Sur la structure mathématique et l'approximation numérique de l'hydrodynamique lagrangienne bidimensionnelle

Ce travail étudie une nouvelle formulation des équations d’Euler compressibles écrites en coordonnées lagrangiennes multidimensionnelles, sous la structure d’un système de lois de conservation associé à une contrainte de divergence nulle. Cette structure s’applique également à une physique plus large, incluant par exemple la magnétohydrodynamique. Elle permet l’étude mathématique du problème global couplant les inconnues physiques avec les inconnues géométriques associées au déplacement de la matière. Nous montrons que la partie physique du système, dont l’ensemble est faiblement hyperbolique, est symétrisable sous cette contrainte, alors que la perte de régularité des inconnues géométriques est caractéristique des cisaillements. Nous construisons ensuite une méthode d’approximation originale, de type Volumes-Finis sur maillage mobile, avec degrés de liberté aux noeuds. Le schéma repose uniquement sur des considérations physiques (principe de conservation, croissance de l’entropie), qui assurent sa stabilité ainsi qu’un résultat de positivité et de non-croisement sur maillage triangulaire. On montre théoriquement qu’il converge avec un ordre 1/2 sur les équations linéaires de l’acoustique. Enfin, une extension à la géométrie axisymétrique généralise la structure symétrisée et la contrainte différentielle, ainsi que la méthode d’approximation associée.This work studies a nex formulation of compressible Euler equations written in multidimensional Lagrangian coordinates, as a system of conservation laws linked to a free divergence constraint : It applies also to an extended physics, including for instance magnetohydrodynamics. This structure allows the mathematical study of the whole Lagrangian problematics, coupling physical unknowns with geometrical one’s, associated to the displacement of matter. We prove that the physical part of the system, whose entire formulation is known to be only weakly hyperbolic, is symmetrizable under the differential constraint, although the loss of regularity of geometrical unknowns is characteristic of shear discontinuities. We then derive an original approximate method, of Finite Volumes kind on moving mesh, whose degree of freedom are placed on nodes. The scheme relies only on physical considerations (conservation principle, entropy production), which ensure its stability as well as a result of positivity and non-crossing on triangular mesh. We prove theoretically its convergence with a rate of 1/2 on the linearized equations of acoustics. Eventually, we extent the symmeterized structure and numerical method to the case of axisymmetric geometry

European Radiometry Buoy and Infrastructure (EURYBIA): A Contribution to the Design of the European Copernicus Infrastructure for Ocean Colour System Vicarious Calibration

In the context of the Copernicus Program, EUMETSAT prioritizes the creation of an ocean color infrastructure for system vicarious calibration (OC-SVC). This work aims to reply to this need by proposing the European Radiometry Buoy and Infrastructure (EURYBIA). EURYBIA is designed as an autonomous European infrastructure operating within the Marine Optical Network (MarONet) established by University of Miami (Miami, FL, USA) based on the Marine Optical Buoy (MOBY) experience and NASA support. MarONet addresses SVC requirements in different sites, consistently and in a traceable way. The selected EURYBIA installation is close to the Lampedusa Island in the central Mediterranean Sea. This area is widely studied and hosts an Atmospheric and Oceanographic Observatory for long-term climate monitoring. The EURYBIA field segment comprises off-shore and on-shore infrastructures to manage the observation system and perform routine sensors calibrations. The ground segment includes the telemetry center for data communication and the processing center to compute data products and uncertainty budgets. The study shows that the overall uncertainty of EURYBIA SVC gains computed for the Sentinel-3 OLCI mission under EUMETSAT protocols is of about 0.05% in the blue-green wavelengths after a decade of measurements, similar to that of the reference site in Hawaii and in compliance with requirements for climate studies

European radiometry buoy and infrastructure (EURYBIA): A contribution to the design of the European copernicus infrastructure for ocean colour system vicarious calibration

In the context of the Copernicus Program, EUMETSAT prioritizes the creation of an ocean color infrastructure for system vicarious calibration (OC-SVC). This work aims to reply to this need by proposing the European Radiometry Buoy and Infrastructure (EURYBIA). EURYBIA is designed as an autonomous European infrastructure operating within the Marine Optical Network (MarONet) established by University of Miami (Miami, FL, USA) based on the Marine Optical Buoy (MOBY) experience and NASA support. MarONet addresses SVC requirements in different sites, consistently and in a traceable way. The selected EURYBIA installation is close to the Lampedusa Island in the central Mediterranean Sea. This area is widely studied and hosts an Atmospheric and Oceanographic Observatory for long-term climate monitoring. The EURYBIA field segment comprises off-shore and on-shore infrastructures to manage the observation system and perform routine sensors calibrations. The ground segment includes the telemetry center for data communication and the processing center to compute data products and uncertainty budgets. The study shows that the overall uncertainty of EURYBIA SVC gains computed for the Sentinel-3 OLCI mission under EUMETSAT protocols is of about 0.05% in the blue-green wavelengths after a decade of measurements, similar to that of the reference site in Hawaii and in compliance with requirements for climate studies

BRDF correction of S3 OLCI water reflectance products

Ocean Optics XXV, 2-7 October 2022, Quy Nhon, Binh Dinh, Vietnam.-- 1 page, figuresOngoing study to minimize the effects of the Bidirectional Reflectance Distribution Function (BRDF) and deliver Sentine3 OLCI fully normalized water reflectancesEUMETSAT Contract Ref.: RB_EUM-CO-21-4600002626-JIGPeer reviewe

An ocean-colour time series for use in climate studies: the experience of the ocean-colour climate change initiate (OC-CCI)

Ocean colour is recognised as an Essential Climate Variable (ECV) by the Global Climate Observing System (GCOS); and spectrally-resolved water-leaving radiances (or remote-sensing reflectances) in the visible domain, and chlorophyll-a concentration are identified as required ECV products. Time series of the products at the global scale and at high spatial resolution, derived from ocean-colour data, are key to studying the dynamics of phytoplankton at seasonal and inter-annual scales; their role in marine biogeochemistry; the global carbon cycle; the modulation of how phytoplankton distribute solar-induced heat in the upper layers of the ocean; and the response of the marine ecosystem to climate variability and change. However, generating a long time series of these products from ocean colour data is not a trivial task: algorithms that are best suited for climate studies have to be selected from a number that are available for atmospheric correction of the satellite signal and for retrieval of chlorophyll-a concentration; since satellites have a finite life span, data from multiple sensors have to be merged to create a single time series, and any uncorrected inter-sensor biases could introduce artefacts in the series, e.g., different sensors monitor radiances at different wavebands such that producing a consistent time series of reflectances is not straightforward. Another requirement is that the products have to be validated against in situ observations. Furthermore, the uncertainties in the products have to be quantified, ideally on a pixel-by-pixel basis, to facilitate applications and interpretations that are consistent with the quality of the data. This paper outlines an approach that was adopted for generating an ocean-colour time series for climate studies, using data from the MERIS (MEdium spectral Resolution Imaging Spectrometer) sensor of the European Space Agency; the SeaWiFS (Sea viewingWide-Field-of-view Sensor) and MODIS-Aqua (Moderate-resolution Imaging Spectroradiometer-Aqua) sensors from the National Aeronautics and Space Administration (USA); and VIIRS (Visible and Infrared Imaging Radiometer Suite) from the National Oceanic and Atmospheric Administration (USA). The time series now covers the period from late 1997 to end of 2018. To ensure that the products meet, as well as possible, the requirements of the user community, marine-ecosystem modellers, and remote-sensing scientists were consulted at the outset on their immediate and longer-term requirements as well as on their expectations of ocean-colour data for use in climate research. Taking the user requirements into account, a series of objective criteria were established, against which available algorithms for processing ocean-colour data were evaluated and ranked. The algorithms that performed best with respect to the climate user requirements were selected to process data from the satellite sensors. Remote-sensing reflectance data from MODIS-Aqua, MERIS, and VIIRS were band-shifted to match the wavebands of SeaWiFS. Overlapping data were used to correct for mean biases between sensors at every pixel. The remote-sensing reflectance data derived from the sensors were merged, and the selected in-water algorithm was applied to the merged data to generate maps of chlorophyll concentration, inherent optical properties at SeaWiFS wavelengths, and the diffuse attenuation coefficient at 490 nm. The merged products were validated against in situ observations. The uncertainties established on the basis of comparisons with in situ data were combined with an optical classification of the remote-sensing reflectance data using a fuzzy-logic approach, and were used to generate uncertainties (root mean square difference and bias) for each product at each pixel

Numerical study of a conservative bifluid model with interpenetration

International audienc

Remote sensing of suspended particulate matter in turbid oyster-farming ecosystems

International audienceHigh resolution satellite data of the Medium Resolution Imaging Spectrometer in full resolution mode (MERIS FR, pixel size is 300 m) were used to study the impact of suspended particulate matter (SPM) on oyster-farming sites in a macrotidal bay of the French Atlantic coast where SPM concentration can exceed 100 g m(-3). Because MERIS standard SPM concentration retrieval saturates at about 50 g m(-3), we developed an alternative method for turbid nearshore waters. The method consists in the combination of the Semi-Analytical Atmospheric and Bio-Optical (SAABIO) atmospheric correction with a regional bio-optical algorithm based on a linear relationship between SPM concentration and the reflectance band ratio at 865 and 560 nm. MERIS FR-derived SPM concentrations were validated from 10 up to 300 g m(-3), and then merged with oyster ecophysiological responses to provide a spatial picture of the impact of SPM concentration on oyster-farming sites. Our approach demonstrates the potential of high resolution satellite remote sensing for aquaculture management and shellfish-farming ecosystems studies