Turbulent viscosity optimized by data assimilation

International audienceAs an alternative approach to classical turbulence modelling using a first or second order closure, the data assimilation method of optimal control is applied to estimate a time and space-dependent turbulent viscosity in a three-dimensional oceanic circulation model. The optimal control method, described for a 3-D primitive equation model, involves the minimization of a cost function that quantifies the discrepancies between the simulations and the observations. An iterative algorithm is obtained via the adjoint model resolution. In a first experiment, a k + L model is used to simulate the one-dimensional development of inertial oscillations resulting from a wind stress at the sea surface and with the presence of a halocline. These results are used as synthetic observations to be assimilated. The turbulent viscosity is then recovered without the k + L closure, even with sparse and noisy observations. The problems of controllability and of the dimensions of the control are then discussed. A second experiment consists of a two-dimensional schematic simulation. A 2-D turbulent viscosity field is estimated from data on the initial and final states of a coastal upwelling event

A reduced-order strategy for 4D-Var data assimilation

This paper presents a reduced-order approach for four-dimensional variational data assimilation, based on a prior EO F analysis of a model trajectory. This method implies two main advantages: a natural model-based definition of a mul tivariate background error covariance matrix $\textbf{B}_r$, and an important decrease of the computational burden o f the method, due to the drastic reduction of the dimension of the control space. % An illustration of the feasibility and the effectiveness of this method is given in the academic framework of twin experiments for a model of the equatorial Pacific ocean. It is shown that the multivariate aspect of $\textbf{B}_r$ brings additional information which substantially improves the identification procedure. Moreover the computational cost can be decreased by one order of magnitude with regard to the full-space 4D-Var method

Contrôle des conditions aux frontières ouvertes d'un modèle de circulation côtière avec une méthode variationnelle d'assimilation de données (application au Golfe du Lion)

La dynamique de la circulation marine en région côtière peut être appréhendée par des moyens d'observation et de modélisation. Si le domaine côtier bénéficie de réseaux de mesure adaptés en résolution et en couverture, la mise en oeuvre d'un outil de modélisation s'avère délicate, particulièrement dans la spécification de conditions initiales et de conditions aux frontières ouvertes appropriées. Cette question de l'estimation des conditions aux limites peut être considérée comme relevant d'une problématique plus générale de détermination des paramètres de fonctionnement d'un modèle à partir de l'information apportée par les observations. Ainsi posé, le problème est abordé par l'outil mathématique du contrôle optimal qui conduit à une opération d'assimilation de données par méthode d'adjoint. L'adaptation et l'application de cette formulation inverse à un problème de modélisation océanographique contrôlé par ses conditions frontières font l'objet de ce travail de thèse. Une approche 4D-variationnelle d'assimilation pour le contrôle des conditions frontières est ainsi développée et implémentée sur la base du modèle aux équations primitives OPA (version toit rigide') et de son adjoint existant. L'algorithme d'inversion est validé sur trois expériences d'identification : (i) les perturbations du forçage barotrope sur la frontière ouverte d'un modèle non stratifié sont détectées par l'assimilation de courants de surface pris à l'intérieur du domaine ; (ii) le développement d'un courant de densité dans un canal semi infini et homogène est retrouvé à partir de profils hydrologiques distribués en aval ; (iii) l'observation du " spin up " d'une circulation de plateau induit par un courant côtier permet d'identifier les conditions amonts prévues par le mécanisme de séparation d'un front de Kelvin barocline en incidence sur un talus. Cette méthode d'assimilation est alors proposée pour des applications s'inscrivant dans la problématique scientifique des échanges côte - large sur la zone du Golfe du Lion. Riche en observations et largement ouverte sur le bassin méditerranéen occidental, cette région est soumise à l'influence du courant Liguro-Provençal qui s'écoule en bord de plateau. L'algorithme d'inversion permet de contrôler cette influence régionale sur la circulation de plateau ; il est donc évalué à travers des expériences réalistes menées dans le mode diagnostique. En particulier, la faculté de réseaux d'observation à détecter des épisodes d'intrusion du courant côtier sur le golfe est traitée suivant leur couverture spatiale et temporelle.The marine circulation dynamics in coastal zones can be assessed by observation and modelisation. If coastal domains are quantitatively observed (routine remote sensing, periodic in situ surveys, long term measurements), consistent model set up remain relatively elusive, especially for the prescription of appropriate initial and open boundary conditions. This issue raised by the specification of model boundary conditions is proposed to be posed in the optimal control framework, which leads to a data assimilation problem solved by an adjoint method : these model parameters are determined according to information from observations. A four-dimensional variational (4DVAR) assimilation method for open boundary control is then developed and implemented on the basis of the primitive equation circulation model OPA and its adjoint. The algorithm is validated with three academic twin experiments: (i) the detection of perturbations on the barotropic forcing along the open boundary of a non-stratified model are obtained by assimilating surface currents taken inside the domain ; (ii) the development of a density current inside a semi-infinite homogeneous channel is retrieved from a synthetic data set figuring density profiles distributed downstream; (iii) the observation of the spin up of a coastal circulation induced by a baroclinic Kelvin front incident to a shallow shelf topography permits to identify the upstream boundary conditions linked to the separation at the shelf break. The Gulf of Lions, which is largely opened to the north-western Mediterranean basin, appears to be an appropriate study case to investigate mechanisms and magnitudes of coastal lateral export to the open ocean. The assimilation method is applied in situations of regional influence on the gulf circulation. It is assessed in the hind cast mode for monitoring applications, especially on the data related aspect. The regional forcing provided by the Liguro-Provençal current flowing along the shelf break is controlled to study the ability of the available observational networks to detect transient cross shelf intrusions according to their spatial and temporal coverage.TOULON-BU Centrale (830622101) / SudocSudocFranceF

Etude expérimentale des instabilités méso à sub-méso échelle du courant Nord Méditerranéen

En océanographie les flux de matière sont très abondamment étudiés depuis longtemps, car ils contrôlent les flux biogéochimiques qui forcent les écosystèmes marins. Les récents problèmes de pollutions en mer rendent cruciale la connaissance du trajet et de la dilution des divers contaminants. L'un des processus majeurs de flux de matière sont les échanges côte large à travers un talus continental sont les tourbillons. Deux algorythmes de détection et identification des paramètres des tourbillons ont été développés en prenant en compte les spécificités de l'étude. L'un, validé par les cartes radar servant de références l'autre, restant à parfaire, sur une analyse temps-fréquence de série temporelles de vitesse. Les campagnes ECOLOPHY ont permis d'identifier les tourbillons de sub-méso échelle. La plupart sont confirmés par l'analyse du champ de température à l'horizontale et à la verticale. Les gyres détectés sont de type anticyclonique. ils sont positionnés entre le Courant nord méditerranéen et la côte, avec une taille allant de 12 à 28 lm de diamètre.Matters fluxes have been studied in details for a long time because they control biogeochemical fluxes which influence marine ecosystems. The knowledge of the path and the dilution of contaminants is made critical in case of sea pollution problems. Oneof the major processes which controls matter flux is the coastal exchanges through the continental shelf vy vortices. two zlgorithms of detection and identification of vortex parameters were developed, taking into account the specificities of the study. The first one, validated by radar maps acting as a reference, is based on a classical kinmatic method, the second one, which could be improved is based on a time-frequency analysis of velocities time series. ECOLOPHY campaigns enaled us to identify submesoscale vortices. Most of them were confrimed by the analysis of the horizontal end vertical temperature field. they are located between the Nothern Current and the coast, their diameter size anges from 12 to 28 km.AIX-MARSEILLE2-BU Sci.Luminy (130552106) / SudocSudocFranceF

Utilisation de mesures de courants cotiers superficiels par radar HF pour valider et optimiser les modeles numeriques de circulation littorale en mer a maree

SIGLECNRS T Bordereau / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Tidal influence on the hydrodynamics of the French Guiana continental shelf

This study investigates the circulation on the French Guiana continental shelf under tidal influence. Indeed, hydrodynamics are characterised by a weak salinity tongue located in the middle of the shelf and induced by the Amazon River, a coastal current flowing from the southeast, and a tidal standing wave whose co-range lines are parallel to the coast. In addition to field observations, a numerical model also is used to evaluate the tidal influence on coastal circulation. The model makes use of the MOBEEHDYCS code, a three-dimensional free surface time-splitting model whose domain is bounded with a closed coastal boundary, two active boundaries (offshore and lateral) and a passive boundary. The boundary configuration and hydrodynamics require a careful choice of passive open boundary conditions. The initial and boundary conditions come from field data. The tidal currents are essentially cross-shore and do not have a great influence on the main current direction on the offshore part of the shelf. The offshore currents remain parallel to the coast. In the inner shelf, the tidal influence is found to be much more important and the tidal currents can reach 0.45 m/s. Vertically, the tidal currents are barotropic, in spite of the high stratification and they induce a horizontal cross-shore migration (about 3 km) of the weak salinity tongue and vertical oscillations of the halocline without complete mixing

Numerical modeling of the Amazon River plume

Marine circulation above the northern Brazilian continental shelf is subject to energetic forcing factors of various origins: high water buoyancy fluxes induced by the Amazon River freshwater discharge, a strong coastal current associated with a mesoscale current (North Brazil Current (NBC)), a forcing by semidiurnal tide and by Northeast or Southeast trade winds according to the season. Using a three-dimensional (3-D) hydrodynamic numerical model (MOBEEHDYCS), and realistic bathymetry and coastline of the northern Brazilian shelf, this paper aims at studying the influence of some specific physical processes on the morphology of the Amazon plume. The very large volume discharge (180000m(3)/s on average) and the weak effect of Coriolis force are additional characteristics of the studied system, which induce a particular dynamics. The various forcing factors are successively introduced into the model in order to simulate and to determine their respective influences upon the plume extent and the hydrodynamics at the shelf scale. Simulation reveal that the coastal current is at the origin of the permanent northwestward Amazon Plume extension while wind effect can either reinforce or moderate this situation. The tide intervenes also to modify the position of the salinity front: a horizontal migration of salinity front is observed under its action

Impact of cross-reef fluxes on the Ouano lagoon circulation.

International audienceIn meso-tidal lagoons the coral reef barrier can be temporarily covered by water at high tide and emerged at low tide, inducing particular cross-reef dynamics. In order to understand the importance of crossreef fluxes on lagoon dynamics a field survey had been conducted on Ouano Lagoon (New Caledonia). The lagoon water dynamics were analyzed and compared to a numerical model output. The main current was found to be northward during the flood, with inward flows through the ocean passes and through the south passage and outward flows through the north passage. During the ebb, currents are usually reversed. Concerning tidally averaged fluxes, they are mainly inward at the ocean passes and southward in passages. Finally, numerical tests were performed to evaluate the impact of cross-reef fluxes on this circulation. The results of this study are, then, discussed

Numerical analysis of the combined action of littoral current, tide and waves on the suspended mud transport and on turbid plumes around French Guiana mudbanks

Large mudbanks migrate westwards in the nearshore zone from the Cabo Cassipore in the Amapa state (Brazil) to the Waini River in Guiana. These mudbanks are noticeable by their size (about 4 x 10(9) m(3) of sediment) and by the sediment dynamics they induce. Notably, visible remote sensing pictures present high turbid mud plume associated to mudbank erosion. The sediment transport is directly linked to the ambient forcing-littoral current, waves, and tide. In this paper, the turbid plume and the suspended mud transport around Guiana mudbanks are studied through a three-dimensional numerical study, under the three main different forcings. The study aims at describing the plume and the action of various physical processes in the suspended mud transport. The model results qualitatively agree with known observations issued from the literature. It is found that, the erosion-at the back of the bank-and the deposition-in front of the bank-could partly explain the migration process of these mudbanks. Waves are fundamental to create the erosion/deposition process, but littoral current and tide modulate it. Bottom flux and plume location vary with tide and these oscillations are accentuated during spring tide. In the same way, the wave incidence angle can explain the variability of erosion and deposition rate velocity along the Guiana coast

Assimilation de données par méthode variationnelle utilisant l’adjoint d’un code de circulation côtière tridimensionnel

The optimal control technique using an adjoint method is applied to fit the parameters of a 3-D primitive equation coastal model due to a data assimilation procedure. Two of the main unknowns of coastal modelling operations - open boundary conditions and turbulent mixing processes in stratified conditions - are successively considered. The aim of the boundary control procedure is to identify boundary forcing to ensure the best fit between data and model results by minimising a function that measures model and data discrepancies. A methodology for proceeding from the continuous to the discrete formulation of a control problem is given. The robustness of the method is tested for the typical barotropic case of a semi-enclosed basin Kelvin wave. The data assimilation method of optimal control is then applied to the turbulence closure problem in the framing of coastal oceanic circulation. Numerical simulation of a schematic destruction of an halocline and an upwelling event resulting from a wind stress imposed at the sea surface in a strongly stratified two-layer case are realized. The adjoint method is used to find out an optimal set of viscosity and diffusivity coefficients which permits the retrieval of the closest computed simulation to hydrodynamic synthetic observations.Une méthode de contrôle optimal est utilisée pour identifier les conditions aux limites ouvertes et les coefficients de viscosité turbulente d’un modèle tridimensionnel de circulation côtière aux équations primitives au moyen d’une méthode d’assimilation de données par méthode variationnelle. L’objectif de cette méthode est d’assurer l’optimisation des paramètres inconnus du modèle en minimisant une fonction de coût mesurant l’écart entre la solution calculée et des observations. La minimisation de cette fonction de coût est réalisée en utilisant l’adjoint du linéarisé tangent du modèle côtier. Une méthode est donnée, dans le cas d’un modèle aux différences finies utilisant une grille décentrée, pour passer de la formulation continue du problème de contrôle optimal et du modèle adjoint à une formulation discrétisée. L’efficacité de la méthode est vérifiée à partir du cas de l’ajustement des conditions aux limites ouvertes pour une circulation associée à une seiche de Kelvin dans un bassin semi-fermé. Elle est ensuite testée vis à vis de l’optimisation du champ de coefficients de viscosité turbulente dans le cas de déstructuration soudaine d’une stratification préalablement existante, comme dans le cas d’une rupture d’une halocline marquée provoquée par un coup de vent. Ces coefficients sont également ajustés dans la phase d’établissement d’un upwelling côtier académique le long d’une côte rectiligne infinie