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Poseidon-4 is a dual frequency redundant radar altimeter, embarked on board of European Commission Copernicus Programme Sentinel-6 MF satellite, which represents a significant breakthrough with respect to its predecessors Jason-class altimeters thanks to its digital architecture (based on an on-board digital matched-filtering) and to novel internal calibrations modes. In this work, we assess Poseidon-4 main instrumental improvements and performances, with the presentation of the more important outcomes from the In-Flight internal calibration modes and from an external calibration analysis over a transponder. The instrumental performances of the radar altimeter, as verified from its internal calibrations, are excellent: Poseidon-4 delivers a range/azimuth instrument impulse response with the highest quality and fidelity in the age of space-borne radar altimetry and its thermal noise response is almost at level of random noise, and this both for its nominal and redundant side. A significant power decay of the level of the transmitted power in Ku Band has been detected both for the nominal and redundant side, which will not lead anyhow to a violation of the mission requirement of the minimum signal-to-noise ratio over ocean at the end of the expected satellite life (5.5 years). The novel CAL1 ECHO-CAL calibration mode allows to characterize very precisely the sensitivity of the instrument impulse response to the in-orbit temperature variations: this has been estimated to be of +0.3 mm for the range and of +0.01 dB for the power in Ku Band. Furthermore, the novel CAL1 INSTR mode successfully allows the monitoring of the transmitted chirp and, in case, to update the chirp replica used on-board for the pulse compression in order to recover for any significant degradation in the impulse response quality during the course of the mission life. The PTR sidelobes in Ku Band do not evolve in a perfect symmetrical manner between the left-hand side and right-hand side but some deviations have been registered for side-A (0.5 mm and 0.025 dB after 10 months). The impact of these dis-symmetries on the range measurement stability will be analyzed in a separate work (S6PP science results, abstract submitted in the same session). The external calibration by transponder analysis highlights a very small end-to-end range bias and a time-tag bias.

The SAR-mode processing in altimetry as it is currently operated in ground segments does not exploit the full capabilities of the SAR system in terms of spatial resolution. The so-called unfocused SAR altimeter (UFSAR) processing performs the coherent summation of pulses over a limited number of successive pulses (64-pulses bursts of a few milliseconds in length) reducing the along-track resolution down to 300 m only. Since recently [2], the concept of coherent summation has been extended to the whole illumination time of the surface (typically more than 2 seconds) allowing to increase the along-track resolution up to the theoretical limit (approximately 0.5 m) and thus improving the SAR-mode capability for imaging reflective surfaces of small size. The benefits of the fully-focused coherent processing have already been demonstrated on various surfaces to differentiate targets of heterogeneous surfaces (like sea-ice, inland-water and coastal) and to achieve the maximum effective number of looks available from SAR altimetry on homogeneous surfaces (like ocean) [2]. The limitations of the FF-SAR in closed-burst mode has already been reported in [2], creating very harmful artificial side lobes in the along-track dimension due to lacunary chronogram. It is extremely challenging to separate real signal from its replicas when they are superimposed, considering that every reflecting focalization point on ground creates its own replicas. Both Sentinel-3 and Cryosat-2 SAR altimetry missions have been designed with a lacunary chronogram, one exception is for the quasi-continuous pulse transmission Sentinel-6 inter-leaved mode. Over heterogeneous targets, replicas interference creates peaks and troughs pattern, with overflow of power outside of the water body boundaries and destruction of power inside the water body boundaries. This clearly jeopardizes confidence in data and its use for large water body detection like lead detection a major goal in SAR altimerty sea-ice application. At level-2, impact of replicas on the estimated geophysical parameters are not completely understood yet. Even at crossing point between Sentinel-3 and Sentinel-6, it might be tricky to compare the results due to not identical footprint and overflight angle, but also altimeters differences apart from chronogram (like the sampling frequency, deramping/match-filtering and SNR). A new methodology of comparison has been developed and implemented at CLS taking Sentinel-6 data and emulating the sparse closed-burst mode chronogram of Sentinel-3 by removing pulses. Thus on same acquisition points open-burst and closed-burst can be compared each other by isolating only replica effect. More than 700 hydrological targets (including narrow rivers, larger rivers, lakes and dam) have been already processed. First results showed as expected global differences in amplitude but more surprisingly a higher range variability of 1.5cm in closed-burst mode compared to open-burst mode. Next progress is replica removal, a very important topic if we expect to exploit the full potential of FF-SAR processing with Sentinel-3 and Cryosat-2 data. We propose a deconvolution technique to recover the open-burst radargram using optimization method starting from Wiener filtered first guess [3] and a model that takes into account replicas. A new model of multi-scatterer FF-SAR impulse response function, based on LRM inland-water model approach in [1], has been developed and validated over diverse rivers data acquisition. This model supposes water presence a priori knowledge, which might be relevant for inland-water (by exploiting water surface masks), but turns out to be completely irrelevant for sea-ice lead targets permanently in movement. To tackle this problem, the replica model is first optimized to determine the position and specularity of water presence that fit at best real data. Once the model fixed, deconvolution is validated by comparison of reference Sentinel-6 open-burst geophysical parameters with deconvoluted degraded Sentinel-6 closed-burst data. Different surfaces captured by Sentinel-6 will be deconvoluted including rivers, lakes, leads and open-ocean. [1] R. Abileah, A. Scozzari, and S. Vignudelli. Envisat RA-2 Individual Echoes: A Unique Dataset for a Better Understanding of Inland Water Altimetry Potentialities. Remote Sensing, 9(6):605, June 2017. [2] A. Egido and W. H. F. Smith. Fully Focused SAR Altimetry: Theory and Applications. IEEE Transactions on Geoscience and Remote Sensing, 55(1):392–406, Jan. 2017. [3] A. Monti-Guarnieri. Adaptive removal of azimuth ambiguities in SAR images. Geoscience and Remote Sensing, IEEE Transactions on, 43:625–633, Apr. 2005.

The main objective of this thesis is to provide a general methodology to use a recently developed data assimilation method called back-and-forth nudging. The name «back-and-forth» referred to the successive back-and-forths in time performed by this method until obtaining a suitable estimation of the state. The back-and-forth nudging method is a low-computational method known for its simplicity of implementation, as it does not require any differentiation of complex operators and any optimization process contrary to variational methods. In addition, it does not require estimation of covariance errors as for sequential methods. This method is able to provide a state estimation over a finite-time domain, which is particularly interesting for chaotic problems highly sensitive to perturbation of initial condition or constant parameters. First, we aim to address the main difficulty of back-and-forth nudging method which is to maintain the continuity of error convergence at the switching times between forward and backward dynamics. To overcome this problem, we have shown the existence of a common Lyapunov function for both dynamics. This convergence result has been found out for a large class of non-autonomous and non-linear dynamics to estimate initial condition as well as model parameter. The second axis is dedicated to the study of physical properties alteration, this phenomenon had been noticed in past experiments using standard nudging method. These alterations are due to the very nature of the method, modifying the physical structure by injecting directly in the model an innovation term. We have demonstrated that data injection using back-and-forth nudging far less invasive for the physical dynamics than using standard nudging. Finally, in order to validate the efficiency of the method in a realistic context, we have investigated the assimilation of operational data from the future SWOT satellite mission in order to provide ocean dynamics estimation at every layer of Gulf-Stream's oceanic region. After a theoretical study of error convergence with the multi-layered quasi-geostrophic model, the method has been tested numerically with imperfect data by injecting additional noise, in order to guarantee the robustness of the method.; L’objectif principal de cette thèse est de fournir une méthodologie générale pour utiliser une méthode récemment développée d’assimilation de données appelée back-and-forth nudging. Le terme back-and-forth fait référence aux aller-retours dans le temps opéré successivement par cette méthode jusqu’à obtenir une estimation convenable de l’état. La méthode du back-and-forth nudging est une méthode à faible coût connue pour sa simplicité d’implémentation, étant donné qu’elle ne nécessite aucune linéarisation, aucune différentiation d’opérateur complexe et aucun processus d’optimisation, contrairement aux méthodes variationnelles. De plus, elle n’utilise pas non plus d’estimation d’erreur de covariance comme les méthodes séquentielles. Cette méthode est capable de fournir une estimation de l’état sur un intervalle fini de temps, ce qui est particulièrement intéressant pour les problèmes chaotiques à forte sensibilité par rapport à la perturbation de l’état initial ou de certains paramètres du modèle. Premièrement, on cherche à traiter la principale difficulté rencontrée lors de l’utilisation du back-and-forth nudging, qui est de maintenir la convergence de l’erreur continue lors des passages entre la dynamique directe et rétrograde. Pour répondre à ce problème, on montre l’existence d’une fonction de Lyapunov commune aux deux dynamiques. Ce résultat a été montré pour une large classe de problèmes incluant les dynamiques non-autonomes et non-linéaires pour estimer l’état initial mais également les paramètres du modèle. Le second axe est dédié à l’étude de l’attraction des propriétés physique, ce phénomène ayant été observé lors d’expériences passées avec la méthode du nudging standard. Ces altérations sont dues à la nature même de la méthode de nudging, qui consiste à modifier la structure du modèle physique en plus injectant directement un terme d’observation. Nous avons montré, grâce à une analyse de sensibilité, que l’injection des observations par la méthode du back-and-forth nudging est bien moins invasive pour la physique du modèle que par la méthode du nudging standard. Finalement, pour évaluer l’efficacité de la méthode du back-and-forth nudging dans un contexte réel, nous avons réalisé une assimilation de données opérationnelles issues du futur satellite SWOT pour fournir une estimation de l’état dans chaque couche de la région océanique du Gulf Stream. Après étude théorique de la convergence de l’erreur avec un modèle quasi-géostrophique barocline, la méthode a été testée numériquement avec données fortement bruitées, afin de garantir la robustesse de la méthode.

The main objective of this thesis is to provide a general methodology to use a recently developed data assimilation method called back-and-forth nudging. The name «back-and-forth» referred to the successive back-and-forths in time performed by this method until obtaining a suitable estimation of the state. The back-and-forth nudging method is a low-computational method known for its simplicity of implementation, as it does not require any differentiation of complex operators and any optimization process contrary to variational methods. In addition, it does not require estimation of covariance errors as for sequential methods. This method is able to provide a state estimation over a finite-time domain, which is particularly interesting for chaotic problems highly sensitive to perturbation of initial condition or constant parameters. First, we aim to address the main difficulty of back-and-forth nudging method which is to maintain the continuity of error convergence at the switching times between forward and backward dynamics. To overcome this problem, we have shown the existence of a common Lyapunov function for both dynamics. This convergence result has been found out for a large class of non-autonomous and non-linear dynamics to estimate initial condition as well as model parameter. The second axis is dedicated to the study of physical properties alteration, this phenomenon had been noticed in past experiments using standard nudging method. These alterations are due to the very nature of the method, modifying the physical structure by injecting directly in the model an innovation term. We have demonstrated that data injection using back-and-forth nudging far less invasive for the physical dynamics than using standard nudging. Finally, in order to validate the efficiency of the method in a realistic context, we have investigated the assimilation of operational data from the future SWOT satellite mission in order to provide ocean dynamics estimation at every layer of Gulf-Stream's oceanic region. After a theoretical study of error convergence with the multi-layered quasi-geostrophic model, the method has been tested numerically with imperfect data by injecting additional noise, in order to guarantee the robustness of the method.; L’objectif principal de cette thèse est de fournir une méthodologie générale pour utiliser une méthode récemment développée d’assimilation de données appelée back-and-forth nudging. Le terme back-and-forth fait référence aux aller-retours dans le temps opéré successivement par cette méthode jusqu’à obtenir une estimation convenable de l’état. La méthode du back-and-forth nudging est une méthode à faible coût connue pour sa simplicité d’implémentation, étant donné qu’elle ne nécessite aucune linéarisation, aucune différentiation d’opérateur complexe et aucun processus d’optimisation, contrairement aux méthodes variationnelles. De plus, elle n’utilise pas non plus d’estimation d’erreur de covariance comme les méthodes séquentielles. Cette méthode est capable de fournir une estimation de l’état sur un intervalle fini de temps, ce qui est particulièrement intéressant pour les problèmes chaotiques à forte sensibilité par rapport à la perturbation de l’état initial ou de certains paramètres du modèle. Premièrement, on cherche à traiter la principale difficulté rencontrée lors de l’utilisation du back-and-forth nudging, qui est de maintenir la convergence de l’erreur continue lors des passages entre la dynamique directe et rétrograde. Pour répondre à ce problème, on montre l’existence d’une fonction de Lyapunov commune aux deux dynamiques. Ce résultat a été montré pour une large classe de problèmes incluant les dynamiques non-autonomes et non-linéaires pour estimer l’état initial mais également les paramètres du modèle. Le second axe est dédié à l’étude de l’attraction des propriétés physique, ce phénomène ayant été observé lors d’expériences passées avec la méthode du nudging standard. Ces altérations sont dues à la nature même de la méthode de nudging, qui consiste à modifier la structure du modèle physique en plus injectant directement un terme d’observation. Nous avons montré, grâce à une analyse de sensibilité, que l’injection des observations par la méthode du back-and-forth nudging est bien moins invasive pour la physique du modèle que par la méthode du nudging standard. Finalement, pour évaluer l’efficacité de la méthode du back-and-forth nudging dans un contexte réel, nous avons réalisé une assimilation de données opérationnelles issues du futur satellite SWOT pour fournir une estimation de l’état dans chaque couche de la région océanique du Gulf Stream. Après étude théorique de la convergence de l’erreur avec un modèle quasi-géostrophique barocline, la méthode a été testée numériquement avec données fortement bruitées, afin de garantir la robustesse de la méthode.

International audience; Oceans and the atmosphere are governed by the general equations of fluid dynamics. Data assimilation consists of estimating the state of a system by combining, via numerical methods, two different sources of information: models and observations. The Back and Forth Nudging (BFN) algorithm is a prototype of a new class of data assimilation methods. The nudging technique consists in adding a feedback term in the model equations, measuring the difference between the observations and the corresponding space states. The BFN algorithm is an iterative sequence of forward and backward resolutions, all of them being performed with an additional nudging feedback term in the model equations. These nudging-based algorithms can be extended with the aim of correcting non-observed variables. This particularly concerns model parameter identification , with the potential of improving the quality and the confidence in the model state for future data assimilation processes.