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International audience; The role of the background error covariance matrix in spreading observational information is particularly crucial in oceanography since some of the state variables are often not observed. Feasibility requirements in actual applications often result in an additional constraint requiring that the effective analysis increment is confined to a lowdimensional subspace of control. This study tackles the problem of adaptation of the definition of the subspace of control and the associated reduced rank error covariance matrix in order to account for additional information which is being gradually gained in data assimilation procedure. The problem has been studied in a framework of a hybrid approach to data assimilation. The skeleton of the hybrid is formed by the 4D-Var enriched with an admixture of an equivalent Kalman smoother. The latter provides a recipe for the evolution of the error covariance matrix which is modified at each transition between successive 4D-Var assimilation windows. In the analysis step it is updated according to the quality of the measurements assimilated into the system. Following system's trajectory, the basis spanning the control subspace is, in turn, adjusted in the forecast step. A series of numerical experiments implementing the hybrid method in a shallow water model has been performed. It has been opted for an initialization of the subspace of control with the empirical orthogonal functions arising from different samples of model trajectory. A number of tests have been performed in various configurations of twin experiments and the circumstances where the hybrid outperforms the standard 4D-Var have been identified. The information content in the initial and final subspaces of control has also been assessed. The general conclusion inferred from this study indicates that propagating the background error covariance matrix may result in compensation of its imperfect initialization.

International audience; Observations may be abundant in nowadays oceanography but they are restricted to some components of the state vector only. Consequently, a need for some prior information on the unobserved variables arises. In the standard 4D-Var it is accounted for via regularising properties of the background error covariance matrix. Secondly, feasibility requirements may result in reduction of the size of the control vector and confine data assimilation correction to a small-size subspace of the original state space. Hence the necessity of an appropriate definition of the control subspace which must be of a small dimension and, at the same time, preserve regularising properties of the background error covariance matrix. The question addressed in this study goes even further and tackles the problem of adapting the definition of the control subspace to account for additional information gained in the data assimilation procedure. The problem has been studied in the framework of a hybrid approach to data assimilation. Hybrid in this study refers to a method merging an incremental 4D-Var with an equivalent Kalman smoother, both in a reduced rank approximation. The skeleton of the hybrid is thus formed by the 4D-Var enriched with an admixture of the smoother delivering a recipe for the evolution of the error covariance matrix. Its update is made at each transition from one assimilation window to another, at both analysis and forecast step. The analysis update modifies the reduced size error covariance matrix accordingly to the quality of the measurements assimilated into the system. Following the system's trajectory evolution in the forecast step, the basis spanning the control subspace is also adjusted. A series of OSSEs implementing the hybrid method into a shallow water model in a wind driven double-gyre circulation has been performed. It has been opted for a definition of the reduced-size control subspace reflecting the directions of the largest variability of the system. These directions have been obtained via principal component analysis of several different samples of model trajectory. A number of tests have been performed in various configurations of twin experiments and the circumstances where the hybrid outperforms the standard 4D-Var have been identified. The general conclusion inferred from this study indicates that the propagation of the basis spanning the control subspace is capable of compensating for imperfect initialization of this subspace. Moreover, as the information contained in the observations is gradually being assimilated into the system's trajectory, the control subspace evolving accordingly.

International audience

International audience; In the standard 4D-Var the regularising background error covariance matrix remains essentially static. In contrast, the hybrid approach we present here has been designed to address the question of possible benefit that the 4D-Var could draw from dynamical adaptation of this matrix. To be more precise, the notion of hybrid in this study refers to a method merging an incremental 4D-Var with an equivalent Kalman smoother, the latter delivering a recipe on how to update the error covariance matrix at each transition between successive assimilation windows. Feasibility requirements may result in a reduction of the size of the control vector and confine data assimilation correction to a low-dimensional subspace of the original state space. Hence, the necessity of an appropriate definition of such a control subspace. An ensemble of vectors spanning the subspace should be of a relatively small size. At the same time it must be capable of preserving the regularising properties of the background error covariance matrix it defines. Consequently, in our hybrid approach which ensures the evolution of the error covariance matrix, the problem of adapting the definition of the control subspace to reflect additional information gained in the data assimilation procedure arises. Indeed, while the analysis update modifies the reduced size error covariance matrix according to the quality of the measurements assimilated into the system, in the forecast step the ensemble spanning the control subspace evolves along the optimised trajectory of the system. A series of OSSEs implementing the hybrid method into a shallow water model mimicking wind driven double-gyre circulation has been performed. It has been opted for a definition of the low-dimensional control subspace which reflects the directions of the largest variability of the system. These directions have been obtained via principal component analysis of several different samples of model trajectory representing either the background or the true state, or both. A number of configurations has been tested and the circumstances where the hybrid outperforms the standard 4D-Var have been identified. The general conclusion inferred from this study indicates that the propagation of the ensemble of vectors spanning the control subspace is capable of compensating for some imperfections in their initialisation. Moreover, as the information contained in the observations is gradually assimilated into the background trajectory, the control subspace evolving accordingly approaches an idealised one defined with the help of the true trajectory of the system.

International audience; The Kalman filter is a data assimilation algorithm that optimally estimates a system state given a model, past, and current observations. This is suitable to initialize numerical predictions. The smoothers also consider future observations in the assimilation process. These are more appropriate to build reanalyses. A smoother designed for oceanic reanalyses is introduced. It is derived from the Singular, Evolutive, Extended Kalman (SEEK) filter and the fixed-lag Kalman smoother. The major difficulty in the derivation lies in the management of model error. Then, extending the SEEK filter with the smoother function is straightforward. The additional computational cost is tiny, what makes the smoother suitable for applications with large systems. The SEEK smoother is tested in twin experiments. The model is an ocean general circulation model in a 1/4 degree double-gyre configuration and simulated satellite observations of Sea Surface Height are assimilated. The smoother slighlty but significantly improves the filter results. To conclude, an outlook to forthcoming real data assimilation experiments and reanalyses making will be presented.

International audience; A data assimilation method based on variational approach is presented. The novelty of the hybrid method consists in a coupling of the cost function of the variational approach with an optimal linear smoother issued from the singular evolutive extended Kalman filter (SEEK). The background error covariance matrix of the usual variational framework remains unchanged. In the hybrid method, however, at each transition between the assimilation windows, it is replaced with the one provided by the smoother. The latter is updated whenever new background states are produced. It can be shown that the background states issued from an appropriately constructed variational framework and some particular optimal linear smoother are mathematically equivalent. Hence the matrix injection into the cost function is done in a consistent manner. The hybrid method has been implemented in a shallow water model which mimics a double-gyre circulation in the North Atlantic. Realistic OSSEs have been performed. Comparisons illustrate superiority of the 4D-Var-smoother hybrid over an ordinary 4D-Var on the one hand and on the other over the 4D-Var-filter hybrid.

International audience

National audience

Atmospheric dispersion models are used to forecast consequences of accidental releases of radioactivity. Models are based on either analytical, as in the case of pX 0.1, or numerical, as for example in Polair3D, solutions to the advection-diffusion equation. Main drawbacks affecting the quality of a forecast are a limited resolution of input meteorological fields and an incomplete knowledge of depletion processes. An investigation of how those drawbacks could be overcome thanks to coupling the models to measurements in data assimilation procedure is presented in this thesis. Model-to-data comparisons have been performed in the first place. The measurements employed in a validation procedure come either from passive tracer experiments or from accidental releases of radionuclides. A wind tunnel experiment for a near-field dispersion on a scale model of Bugey nuclear power station and continental scale ETEX-I experiment as well as the accidental releases in Chernobyl and Algeciras have been studied here. Secondly, measurements have been coupled to the models in order to improve an evaluation of consequences of accidental releases and to invert their sources, should model performance turn out to be sufficiently good. The standard variational method has been used for a near-field dispersion problem. An adjoint of pX 0.1 has been constructed with the help of an automatic differentiator, and the wind tunnel measurements have been assimilated. Capacity of finding the true source emission rate has been tackled in the first place. Next, data assimilation has been employed to accommodate the modelled and measured concentration fields. The required result has been achieved by optimising the parameters which drive the spatial distribution of a plume. Benefit from data assimilation is subject to the quantity of information contained in the measurements. Therefore, posterior analysis of the monitoring network has been carried out and the possibilities of size reduction in view of operational applications have been addressed. At continental scale, despite working exclusively with the grid boxes containing nuclear installations, the space spanned by sources is of significantly greater dimension than the one spanned by observations. Hence, the reconstruction of source position and its emission profile is an ill-posed problem. Its regularisation has been tackled with the maximum entropy on the mean principle. New cost functions, which embody spatial and temporal confinement of an accidental source, have been built. A source-measurement link has been provided by the adjoint of Polair3D. The method has been tested with both perfect and noisy synthetic measurements. A series of sensitivity studies have been conducted and the quality of reconstruction assessed with an objective indicator. An algorithm meant for operational usage which allows to reduce the number of suspected sites has also been tested. Finally, the results of inversion of the temporal profile of the Algeciras accidental source have been shown.; La prévision des conséquences de rejets radioactifs dans l'atmosphère repose sur des modèles de dispersion qui fournissent des solutions analytiques (pX 0.1 développé par IRSN/ECL) ou numériques (Polair3D développé au CEREA) de l'équation d'advection-diffusion. Les modèles s'appuient d'une part sur des champs météorologiques possédant une résolution limitée et intègrent d'autre part des processus d'appauvrissement d'un nuage radioactif dont la description est imparfaite. Afin de contourner ces difficultés nous exploitons dans cette thèse les opportunités offertes par le couplage des modèles aux mesures, connu sous le nom d'assimilation de données. Dans un premier temps nous confrontons les modèles utilisés à des observations. Ces dernières sont fournies par des expériences effectuées avec des traceurs passifs ou collectées suite a des rejets de radionucléides. La dispersion sur une maquette de la centrale de Bugey dans une soufflerie en champ proche, l'expérience ETEX-I à l'échelle continentale et les rejets accidentels de Tchernobyl et Algésiras font l'objet d'études dans ce travail. Dans un deuxième temps, les modèles de dispersion sont associés aux mesures dans le but d'améliorer l'évaluation de conséquences de rejets radioactifs et d'inverser leur sources si la qualité du modèle le permet. En champ proche, l'approche variationnelle standard est utilisée. L'adjoint de pX 0.1 est construit à l'aide d'un différenciateur automatique. Les mesures collectées dans la soufflerie sont assimilées afin d'inverser le débit de la source. Dans le but d'obtenir un meilleur accord entre le modèle et les mesures, l'optimisation des paramètres gouvernant la distribution spatiale du panache est ensuite abordée. L'avantage de l'emploi de mesures est conditionné par leur contenu informatif. Ainsi, l'analyse a posteriori du réseau de mesures est effectuée et des possibilités de réduire sa taille en vue des applications opérationnelles sont exploitées. A l'échelle continentale, malgré la restriction aux mailles contenant des sites nucléaires, l'espace engendré par des sources est de dimension considérablement plus grande que l'espace d'observations. Par conséquent le problème inverse de reconstruction de la position et du profil temporel des sources est mal posé. Ce problème est régularisé en utilisant le principe du maximum d'entropie sur la moyenne. Des nouvelles fonctions coût prenant en compte le confinement spatio-temporel des sources accidentelles sont construites dans l'espace d'observations. Le lien entre la source recherchée et les mesures est décrit par l'adjoint de Polair3D. Les observations assimilées par la méthode sont constituées de mesures synthétiques, parfaites ou bruitées. Une série d'expériences se focalisant sur des sensibilités de la méthode est menée et leur qualité évaluée à l'aide d'un indicateur objectif. Un algorithme de réduction des sites suspectés pour des applications opérationnelles est testé. Finalement, les résultats de l'inversion du profil temporel de la source de l'accident d'Algésiras sont présentés.

International audience; No abstract

International audience; No abstract

International audience; No abstract