L'assimilation de données vise à fournir aux modèles de prévision numérique du temps un état initial de l'atmosphère le plus précis possible. Pour cela, elle utilise deux sources d'information principales : des observations et une prévision récente appelée "ébauche", toutes deux entachées d'erreurs. La distribution de ces erreurs permet d'attribuer un poids relatif à chaque source d'information, selon la confiance que l'on peut lui accorder, d'où l'importance de pouvoir estimer précisément les covariances de l'erreur d'ébauche. Les méthodes de type Monte-Carlo, qui échantillonnent ces covariances à partir d'un ensemble de prévisions perturbées, sont considérées comme les plus efficaces à l'heure actuelle. Cependant, leur coût de calcul considérable limite de facto la taille de l'ensemble. Les covariances ainsi estimées sont donc contaminées par un bruit d'échantillonnage, qu'il est nécessaire de filtrer avant toute utilisation. Cette thèse propose des méthodes de filtrage du bruit d'échantillonnage dans les covariances d'erreur d'ébauche pour le modèle à échelle convective AROME de Météo-France. Le premier objectif a consisté à documenter la structure des covariances d'erreur d'ébauche pour le modèle AROME. Une assimilation d'ensemble de grande taille a permis de caractériser la nature fortement hétérogène et anisotrope de ces covariances, liée au relief, à la densité des observations assimilées, à l'influence du modèle coupleur, ainsi qu'à la dynamique atmosphérique. En comparant les covariances estimées par deux ensembles indépendants de tailles très différentes, le bruit d'échantillonnage a pu être décrit et quantifié. Pour réduire ce bruit d'échantillonnage, deux méthodes ont été développées historiquement, de façon distincte : le filtrage spatial des variances et la localisation des covariances. On montre dans cette thèse que ces méthodes peuvent être comprises comme deux applications directes du filtrage linéaire des covariances. L'existence de critères d'optimalité spécifiques au filtrage linéaire de covariances est démontrée dans une seconde partie du travail. Ces critères présentent l'avantage de n'impliquer que des grandeurs pouvant être estimées de façon robuste à partir de l'ensemble. Ils restent très généraux et l'hypothèse d'ergodicité nécessaire à leur estimation n'est requise qu'en dernière étape. Ils permettent de proposer des algorithmes objectifs de filtrage des variances et pour la localisation des covariances. Après un premier test concluant dans un cadre idéalisé, ces nouvelles méthodes ont ensuite été évaluées grâce à l'ensemble AROME. On a pu montrer que les critères d'optimalité pour le filtrage homogène des variances donnaient de très bons résultats, en particulier le critère prenant en compte la non-gaussianité de l'ensemble. La transposition de ces critères à un filtrage hétérogène a permis une légère amélioration des performances, à un coût de calcul plus élevé cependant. Une extension de la méthode a ensuite été proposée pour les composantes du tenseur de la hessienne des corrélations locales. Enfin, les fonctions de localisation horizontale et verticale ont pu être diagnostiquées, uniquement à partir de l'ensemble. Elles ont montré des variations cohérentes selon la variable et le niveau concernés, et selon la taille de l'ensemble. Dans une dernière partie, on a évalué l'influence de l'utilisation de variances hétérogènes dans le modèle de covariances d'erreur d'ébauche d'AROME, à la fois sur la structure des covariances modélisées et sur les scores des prévisions. Le manque de réalisme des covariances modélisées et l'absence d'impact positif pour les prévisions soulèvent des questions sur une telle approche. Les méthodes de filtrage développées au cours de cette thèse pourraient toutefois mener à d'autres applications fructueuses au sein d'approches hybrides de type EnVar, qui constituent une voie prometteuse dans un contexte d'augmentation de la puissance de calcul disponible. / Data assimilation aims at providing an initial state as accurate as possible for numerical weather prediction models, using two main sources of information : observations and a recent forecast called the “background”. Both are affected by systematic and random errors. The precise estimation of the distribution of these errors is crucial for the performance of data assimilation. In particular, background error covariances can be estimated by Monte-Carlo methods, which sample from an ensemble of perturbed forecasts. Because of computational costs, the ensemble size is much smaller than the dimension of the error covariances, and statistics estimated in this way are spoiled with sampling noise. Filtering is necessary before any further use. This thesis proposes methods to filter the sampling noise of forecast error covariances. The final goal is to improve the background error covariances of the convective scale model AROME of Météo-France. The first goal is to document the structure of background error covariances for AROME. A large ensemble data assimilation is set up for this purpose. It allows to finely characterize the highly heterogeneous and anisotropic nature of covariances. These covariances are strongly influenced by the topography, by the density of assimilated observations, by the influence of the coupling model, and also by the atmospheric dynamics. The comparison of the covariances estimated from two independent ensembles of very different sizes gives a description and quantification of the sampling noise. To damp this sampling noise, two methods have been historically developed in the community : spatial filtering of variances and localization of covariances. We show in this thesis that these methods can be understood as two direct applications of the theory of linear filtering of covariances. The existence of specific optimality criteria for the linear filtering of covariances is demonstrated in the second part of this work. These criteria have the advantage of involving quantities that can be robustly estimated from the ensemble only. They are fully general and the ergodicity assumption that is necessary to their estimation is required in the last step only. They allow the variance filtering and the covariance localization to be objectively determined. These new methods are first illustrated in an idealized framework. They are then evaluated with various metrics, thanks to the large ensemble of AROME forecasts. It is shown that optimality criteria for the homogeneous filtering of variances yields very good results, particularly with the criterion taking the non-gaussianity of the ensemble into account. The transposition of these criteria to a heterogeneous filtering slightly improves performances, yet at a higher computational cost. An extension of the method is proposed for the components of the local correlation hessian tensor. Finally, horizontal and vertical localization functions are diagnosed from the ensemble itself. They show consistent variations depending on the considered variable and level, and on the ensemble size. Lastly, the influence of using heterogeneous variances into the background error covariances model of AROME is evaluated. We focus first on the description of the modelled covariances using these variances and then on forecast scores. The lack of realism of the modelled covariances and the negative impact on scores raise questions about such an approach. However, the filtering methods developed in this thesis are general. They are likely to lead to other prolific applications within the framework of hybrid approaches, which are a promising way in a context of growing computational resources.

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...

Due to the recursive and integrative nature of zero-velocity-update-aided (ZUPT-aided) inertial navigation systems (INSs), the error covariance increases throughout each ZUPT-less period followed by a drastic decrease and large state estimate corrections as soon as ZUPTs are applied. For dead-reckoning with foot-mounted inertial sensors, this gives undesirable discontinuities in the estimated trajectory at the end of each step. However, for many applications, some degree of lag can be tolerated and the information provided by the ZUPTs at the end of a step can be made available throughout the step, eliminating the discontinuities. For this purpose, we propose a smoothing algorithm for ZUPT-aided INSs. For near real-time applications, smoothing is applied to the data in a step-wise manner requiring a suggested varying-lag segmentation rule. For complete off-line processing, full data set smoothing is examined. Finally, the consequences and impact of smoothing are analyzed and quantified based on real-data. / <p>QC 20130114</p>

Satellite instruments currently provide the largest source of infor- mation to today's data assimilation (DA) systems for numerical weather predic- tion (NWP). With the development of high-resolution models, the efficient use of observations at high density is essential to improve small-scale information in the weather forecast. However, a large amount of satellite radiances has to be removed from DA by horizontal data thinning due to uncorrelated observation error assumptions. Moreover, satellite radiances include systematic errors (biases) that may be even larger than the observation signal itself, and must be properly removed prior to DA. Although the Variational Bias Correction (VarBC) scheme is widely used by global NWP centers, there are still open questions regarding its use in Limited-Area Models (LAMs). This thesis aims to tackle the obser- vation error difficulties in assimilating polar satellite radiances in the meso-scale ALADIN system. Firstly, we evaluate spatial- and inter-channel error correla- tions to enhance the positive effect of data thinning. Secondly, we study satellite radiance bias characteristics with the key aspects of the VarBC in LAMs, and we compare the different VarBC configurations with regards to forecast performance. This work is a step towards improving the...