuyant sur la littérature et une justification mathématique du processus d'homogénéisation (convergence «2-scale») est donnée. Enfin, une étude de l'impact des déformations mécaniques dans les lois de conservation avec la théorie des mélanges est faite.Comme les techniques d'imagerie ne fournissent globalement que des surfaces pour les oreillettes cardiaques dont l'épaisseur est très faible, une réduction dimensionnelle du modèle bidomaine dans une couche mince à une formulation posée sur la surface associée est étudiée. À l'aide de techniques développées pour les modèles de coques, une analyse asymptotique des termes de diffusion est faite sous des hypothèses de gradient d'anisotropie fort à travers l'épaisseur. Puis, une modélisation couplée du cœur - asymptotique pour les oreillettes et volumique pour les ventricules - permet la simulation d'électrocardiogramme complet. De plus, les méthodes asymptotiques sont utilisées pour obtenir des résultats de convergence forte pour les modèles de coque-3D.Enfin, afin de «personnaliser» les modèles, une méthode d'estimation est proposée. Les données médicales intégrées dans notre modèle - au moyen d'un filtre d'état de type Luenberger spécialement conçu - sont les cartes d'activation électrique. Ces problématiques apparaissent dans d'autres domaines où les modèles (réaction-diffusion) et les données (position du front) sont similaires, comme la propagation de feux ou la croissance tumorale. / This thesis aims at developing innovative mathematical tools to improve cardiac electrophysiological modeling. A detailed presentation of the bidomain model - a system of reaction-diffusion equations - with a fixed domain is given based on the literature and we mathematically justify the homogenization process using the 2-scale convergence. Then, a study of the impact of the mechanical deformations in the conservation laws is performed using the mixture theory.As the atria walls are very thin and generally appear as thick surfaces in medical imaging, a dimensional reduction of the bidomain model in a thin domain to a surface-based formulation is studied. The challenge is crucial in terms of computational efficiency. Following similar strategies used in shell mechanical modeling, an asymptotic analysis of the diffusion terms is done with assumptions of strong anisotropy through the thickness, as in the atria. Simulations in 2D and 3D illustrate these results. Then, a complete modeling of the heart - with the asymptotic model for the atria and the volume model for the ventricles - allow the simulation of full electrocardiogram cycles. Furthermore, the asymptotic methods are used to obtain strong convergence results for the 3D-shell models.Finally, a specific data assimilation method is proposed in order to «personalize» the electrophysiological models. The medical data assimilated in the model - using a Luenberger-like state filter specially designed - are the maps of electrical activation. The proposed methods can be used in other application fields where models (reaction-diffusion) and data (front position) are very similar, as for fire propagation or tumor growth.

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第23320号 / 情博第756号 / 新制||情||129(附属図書館) / 京都大学大学院情報学研究科社会情報学専攻 / (主査)教授 吉川 正俊, 教授 伊藤 孝行, 教授 畑山 満則 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

One of the most challenging tasks in the oil industry is the production of reliable reservoir forecast models. Because of different sources of uncertainties the numerical models employed are often only crude approximations of the reality. This problem is tackled by the conditioning of the model with production data through data assimilation. This process is known in the oil industry as history matching. Several recent advances are being used to improve history matching reliability, notably the use of time-lapse seismic data and automated history matching software tools. One of the most promising data assimilation techniques employed in the oil industry is the ensemble Kalman filter (EnKF) because its ability to deal with highly non-linear models, low computational cost and easy computational implementation when compared with other methods. A synthetic reservoir model was used in a history matching study designed to predict the peak production allowing decision makers to properly plan field development actions. If only production data is assimilated, a total of 12 years of historical data is required to properly characterize the production uncertainty and consequently the correct moment to take actions and decommission the field. However if time-lapse seismic data is available this conclusion can be reached 4 years in advance due to the additional fluid displacement information obtained with the seismic data. Production data provides geographically sparse data in contrast with seismic data which are sparse in time. Several types of seismic attributes were tested in this study. Poisson’s ratio proved to be the most sensitive attribute to fluid displacement. In practical applications, however the use of this attribute is usually avoided due to poor quality of the data. Seismic impedance tends to be more reliable. Finally, a new conceptual idea was proposed to obtain time-lapse information for a history matching study. The use of crosswell time-lapse seismic tomography to map velocities in the interwell region was demonstrated as a potential tool to ensure survey reproducibility and low acquisition cost when compared with full scale surface surveys. This approach relies on the higher velocity sensitivity to fluid displacement at higher frequencies. The velocity effects were modeled using the Biot velocity model. This method provided promising results leading to similar RRMS error reductions when compared with conventional history matched surface seismic data.

The thesis deals with the preparation of initial conditions for nume- rical weather prediction in high resolution limited area models. It focuses on the problem of preserving the large-scale part of the global driving model analysis, which can not be determined in sufficient quality in limited-area models. For this purpose, the so-called BlendVar scheme is used. The scheme consists of the appli- cation of the Digital Filter (DF) Blending method, which assures the transmission of a large-scale part of the analysis of the driving model to the limited area model, and of the three-dimensional variational method (3D-Var) at high resolution. The thesis focuses on the appropriate background error specification, which is one of the key components of 3D-Var. Different approaches to modeling of background errors are examined, including the possibility of taking into account the flow- dependent character of background errors. Approaches are also evaluated from the point of view of practical implementation. Study of evolution of background errors during DF Blending and BlendVar assimilation cycles leads to a new pro- posal for the preparation of a background error covariance matrix suitable for the BlendVar assimilation scheme. The use of the new background error covariance matrix gives the required property...

<div>Global Navigation Satellite System Reflectometry (GNSS-R) is a remote sensing technique that uses reflected satellite navigation signals from the Earth surface in a bistatic radar configuration. GNSS-R observations have been collected using receivers on stationary, airborne and spaceborne platforms. The delay-Doppler map (DDM) is the fundamental GNSS-R measurement from which ocean surface wind speed can be retrieved. GNSS-R observations can be assimilated into numerical weather prediction models to improve weather analyses and forecasts. The direct assimilation of DDM observations shows potential superiority over the assimilation of wind retrievals.</div><div><br></div><div>This dissertation demonstrates the direct assimilation of GNSS-R DDMs using a two-dimensional variational analysis method (VAM). First, the observation forward model and its Jacobian are developed. Then, the observation's bias correction, quality control, and error characterization are presented. The DDM assimilation was applied to a global and a regional case. </div><div><br></div><div>In the global case, DDM observations from the NASA Cyclone Global Navigation Satellite System (CYGNSS) mission are assimilated into global ocean surface wind analyses using the European Centre for Medium-Range Weather Forecasts (ECMWF) 10-meter winds as the background. The wind analyses are improved as a result of the DDM assimilation. VAM can also be used to derive a new type of wind vector observation from DDMs (VAM-DDM).</div><div><br></div><div>In the regional case, an observing system experiment (OSE) is used to quantify the impact of VAM-DDM wind vectors from CYGNSS on hurricane forecasts, in the case of Hurricane Michael (2018). It is found that the assimilation of VAM-DDM wind vectors at the early stage of the hurricane improves the forecasted track and intensity.</div><div><br></div><div>The research of this dissertation implies potential benefits of DDM assimilation for future research and operational applications.</div>

<p>Storms in the SE-US often evolve in different environments than those in the central Plains. Many poorly understood aspects of these differing environments may impact the tornadic potential of SE-US storms. Among these differences are potential variations in the CCN concentration owing to differences in land cover, combustion, industrial and urban activity, and proximity to maritime environments. The relative influence of warm and cold rain processes is sensitive to CCN concentration, with higher CCN concentrations producing smaller cloud droplets and more efficient cold rain processes. Cold rain processes result in DSDs with relatively larger drops from melting ice compared to warm rain processes. Differences in DSDs impact cold pool and downdraft size and strength, that influence tornado potential. This study investigates the impact of CCN concentration on DSDs in the SE-US by comparing DSDs from ARPS-EnKF model analyses and forecasts to observed DSDs from portable disdrometer-equipped probes collected by a collaboration between Purdue University, the University of Oklahoma (OU), the National Severe Storms Laboratory (NSSL), and the University of Massachusetts in a tornadic QLCS on 30 April 2017 during VORTEX-SE.</p><p>The ARPS-EnKF configuration, which consists of 40 ensemble members, is used with the NSSL triple-moment microphysics scheme. Surface and radar observations are both assimilated. Data assimilation experiments with CCN concentrations ranging from 100 cm^-3 (maritime) to 2,000 cm^-3 (continental) are conducted to characterize the variability of DSDs and the model output DSDs are verified against the disdrometer observations. The sensitivity of the DSD variability to CCN concentrations is evaluated. Results indicate continental CCN concentrations (close to CCN 1,000 cm³) produce DSDs that align closest to the observed DSDs. Other thermodynamic variables also accord better to observations in intermediate CCN concentration environments.</p>

Cette thèse a développé et mis en œuvre des algorithmes itératifs d'assimilation de données pour un modèle d'océan aux équations primitives, et les a comparés avec d'autres méthodes d'AD bien établis tels que le 4Dvar et le Singular Evolutive Extended Kalman (SEEK) Filtre /lisseur. Le modèle numérique utilisé est le modèle NEMO. Il a été configuré pour simuler la circulation typique subtropicale en double gyre. Les nouveaux algorithmes itératifs proposés, semblables au Nudging direct et rétrograde - BFN, sont tous basés sur une séquence d'intégrations alternées du modèle direct et rétrograde. Ce sont le ``Backward Smoother'' (BS), qui utilise le modèle rétrograde pour propager librement des observations "futures" en rétrograde dans le temps, et le ``Back and Forth Kalman Filter'' (BFKF), qui utilise également le modèle rétrograde pour propager les observations en arrière dans le temps, mais qui à chaque fois qu'un lot d'observations est disponible, réalise une étape de mise à jour du système similaire à l'étape de mise à jour du filtre SEEK. Le formalisme Bayésien a été utilisé pour dériver ces méthodes, ce qui signifie qu'ils peuvent être utilisés avec n'importe quelle méthode qui estime la probabilité postérieure du système par des méthodes séquentielles. Les résultats montrent que l'avantage principal des méthodes basées sur le BFN est l'utilisation du modèle rétrograde pour propager les informations des observations en arrière dans le temps. / This thesis developed and implemented iterative data assimilation algorithms for a primitive equation ocean model, and compared them with other well established DA methods such as the 4Dvar and the Singular Evolutive Extended Kalman (SEEK) Filter/Smoother. The new proposed iterative algorithms, similarly to the Back and Forth Nudging (BFN), are all based on a sequence of alternating forward and backward model integrations. Namely, they are the Backward Smoother (BS), which uses the backward model to freely propagate “future” observations backward in time, and the Back and Forth Kalman Filter, which also uses the backward model to propagate the observations backward in time but, at every time an observation batch is available, an update step similar to the SEEK filter step is carried out. The Bayesian formalism was used to derive these methods, which means that they may be used with any algorithm that estimates the “a posteriori” conditional probability of the model state by means of sequential methods. The results show that the main advantage of the methods based on the BFN is the use of the backward model to propagate the observation informations backward in time. By this way, it avoids the use of the adjoint model, needed by the 4Dvar, and of unknown temporal correlations, needed by the Kalman Smoother, to produce initial states or past model trajectories. The advantages of using the Back and Forth (BF) idea rely on the implicit use of the unstable forward subspace, which became stable when stepping backwards, that allows the errors components projecting onto this subspace to be naturally damped during the backward integration.

This thesis presents our efforts to build an operational ensemble forecasting system for the Red Sea, based on the Data Research Testbed (DART) package for ensemble data assimilation and the Massachusetts Institute of Technology general circulation ocean model (MITgcm) for forecasting. The Red Sea DART-MITgcm system efficiently integrates all the ensemble members in parallel, while accommodating different ensemble assimilation schemes. The promising ensemble adjustment Kalman filter (EAKF), designed to avoid manipulating the gigantic covariance matrices involved in the ensemble assimilation process, possesses relevant features required for an operational setting. The need for more efficient filtering schemes to implement a high resolution assimilation system for the Red Sea and to handle large ensembles for proper description of the assimilation statistics prompted the design and implementation of new filtering approaches. Making the most of our world-class supercomputer, Shaheen, we first pushed the system limits by designing a fault-tolerant scheduler extension that allowed us to test for the first time a fully realistic and high resolution 1000 ensemble members ocean ensemble assimilation system. In an operational setting, however, timely forecasts are of essence, and running large ensembles, albeit preferable and desirable, is not sustainable. New schemes aiming at lowering the computational burden while preserving reliable assimilation results, were developed. The ensemble Optimal Interpolation (EnOI) algorithm requires only a single model integration in the forecast step, using a static ensemble of preselected members for assimilation, and is therefore computationally significantly cheaper than the EAKF. To account for the strong seasonal variability of the Red Sea circulation, an EnOI with seasonally-varying ensembles (SEnOI) was first implemented. To better handle intra-seasonal variabilities and enhance the developed seasonal EnOI system, an automatic procedure to adaptively select the ensemble members through the assimilation cycles was then introduced. Finally, an efficient Hybrid scheme combining the dynamical flow-dependent covariance of the EAKF and a static covariance of the EnOI was proposed and successfully tested in the Red Sea. The developed Hybrid ensemble data assimilation system will form the basis of the first operational Red Sea forecasting system that is currently being implemented to support Saudi Aramco operations in this basin.

Les radars à nuages sont des atouts indéniables pour la Prévision Numérique du Temps (PNT). De par leur petite longueur d’onde, ils possèdent une excellente sensibilité aux particules nuageuses et ils sont facilement déployables à bord de plates-formes mobiles. Cette thèse a permis d’évaluer l’apport des observations de radars à nuages pour la validation et l’initialisation de modèles de PNT à échelle kilométrique. Dans la première partie, un opérateur d’observation pour la réflectivité en bande W a été conçu en cohérence avec le schéma microphysique à un moment d'Arome, le modèle de PNT à échelle kilométrique de Météo-France, mais de façon suffisamment générale pour pouvoir être adapté à un autre modèle de PNT à échelle kilométrique. Il est adaptable pour des radars à visée verticale aéroportés ou au sol. Afin de dissocier les erreurs de positionnement des nuages prévus par Arome, de celles présentes dans l’opérateur d’observation, une nouvelle méthode de validation, appelée "la méthode de la colonne la plus ressemblante (CPR), a été élaborée. Cette méthode a été employée afin de valider et de calibrer l'opérateur d'observation en utilisant les profils de réflectivité collectés par le radar à nuages aéroporté Rasta dans des conditions variées durant la première période d’observations (SOP1) du programme international HyMeX, qui vise à améliorer notre compréhension du cycle de l'eau en méditerranée. La seconde partie s'est intéressée à l'apport respectif de l'assimilation de profils verticaux de réflectivité et de vents horizontaux mesurés par le radar à nuages Rasta dans le système d'assimilation variationnel tridimensionnel (3DVar) d'Arome. Le bénéfice apporté par des conditions thermodynamiques, via l'assimilation de la réflectivité en bande W, et dynamiques, via l'assimilation des profils de vents horizontaux, cohérentes dans l'état initial a également été étudié. Pour assimiler la réflectivité en bande W, la méthode d'assimilation "1D+3DVar", qui est opérationnelle dans Arome pour assimiler les réflectivités des radars de précipitation au sol, a été employée. La méthode de restitution bayésienne 1D de profils d'humidité a été validée avec des mesures d'humidité in situ indépendantes. Puis, les expériences d'assimilation ont été menées sur un événement fortement convectif, ainsi que sur une plus longue période de 45 jours. Les résultats suggèrent notamment que l'assimilation conjointe des profils de réflectivité en bande W et des profils verticaux de vents horizontaux permet d'améliorer les analyses d'humidité, mais suggèrent également une légère amélioration des prévisions des cumuls de précipitation / Cloud radars are an undeniable assets for Numerical Weather Prediction (NWP) models. Because of their very short wavelength, they are extremely sensitive to cloud microphysical properties and are easily deployable aboard moving platforms such as aircraft or spacecraft. This PhD has explored the potential of cloud radar data for the validation and initialisation of kilometre-scale NWP models. In the first part of the PhD, a W-band reflectivity forward operator was designed. It is consistent with the one-moment microphysical scheme used in the Météo-France kilometre-scale NWP model AROME, but in a sufficiently general way that it could be adapted to other kilometrescale NWP models. It was designed in particular for airborne or ground-based vertically pointing cloud radars. To disentangle spatial location errors in the model from errors in the forward operator, a neighbourhood validation method, called the “Most Resembling Method” (MRC), was designed. This validation method was used to validate and calibrate the forward operator using the data collected by the airborne cloud radar RASTA in diverse conditions during the first Special Observation Period (SOP1) of the HyMeX international program, which aims to improve our understanding of the Mediterranean water cycle. The second part focused on the respective roles of the assimilation of reflectivity and horizontal wind profiles, measured by the cloud radar RASTA, in the three dimensional variational (3DVar) assimilation system of AROME. The benefit brought by consistent thermodynamic conditions in the initial state, through the assimilation of the W-band reflectivity, and dynamic ones, through the assimilation of horizontal wind profiles, was also investigated.To assimilate the W-band reflectivity, the two-step assimilation method “1D+3DVar”, operationally employed in AROME to assimilate ground-based precipitation radar data, was used. The efficiency of the 1D Bayesian method in retrieving humidity fields is assessed using independent in-flight humidity measurements. The assimilation experiments were performed for a heavy convective event, as well as over a longer period of 45 days. In particular, the results indicate that the joint assimilation of W-band reflectivity and horizontal wind profiles suggest an improvement of moisture analyses, along with a slight improvement of the rainfall precipitation forecasts.