R. J. Adrian, Particle-imaging techniques for experimental fluid mechanics. Annual review of fluid mechanics, pp.261-304, 1991.

L. Amodei and M. N. Benbourhim, A vector spline approximation, Journal of Approximation Theory, vol.67, issue.1, pp.1-29, 1991.
DOI : 10.1016/0021-9045(91)90025-6

D. L. Anderson, Comparison of the ECMWF seasonal forecast systems 1 and 2, including the relative performance for the 1997, El Nino. . ECMWF Technical Memorandum, vol.8, issue.404, pp.1-93, 2003.

V. Artale, G. Boffetta, A. Celani, M. Cencini, and A. Vulpiani, Dispersion of passive tracers in closed basins: Beyond the diffusion coefficient, Physics of Fluids, vol.9, issue.11, pp.9-3162, 1997.
DOI : 10.1063/1.869433

G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing, 2006.

E. Aurell, G. Boffetta, A. Crisanti, G. Paladin, and A. Vulpiani, Predictability in the large: an extension of the concept of Lyapunov exponent, Journal of Physics A: Mathematical and General, vol.30, issue.1, pp.1-26, 1997.
DOI : 10.1088/0305-4470/30/1/003

D. Auroux and J. Blum, A nudging-based data assimilation method: the Back and Forth Nudging (BFN) algorithm, Nonlinear Processes in Geophysics, vol.15, issue.2, pp.305-319, 2008.
DOI : 10.5194/npg-15-305-2008

URL : https://hal.archives-ouvertes.fr/inria-00327422

D. Auroux and J. Fehrenbach, Identification of velocity fields for geophysical fluids from a sequence of images, Experiments in Fluids, vol.28, issue.1, pp.313-328, 2010.
DOI : 10.1007/s00348-010-0926-9

URL : https://hal.archives-ouvertes.fr/hal-00905015

M. A. Balmaseda, D. L. Anderson, and A. Vidard, Impact of Argo on analyses of the global ocean, Geophysical Research Letters, vol.135, issue.16, p.34, 2007.
DOI : 10.1175/MWR3310.1

URL : https://hal.archives-ouvertes.fr/inria-00181749

M. A. Balmaseda, D. P. Dee, A. Vidard, and D. L. Anderson, A multivariate treatment of bias for sequential data assimilation: Application to the tropical oceans, Quarterly Journal of the Royal Meteorological Society, vol.131, issue.622, pp.133-167, 2007.
DOI : 10.1002/qj.12

URL : https://hal.archives-ouvertes.fr/inria-00176159

M. A. Balmaseda, G. C. Smith, D. L. Haines, T. N. Anderson, A. Palmer et al., Historical reconstruction of the Atlantic Meridional Overturning Circulation from the ECMWF operational ocean reanalysis, Geophysical Research Letters, vol.36, issue.23, 2007.
DOI : 10.1029/2007GL031645

URL : https://hal.archives-ouvertes.fr/inria-00181739

M. A. Balmaseda, A. Vidard, and D. L. Anderson, Climate variability from the new System 3 ocean analysis, ECMWF newsletter, p.113, 2007.

M. A. Balmaseda, A. Vidard, and D. L. Anderson, The ECMWF System 3 ocean analysis, ECMWF Technical Memorandum, vol.508, pp.1-47, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00176165

M. A. Balmaseda, A. Vidard, and D. L. Anderson, The ECMWF Ocean Analysis System: ORA-S3, Monthly Weather Review, vol.136, issue.8, pp.3018-3034, 2008.
DOI : 10.1175/2008MWR2433.1

URL : https://hal.archives-ouvertes.fr/inria-00182186

T. Bengtsson, C. Snyder, and D. Nychka, Toward a nonlinear ensemble filter for high-dimensional systems, Journal of Geophysical Research: Atmospheres, vol.104, issue.C5, p.8775, 2003.
DOI : 10.1029/2002JD002900

F. J. Beron-vera, Mixing by low- and high-resolution surface geostrophic currents, Journal of Geophysical Research, vol.104, issue.C9, p.15, 2010.
DOI : 10.1029/2009JC006006

F. J. Beron-vera and M. J. Olascoaga, An Assessment of the Importance of Chaotic Stirring and Turbulent Mixing on the West Florida Shelf, Journal of Physical Oceanography, vol.39, issue.7, pp.1743-1755, 2009.
DOI : 10.1175/2009JPO4046.1

F. J. Beron-vera, M. J. Olascoaga, and G. J. Goni, Surface Ocean Mixing Inferred from Different Multisatellite Altimetry Measurements, Journal of Physical Oceanography, vol.40, issue.11, pp.40-2466, 2010.
DOI : 10.1175/2010JPO4458.1

F. Birol, J. M. Brankart, J. Lemoine, P. Brasseur, and J. Verron, Assimilation of satellite altimetry referenced to the new GRACE geoid estimate, Geophysical Research Letters, vol.107, issue.C2, 2005.
DOI : 10.1029/2004GL021329

URL : https://hal.archives-ouvertes.fr/hal-00409271

E. Blayo, S. Durbiano, A. Vidard, and F. Dimet, Reduced order strategies for variational data assimilation in oceanic models. Data Assimilation for Geophysical Flows, Sportisse and F.-X, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00325368

A. Boilley and J. Mahfouf, Assimilation of low-level wind in a high-resolution mesoscale model using the back and forth nudging algorithm, Tellus A: Dynamic Meteorology and Oceanography, vol.118, issue.1, p.64, 2012.
DOI : 10.3402/tellusa.v64i0.18697

N. Bormann and P. Bauer, 2010: Estimates of spatial and interchannel observation-error characteristics for current sounder radiances for numerical weather prediction. I: Methods and application to ATOVS data. Q, J.R. Meteorol. Soc, issue.649, pp.136-1036

N. Bormann, A. Collard, and P. Bauer, Estimates of spatial and interchannel observation-error characteristics for current sounder radiances for numerical weather prediction. II: Application to AIRS and IASI data, Quarterly Journal of the Royal Meteorological Society, vol.125, issue.649, pp.136-1051, 2010.
DOI : 10.1002/qj.615

N. Bormann, S. Saarinen, and G. Kelly, The Spatial Structure of Observation Errors in Atmospheric Motion Vectors from Geostationary Satellite Data, Monthly Weather Review, vol.131, issue.4, pp.706-718, 2003.
DOI : 10.1175/1520-0493(2003)131<0706:TSSOOE>2.0.CO;2

J. Brankart, E. Cosme, C. Testut, P. Brasseur, and J. Verron, Efficient Adaptive Error Parameterizations for Square Root or Ensemble Kalman Filters: Application to the Control of Ocean Mesoscale Signals, Monthly Weather Review, vol.138, issue.3, pp.932-950, 2010.
DOI : 10.1175/2009MWR3085.1

URL : https://hal.archives-ouvertes.fr/hal-00491337

J. Brankart, E. Cosme, C. Testut, P. Brasseur, and J. Verron, Efficient Local Error Parameterizations for Square Root or Ensemble Kalman Filters: Application to a Basin-Scale Ocean Turbulent Flow, Monthly Weather Review, vol.139, issue.2, pp.474-493, 2011.
DOI : 10.1175/2010MWR3310.1

P. Brasseur, Ocean data assimilation using sequential methods based on the Kalman Filter. Ocean weather forecasting: An integrated view of oceanography, pp.271-316, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00232778

P. Brasseur and J. Verron, The SEEK filter method for data assimilation in oceanography: a synthesis, Ocean Dynamics, vol.11, issue.C3, pp.5-6, 2006.
DOI : 10.1007/s10236-006-0080-3

URL : https://hal.archives-ouvertes.fr/hal-00220505

P. Brasseur, Data assimilation for marine monitoring and prediction: The MERCATOR operational assimilation systems and the MERSEA developments, Quarterly Journal of the Royal Meteorological Society, vol.131, issue.41, pp.131-3561, 2005.
DOI : 10.1256/qj.05.142

URL : https://hal.archives-ouvertes.fr/hal-00434520

M. Buehner, P. L. Houtekamer, C. Charette, H. L. Mitchell, and B. He, Intercomparison of Variational Data Assimilation and the Ensemble Kalman Filter for Global Deterministic NWP. Part I: Description and Single-Observation Experiments, Monthly Weather Review, vol.138, issue.5, pp.1550-1566, 2010.
DOI : 10.1175/2009MWR3157.1

M. Buehner, P. L. Houtekamer, C. Charette, H. L. Mitchell, and B. He, Intercomparison of Variational Data Assimilation and the Ensemble Kalman Filter for Global Deterministic NWP. Part II: One-Month Experiments with Real Observations, Monthly Weather Review, vol.138, issue.5, pp.1567-1586, 2010.
DOI : 10.1175/2009MWR3158.1

D. G. Cacuci, Sensitivity and Uncertainty Analysis: Theory, 2003.
DOI : 10.1201/9780203498798

E. Candès and D. L. Donoho, singularities, Communications on Pure and Applied Mathematics, vol.9, issue.7, pp.219-266, 2003.
DOI : 10.1002/cpa.10116

F. Castruccio, J. Verron, L. Gourdeau, J. M. Brankart, and P. Brasseur, On the role of the GRACE mission in the joint assimilation of altimetric and TAO data in a tropical Pacific Ocean model, Geophysical Research Letters, vol.104, issue.22, 2006.
DOI : 10.1029/2006GL025823

T. F. Chan and J. Shen, Image processing and analysis. variational, PDE, wavelet, and stochastic methods, 2005.

G. Chastaing, F. Gamboa, and C. Prieur, 2012: Generalized Hoeffding-Sobol Decomposition for Dependent Variables-Application to Sensitivity Analysis, Electronic Journal of Statistics, pp.1-34

C. Chauvin, M. Nodet, A. Vidard, and P. Bouttier, Assimilation of Lagrangian Data in an operational framework, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00652456

P. C. Chu, L. Ivanov, and T. Margolina, On non-linear sensitivity of marine biological models to parameter variations, Ecological Modelling, vol.206, issue.3-4, pp.3-4, 2007.
DOI : 10.1016/j.ecolmodel.2007.04.006

J. A. Church and N. J. White, A 20th century acceleration in global sea-level rise, Geophysical Research Letters, vol.19, issue.D14, 2006.
DOI : 10.1029/2005GL024826

T. Corpetti, P. Héas, ´. E. Memin, and N. Papadakis, Pressure image assimilation for atmospheric motion estimation, Tellus A, vol.28, issue.3, pp.160-178, 2009.
DOI : 10.1111/j.1600-0870.2008.00370.x

URL : https://hal.archives-ouvertes.fr/inria-00273838

P. Courtier, J. Thépaut, and A. Hollingsworth, A strategy for operational implementation of 4D-Var, using an incremental approach, Quarterly Journal of the Royal Meteorological Society, vol.45, issue.519, pp.1-21, 1994.
DOI : 10.1002/qj.49712051912

M. Davey, Multi-model multi-method multi-decadal ocean analyses from the ENACT project, Clivar exchange, vol.11, issue.3, pp.22-25, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00171445

D. P. Dee and S. Uppala, Variational bias correction of satellite radiance data in the ERA-Interim reanalysis, Quarterly Journal of the Royal Meteorological Society, vol.109, issue.D3, pp.1-12, 2009.
DOI : 10.1002/qj.493

J. Derber and F. Bouttier, A reformulation of the background error covariance in the ECMWF global data assimilation system, Tellus A: Dynamic Meteorology and Oceanography, vol.51, issue.123, pp.195-221, 1999.
DOI : 10.3402/tellusa.v51i2.12316

F. Ovidio, V. Fernández, E. Hernández-garcía, and C. López, Mixing structures in the Mediterranean Sea from finite-size Lyapunov exponents, Geophys. Res. Lett, pp.31-35, 2004.

F. Ovidio, J. Isern-fontanet, C. López, E. Hernández-garcía, and E. García-ladona, Comparison between Eulerian diagnostics and finite-size Lyapunov exponents computed from altimetry in the Algerian basin. Deep Sea Research Part I: Oceanographic Research Papers, pp.15-31, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00759988

F. Ovidio, V. Taillandier, I. Taupier-letage, and L. Mortier, Lagrangian validation of the Mediterranean mean dynamic topography by extraction of tracer frontal structures, Mercator Ocean Quarterly Newsletter, vol.32, pp.24-32, 2009.

S. Durbiano, Vecteurs caractéristiques de modèles océaniques pour la réduction d'ordre en assimilation de données, 2001.

G. Evensen, Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, Journal of Geophysical Research, vol.109, issue.Part 4, pp.143-153, 1994.
DOI : 10.1029/94JC00572

G. Evensen, The Ensemble Kalman Filter: theoretical formulation and practical implementation, Ocean Dynamics, vol.53, issue.4, pp.343-367, 2003.
DOI : 10.1007/s10236-003-0036-9

B. Ferron, 2011: A 4D-variational approach applied to an eddy-permitting North Atlantic configuration: synthetic and real data assimilation of altimeter observations. Ocean Modelling, pp.370-385

E. J. Fertig, J. Harlim, and B. R. Hunt, A comparative study of 4D-VAR and a 4D Ensemble Kalman Filter: perfect model simulations with Lorenz-96, Tellus A: Dynamic Meteorology and Oceanography, vol.132, issue.133, pp.96-100, 2007.
DOI : 10.1111/j.1600-0870.2006.00205.x

M. Fisher and H. Auvinen, 2012: Long Window 4D-Var, Proceedings of the ECMWF Seminar Series on Data assimilation for atmosphere and ocean, pp.6-9, 2011.

L. Fu and A. Cazenave, Satellite altimetry and earth sciences, A handbook of techniques and applications, 2001.

J. Gao and M. Xue, An Efficient Dual-Resolution Approach for Ensemble Data Assimilation and Tests with Simulated Doppler Radar Data, Monthly Weather Review, vol.136, issue.3, pp.945-963, 2008.
DOI : 10.1175/2007MWR2120.1

L. Gaultier, J. Verron, J. Brankart, O. Titaud, and P. Brasseur, On the inversion of submesoscale tracer fields to estimate the surface ocean circulation, Journal of Marine Systems, vol.126, 2012.
DOI : 10.1016/j.jmarsys.2012.02.014

I. Y. Gejadze, G. J. Copeland, F. Dimet, and V. Shutyaev, Computation of the analysis error covariance in variational data assimilation problems with nonlinear dynamics, Journal of Computational Physics, vol.230, issue.22, pp.230-7923, 2011.
DOI : 10.1016/j.jcp.2011.03.039

S. Geman and D. Geman, Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images, IEEE Trans. Pattern Anal. Mach. Intell, vol.6, pp.721-741, 1984.

R. J. Greatbatch, 1994: A note on the representation of steric sea level in models that conserve volume rather than mass, J. Geophys. Res, vol.99, issue.12, pp.767-779

A. K. Griffith and N. K. Nichols, Adjoint methods in data assimilation for estimating model error. Flow, Turbulence and Combustion, pp.469-488, 2000.

S. A. Haben, A. S. Lawless, and N. K. Nichols, Conditioning and preconditioning of the variational data assimilation problem, Computers & Fluids, vol.46, issue.1, pp.252-256, 2011.
DOI : 10.1016/j.compfluid.2010.11.025

K. Haines, J. D. Blower, J. P. Drecourt, A. Vidard, I. Astin et al., ): Covariance Relationships, Monthly Weather Review, vol.134, issue.3, pp.759-771, 2006.
DOI : 10.1175/MWR3089.1

G. Haller, Finding finite-time invariant manifolds in two-dimensional velocity fields, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.10, issue.1, pp.99-108, 2000.
DOI : 10.1063/1.166479

G. Haller, Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence, Physics of Fluids, vol.13, issue.11, pp.13-3365, 2001.
DOI : 10.1063/1.1403336

G. Haller, Lagrangian coherent structures from approximate velocity data, Physics of Fluids, vol.14, issue.6, pp.1851-1861, 2002.
DOI : 10.1063/1.1477449

G. Haller, A variational theory of hyperbolic Lagrangian Coherent Structures, Physica D: Nonlinear Phenomena, vol.240, issue.7, pp.574-598
DOI : 10.1016/j.physd.2010.11.010

G. Haller and G. Yuan, Lagrangian coherent structures and mixing in two-dimensional turbulence, Physica D: Nonlinear Phenomena, vol.147, issue.3-4, pp.3-4, 2000.
DOI : 10.1016/S0167-2789(00)00142-1

T. M. Hamill and C. Snyder, A Hybrid Ensemble Kalman Filter???3D Variational Analysis Scheme, Monthly Weather Review, vol.128, issue.8, pp.2905-2919, 2010.
DOI : 10.1175/1520-0493(2000)128<2905:AHEKFV>2.0.CO;2

T. Homma and A. Saltelli, Importance measures in global sensitivity analysis of nonlinear models, Reliability Engineering & System Safety, vol.52, issue.1, pp.1-17, 1996.
DOI : 10.1016/0951-8320(96)00002-6

B. K. Horn and B. G. Schunck, Determining optical flow, Artificial Intelligence, vol.17, issue.1-3, pp.185-203, 1981.
DOI : 10.1016/0004-3702(81)90024-2

I. Hoteit, X. Luo, and D. T. Pham, Particle Kalman Filtering: A Nonlinear Bayesian Framework for Ensemble Kalman Filters*, Monthly Weather Review, vol.140, issue.2, 2011.
DOI : 10.1175/2011MWR3640.1

I. Hoteit, D. Pham, and G. Triantafyllou, Particle Kalman filtering for data assimilation in meteorology and oceanography, Proceedings of the 3rd International Conference on Reanalysis (WCRP '08), pp.1-6, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00853919

I. Hoteit, D. Pham, G. Triantafyllou, and G. Korres, A New Approximate Solution of the Optimal Nonlinear Filter for Data Assimilation in Meteorology and Oceanography, Monthly Weather Review, vol.136, issue.1, pp.317-334, 2008.
DOI : 10.1175/2007MWR1927.1

URL : https://hal.archives-ouvertes.fr/hal-00853121

B. R. Hunt, Four-dimensional ensemble Kalman filtering, Tellus A: Dynamic Meteorology and Oceanography, vol.33, issue.130, pp.273-277
DOI : 10.3402/tellusa.v56i4.14424

B. Ingleby and M. Huddleston, Quality control of ocean temperature and salinity profiles ??? Historical and real-time data, Journal of Marine Systems, vol.65, issue.1-4, pp.1-4, 2007.
DOI : 10.1016/j.jmarsys.2005.11.019

B. Ingleby and A. C. Lorenc, Bayesian quality control using multivariate normal distributions, Quarterly Journal of the Royal Meteorological Society, vol.114, issue.513, pp.1195-1225, 1993.
DOI : 10.1002/qj.49711951316

A. H. Jazwinski, Stochastic processes and filtering theory, 1970.

R. Kalman, A New Approach to Linear Filtering and Prediction Problems, Journal of Basic Engineering, vol.82, issue.1, 1960.
DOI : 10.1115/1.3662552

E. Kalnay, H. Li, T. Miyoshi, S. Yang, and J. Ballabrera-poy, -D-Var or ensemble Kalman filter? Tellus A, pp.758-773, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00302201

G. Korotaev, E. Huot, F. L. Dimet, I. Herlin, S. Stanichny et al., Retrieving ocean surface current by 4-D variational assimilation of sea surface temperature images, Remote Sensing of Environment, vol.112, issue.4, pp.1464-1475, 2008.
DOI : 10.1016/j.rse.2007.04.020

URL : https://hal.archives-ouvertes.fr/hal-00283896

T. Kraus, P. Kuhl, L. Wirsching, H. G. Bock, and M. Diehl, A Moving Horizon State Estimation algorithm applied to the Tennessee Eastman Benchmark Process, 2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems, pp.377-382, 2006.
DOI : 10.1109/MFI.2006.265620

M. Krysta, E. Blayo, E. Cosme, and J. Verron, 2011: A consistent hybrid variational-smoothing data assimilation method: Application to a simple shallow-water model of the turbulent mid-latitude ocean, Mon. Wea. Rev

S. Kucherenko, M. Rodriguez-fernandez, C. Pantelides, and N. Shah, Monte Carlo evaluation of derivative-based global sensitivity measures, Reliability Engineering & System Safety, vol.94, issue.7, pp.94-1135, 2009.
DOI : 10.1016/j.ress.2008.05.006

T. Lagarde, Nouvelle approche des méthodes d'assimilation de données: les algorithmes de point selle, 2000.

G. Lapeyre, Characterization of finite-time Lyapunov exponents and vectors in two-dimensional turbulence, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.12, issue.3, pp.688-699, 2002.
DOI : 10.1063/1.1499395

URL : https://hal.archives-ouvertes.fr/hal-00310234

C. Lauvernet, J. M. Brankart, F. Castruccio, G. Broquet, P. Brasseur et al., A truncated Gaussian filter for data assimilation with inequality constraints: Application to the hydrostatic stability condition in ocean models, Ocean Modelling, vol.27, issue.1-2, pp.1-17, 2009.
DOI : 10.1016/j.ocemod.2008.10.007

L. Dimet, F. , and O. Talagrand, Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects, Tellus A, vol.109, issue.2, pp.97-110, 1986.
DOI : 10.1111/j.1600-0870.1986.tb00459.x

D. J. Lea, J. Drécourt, K. Haines, and M. J. Martin, Ocean altimeter assimilation with observational- and model-bias correction, Quarterly Journal of the Royal Meteorological Society, vol.112, issue.C1, pp.134-135, 2008.
DOI : 10.1002/qj.320

Y. Lehahn, F. Ovidio, M. Lévy, and E. Heifetz, Stirring of the northeast Atlantic spring bloom: A Lagrangian analysis based on multisatellite data, Journal of Geophysical Research, vol.14, issue.C4, p.15, 2007.
DOI : 10.1029/2006JC003927

URL : https://hal.archives-ouvertes.fr/hal-00770691

B. Lemieux and A. Vidard, Weak constraint 4D-Var in NEMOVAR, a multiple snapshot approach, 2011.

M. Lévy, D. Iovino, S. Masson, G. Madec, P. Klein et al., Remote impacts of Sub-Mesoscale Dynamics on new production, Mercator Ocean Quarterly Newsletter, vol.13, pp.13-17, 2009.

M. Liu, Variational assimilation of acoustic tomography, 1995.

Z. Q. Liu and F. Rabier, The potential of high-density observations for numerical weather prediction: A study with simulated observations, Quarterly Journal of the Royal Meteorological Society, vol.124, issue.594, pp.3013-3035, 2006.
DOI : 10.1256/qj.02.170

A. C. Lorenc, A Global Three-Dimensional Multivariate Statistical Interpolation Scheme, Monthly Weather Review, vol.109, issue.4, pp.701-721, 1981.
DOI : 10.1175/1520-0493(1981)109<0701:AGTDMS>2.0.CO;2

B. Luong, J. Blum, and J. Verron, A variational method for the resolution of a data assimilation problem in oceanography, Inverse Problems, vol.14, issue.4, pp.1-20, 1998.
DOI : 10.1088/0266-5611/14/4/014

J. Ma, O. Titaud, A. Vidard, and F. Dimet, Spatio-temporal structure extraction and denoising of geophysical fluid image sequences using 3D curvelet transforms, INRIA Research report, vol.6683, pp.1-30, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00329599

P. C. Mahalanobis, On the generalised distance in statistics, Proceedings of the National Institute of Sciences of India, pp.49-55, 1936.

S. G. Mallat, A wavelet tour of signal processing, 1998.

M. Mathur, G. Haller, T. Peacock, J. E. Ruppert-felsot, and H. L. Swinney, Uncovering the Lagrangian Skeleton of Turbulence, Physical Review Letters, vol.98, issue.14, pp.98-502, 2007.
DOI : 10.1103/PhysRevLett.98.144502

N. Maximenko, P. Niiler, L. Centurioni, M. Rio, O. Melnichenko et al., Mean Dynamic Topography of the Ocean Derived from Satellite and Drifting Buoy Data Using Three Different Techniques*, Journal of Atmospheric and Oceanic Technology, vol.26, issue.9, pp.1910-1919, 2009.
DOI : 10.1175/2009JTECHO672.1

M. J. Mcphaden, The Tropical Ocean-Global Atmosphere observing system: A decade of progress, Journal of Geophysical Research: Oceans, vol.10, issue.44, pp.169-183, 1998.
DOI : 10.1029/97JC02906

Y. Michel, Displacing Potential Vorticity Structures by the Assimilation of Pseudo-Observations, Monthly Weather Review, vol.139, issue.2, pp.549-565, 2011.
DOI : 10.1175/2010MWR3395.1

Y. Michel and F. Bouttier, Automated tracking of dry intrusions on satellite water vapour imagery and model output, Quarterly Journal of the Royal Meteorological Society, vol.78, issue.620, pp.2257-2276, 2006.
DOI : 10.1256/qj.05.179

I. Mirouze and A. T. Weaver, Representation of correlation functions in variational assimilation using an implicit diffusion operator, Quarterly Journal of the Royal Meteorological Society, vol.22, issue.651, pp.1421-1443, 2010.
DOI : 10.1002/qj.643

K. S. Mogensen, M. A. Balmaseda, M. Martin, and A. Vidard, NEMOVAR: A variational data assimilation system for the NEMO ocean model, ECMWF newsletter, vol.120, pp.17-21, 2009.

F. Molteni, R. Buizza, T. N. Palmer, and T. Petroliagis, The ECMWF Ensemble Prediction System: Methodology and validation, Quarterly Journal of the Royal Meteorological Society, vol.117, issue.529, pp.122-73, 1996.
DOI : 10.1002/qj.49712252905

A. M. Moore, H. G. Arango, E. D. Lorenzo, B. Cornuelle, A. Miller et al., A comprehensive ocean prediction and analysis system based on the tangent linear and adjoint of a regional ocean model, Ocean Modelling, vol.7, issue.1-2, pp.227-258, 2004.
DOI : 10.1016/j.ocemod.2003.11.001

M. Morris, Factorial Sampling Plans for Preliminary Computational Experiments, Technometrics, vol.1, issue.2, pp.161-174, 1991.
DOI : 10.2307/1266468

M. Mu, W. Duan, and B. Wang, Conditional nonlinear optimal perturbation and its applications, Nonlinear Processes in Geophysics, vol.10, issue.6, pp.493-501, 2003.
DOI : 10.5194/npg-10-493-2003

URL : https://hal.archives-ouvertes.fr/hal-00302254

M. Mu, G. Huan, W. Jiafeng, and L. Yong, The impact of nonlinear stability and instability on the validity of the tangent linear model, Adv. Atmos. Sci, vol.17, issue.3, pp.375-390, 2000.

M. Mu, F. Zhou, and H. Wang, A Method for Identifying the Sensitive Areas in Targeted Observations for Tropical Cyclone Prediction: Conditional Nonlinear Optimal Perturbation, Monthly Weather Review, vol.137, issue.5, pp.1623-1639, 2009.
DOI : 10.1175/2008MWR2640.1

L. Nerger, W. Hiller, and J. Shröter, A comparison of error subspace Kalman filters, Tellus A: Dynamic Meteorology and Oceanography, vol.130, issue.3, pp.715-735, 2005.
DOI : 10.3402/tellusa.v57i5.14732

´. E. Neveu, Application des méthodes multigrillesàmultigrilles`multigrillesà l'assimilation variationnelle de données en géophysique, 2011.

S. Nieman, P. Menzel, C. Hayden, D. Gray, S. Wanzong et al., Fully Automated Cloud-Drift Winds in NESDIS Operations, Bulletin of the American Meteorological Society, vol.78, issue.6, pp.1121-1133, 1997.
DOI : 10.1175/1520-0477(1997)078<1121:FACDWI>2.0.CO;2

M. Nodet, Variational assimilation of Lagrangian data in oceanography, Inverse Problems, vol.22, issue.1, p.245, 2006.
DOI : 10.1088/0266-5611/22/1/014

URL : https://hal.archives-ouvertes.fr/inria-00173069

M. Nodet, Optimal control of the Primitive Equations of the ocean with Lagrangian observations, ESAIM: Control, Optimisation and Calculus of Variations, vol.16, issue.2, pp.400-419, 2009.
DOI : 10.1051/cocv/2009003

URL : https://hal.archives-ouvertes.fr/inria-00268804

M. J. Olascoaga, F. J. Beron-vera, L. E. Brand, and H. K. , Tracing the early development of harmful algal blooms on the West Florida Shelf with the aid of Lagrangian coherent structures, Journal of Geophysical Research, vol.19, issue.C6, p.pp, 2008.
DOI : 10.1029/2007JC004533

E. Ott, Chaos in Dynamical Systems, Chaos in Dynamical Systems, 1993.

E. Ott, A local ensemble Kalman filter for atmospheric data assimilation, Tellus A: Dynamic Meteorology and Oceanography, vol.56, issue.131, pp.415-428, 2004.
DOI : 10.3402/tellusa.v56i5.14462

J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos, and Transport, 1989.

N. Papadakis and . Memin, Variational Assimilation of Fluid Motion from Image Sequence, SIAM Journal on Imaging Sciences, vol.1, issue.4, pp.343-363, 2008.
DOI : 10.1137/080713896

URL : https://hal.archives-ouvertes.fr/hal-00596149

D. T. Pham, A singular evolutive interpolated Kalman filter for data assimilation in oceanography, pp.1-22, 1996.

D. T. Pham, Stochastic Methods for Sequential Data Assimilation in Strongly Nonlinear Systems, Monthly Weather Review, vol.129, issue.5, pp.1194-1207, 2001.
DOI : 10.1175/1520-0493(2001)129<1194:SMFSDA>2.0.CO;2

URL : https://hal.archives-ouvertes.fr/inria-00073082

D. T. Pham, J. Verron, and M. Roubaud, A singular evolutive extended Kalman filter for data assimilation in oceanography, Journal of Marine Systems, vol.16, pp.3-4, 1998.

C. Pires, R. Vautard, and T. Olivier, On extending the limits of variational assimilation in nonlinear chaotic systems, Tellus A: Dynamic Meteorology and Oceanography, vol.118, issue.143, pp.96-121, 1996.
DOI : 10.3402/tellusa.v48i1.11634

X. Qin and M. Mu, Influence of conditional nonlinear optimal perturbations sensitivity on typhoon track forecasts, Quarterly Journal of the Royal Meteorological Society, vol.137, issue.662, 2011.
DOI : 10.1002/qj.902

F. Rabier, Overview of global data assimilation developments in numerical weather-prediction centres, Quarterly Journal of the Royal Meteorological Society, vol.121, issue.613, pp.3215-3233, 2005.
DOI : 10.1256/qj.05.129

L. Raynaud, L. Berre, and G. Desroziers, An extended specification of flow-dependent background error variances in the M??t??o-France global 4D-Var system, Quarterly Journal of the Royal Meteorological Society, vol.136, issue.656, pp.607-619, 2011.
DOI : 10.1002/qj.795

J. G. Richman, R. N. Miller, and Y. Spitz, Error estimates for assimilation of satellite sea surface temperature data in ocean climate models, Geophysical Research Letters, vol.104, issue.18, p.32, 2005.
DOI : 10.1029/2005GL023591

M. H. Rio and F. Hernandez, A mean dynamic topography computed over the world ocean from altimetry, in situ measurements, and a geoid model, Journal of Geophysical Research, vol.16, issue.4, pp.12-032, 2004.
DOI : 10.1029/2003JC002226

O. Rivì-ere, G. Lapeyre, and O. Talagrand, A novel technique for nonlinear sensitivity analysis: application to moist predictability, Quarterly Journal of the Royal Meteorological Society, vol.45, issue.643, pp.1520-1537, 2009.
DOI : 10.1002/qj.460

A. Saltelli, K. Chan, and E. Scott, Sensitivity analysis. Wiley series in probability and statistics, 2000.
URL : https://hal.archives-ouvertes.fr/inria-00386559

J. Schmetz, K. Holmlund, J. Hoffman, B. Strauss, B. Mason et al., Operational Cloud-Motion Winds from Meteosat Infrared Images, Journal of Applied Meteorology, vol.32, issue.7, pp.32-1206, 1993.
DOI : 10.1175/1520-0450(1993)032<1206:OCMWFM>2.0.CO;2

S. C. Shadden, F. Lekien, and J. E. Marsden, Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic??flows, Physica D: Nonlinear Phenomena, vol.212, issue.3-4, pp.3-4, 2005.
DOI : 10.1016/j.physd.2005.10.007

S. C. Shadden, F. Lekien, J. D. Paduan, F. P. Chavez, and J. E. Marsden, The correlation between surface drifters and coherent structures based on high-frequency radar data in Monterey Bay, Deep Sea Research Part II: Topical Studies in Oceanography, vol.56, issue.3-5, pp.3-5, 2009.
DOI : 10.1016/j.dsr2.2008.08.008

E. Simon and L. Bertino, Application of the Gaussian anamorphosis to assimilation in a 3-D coupled physical-ecosystem model of the North Atlantic with the EnKF: a twin experiment, Ocean Science, vol.5, issue.4, pp.495-510, 2009.
DOI : 10.5194/os-5-495-2009

N. R. Smith, J. E. Blomley, and G. Meyers, A univariate statistical interpolation scheme for subsurface thermal analyses in the tropical oceans, Progress in Oceanography, vol.28, issue.3, pp.219-256, 1991.
DOI : 10.1016/0079-6611(91)90009-B

I. M. Sobol, Sensitivity estimates for nonlinear mathematical models, Matem. Mod, vol.2, issue.1, 1990.

I. M. Sobol and S. Kucherenko, Derivative based global sensitivity measures and their link with global sensitivity indices, Mathematics and Computers in Simulation, vol.79, issue.10, pp.79-3009, 2009.
DOI : 10.1016/j.matcom.2009.01.023

I. Souopgui, Assimilation d'images pour les fluides géophysiques, 2010.

V. N. Stepanov, K. Haines, and G. C. Smith, 2012: Assimilation of RAPID array observations into an ocean model. Q, J.R. Meteorol. Soc

L. Stewart, S. Dance, and N. Nichols, Correlated observation errors in data assimilation, International Journal for Numerical Methods in Fluids, vol.2, issue.8, pp.56-1521, 2008.
DOI : 10.1002/fld.1636

A. Storto, S. Dobricic, S. Masina, and P. D. Pietro, Assimilating Along-Track Altimetric Observations through Local Hydrostatic Adjustment in a Global Ocean Variational Assimilation System, Monthly Weather Review, vol.139, issue.3, pp.738-754, 2011.
DOI : 10.1175/2010MWR3350.1

B. D. Tapley, D. P. Chambers, S. Bettadpur, and J. Ries, Large scale ocean circulation from the GRACE GGM01 Geoid, Geophysical Research Letters, vol.4, issue.1, p.30, 2003.
DOI : 10.1029/2003GL018622

A. Tikhonov, Regularization of incorrectly posed problems, Soviet Math. Dokl, vol.4, pp.1624-1627, 1963.

O. Titaud, J. Brankart, and J. Verron, On the use of Finite-Time Lyapunov Exponents and Vectors for direct assimilation of tracer images into ocean models, Tellus A: Dynamic Meteorology and Oceanography, vol.16, issue.3, pp.1038-1051, 2011.
DOI : 10.1111/j.1600-0870.2009.00416.x

O. Titaud, A. Vidard, I. Souopgui, and F. Dimet, Assimilation of image sequences in numerical models, Tellus A: Dynamic Meteorology and Oceanography, vol.105, issue.8, pp.30-47, 2010.
DOI : 10.1111/j.1600-0870.2009.00416.x

URL : https://hal.archives-ouvertes.fr/inria-00332815

Z. Toth and E. Kalnay, Ensemble Forecasting at NCEP and the Breeding Method, Monthly Weather Review, vol.125, issue.12, pp.3297-3319, 1997.
DOI : 10.1175/1520-0493(1997)125<3297:EFANAT>2.0.CO;2

T. Mahamadou-kele and H. , Interfacing image processing libraries with geophysical fluid forecasting numerical systems, Tech. rep., ENSIMAG, 2009.

Y. Trémolet, Accounting for an imperfect model in 4D-Var, Quarterly Journal of the Royal Meteorological Society, vol.121, issue.621, pp.2483-2504, 2007.
DOI : 10.1256/qj.05.224

Y. Trémolet, Incremental 4D-Var convergence study, Tellus A: Dynamic Meteorology and Oceanography, vol.124, issue.1, pp.706-718, 2007.
DOI : 10.1111/j.1600-0870.2007.00271.x

Y. Trémolet, Model-error estimation in 4D-Var, Quarterly Journal of the Royal Meteorological Society, vol.125, issue.626, pp.1267-1280
DOI : 10.1002/qj.94

P. J. Van-leeuwen and M. Ades, 2012: Efficient fully nonlinear data assimilation for geophysical fluid dynamics, Computers & Geosciences, pp.1-36

F. Veersé, D. T. Pham, and J. Verron, SEEK: a consistent hybrid variational-smoothing data assimilation method, INRIA Research report, vol.3902, pp.4-5, 2000.

F. Veersé and J. Thépaut, Multiple-truncation incremental approach for four-dimensional variational data assimilation, Quarterly Journal of the Royal Meteorological Society, vol.124, issue.1, pp.1889-1908, 1998.
DOI : 10.1002/qj.49712455006

M. Verlaan and A. W. Heemink, Tidal flow forecasting using reduced rank square root filters, Stochastic Hydrology and Hydraulics, vol.19, issue.4, pp.349-368, 1997.
DOI : 10.1007/BF02427924

M. Verlaan and A. W. Heemink, Nonlinearity in Data Assimilation Applications: A Practical Method for Analysis, Monthly Weather Review, vol.129, issue.6, pp.1578-1589, 2001.
DOI : 10.1175/1520-0493(2001)129<1578:NIDAAA>2.0.CO;2

G. Vernieres, C. K. Jones, and K. Ide, Capturing eddy shedding in the Gulf of Mexico from Lagrangian observations, Physica D: Nonlinear Phenomena, vol.240, issue.2, pp.166-179, 2011.
DOI : 10.1016/j.physd.2010.06.008

A. Vidard, Vers une prise en compte des erreurs-modèle en assimilation de données 4D-variationnelle. ApplicationàApplication`Applicationà un modèle réaliste d'océan, 2001.

A. Vidard, 2010: Simplification operator and its inverse for multi-incremental assimilation, pp.1-15

A. Vidard, D. L. Anderson, and M. A. Balmaseda, Impact of Ocean Observation Systems on Ocean Analysis and Seasonal Forecasts, Monthly Weather Review, vol.135, issue.2, pp.409-429, 2007.
DOI : 10.1175/MWR3310.1

URL : https://hal.archives-ouvertes.fr/inria-00176154

A. Vidard, M. A. Balmaseda, and D. L. Anderson, Assimilation of Altimeter Data in the ECMWF Ocean Analysis System 3, Monthly Weather Review, vol.137, issue.4, pp.1393-1408, 2009.
DOI : 10.1175/2008MWR2668.1

URL : https://hal.archives-ouvertes.fr/inria-00325685

A. Vidard, E. Blayo, F. Dimet, and A. Piacentini, Variational Data Analysis with Imperfect Model. Flow, Turbulence and Combustion, pp.4-7, 2000.
URL : https://hal.archives-ouvertes.fr/inria-00325356

A. Vidard, F. Dimet, and A. Piacentini, Determination of optimal nudging coefficients, Tellus A: Dynamic Meteorology and Oceanography, vol.118, issue.5, pp.1-15, 2003.
DOI : 10.3402/tellusb.v43i4.15398

URL : https://hal.archives-ouvertes.fr/inria-00325360

A. Vidard, A. Piacentini, and F. Dimet, Variational data analysis with control of the forecast bias, Tellus A, vol.56, issue.3, pp.1-12, 2004.
URL : https://hal.archives-ouvertes.fr/inria-00325592

A. Vidard, F. Vigilant, C. Deltel, and R. Benshila, NEMOTAM Short and long term development strategies, pp.1-14, 2009.

A. Vidard, F. Vigilant, C. Deltel, and R. Benshila, 2010: NEMO Tangent & Adjoint Models (NemoTam) Reference Manual & User's Guide, pp.1-38
DOI : 10.5194/gmd-8-1245-2015

URL : http://doi.org/10.5194/gmd-8-1245-2015

A. Vidard, F. Vigilant, C. Deltel, and R. Benshila, 2012: NEMO Tangent & Adjoint Models Reference Manual & User's Guide, pp.1-36
DOI : 10.5194/gmd-8-1245-2015

URL : http://doi.org/10.5194/gmd-8-1245-2015

X. Vigan, C. Provost, R. Bleck, and P. Courtier, Sea surface velocities from sea surface temperature image sequences: 1. Method and validation using primitive equation model output, Journal of Geophysical Research: Oceans, vol.28, issue.C8, pp.499-518, 2000.
DOI : 10.1029/2000JC900027

A. T. Weaver and P. Courtier, Correlation modelling on the sphere using a generalized diffusion equation, Quarterly Journal of the Royal Meteorological Society, vol.108, issue.575, pp.1815-1846, 2001.
DOI : 10.1002/qj.49712757518

A. T. Weaver, C. Deltel, E. Machu, S. Ricci, and N. Daget, A multivariate balance operator for variational ocean data assimilation, Quarterly Journal of the Royal Meteorological Society, vol.131, issue.41, pp.131-3605, 2005.
DOI : 10.1256/qj.05.119

URL : https://hal.archives-ouvertes.fr/hal-00125249

A. T. Weaver and I. Mirouze, 2012: On the diffusion equation and its application to isotropic and anisotropic correlation modelling in variational assimilation. Q, J.R. Meteorol. Soc

A. T. Weaver and A. Piacentini, Representation of correlated observation error in the absolute dynamic topography: theory and numerical implementation in NEMOVAR, pp.1-9, 2012.

P. Weston, 2011: Progress toward the implementation of correlated observation errors in 4D-Var, pp.1-33

M. Yaremchuk, D. Nechaev, and C. Pan, A Hybrid Background Error Covariance Model for Assimilating Glider Data into a Coastal Ocean Model, Monthly Weather Review, vol.139, issue.6, 2011.
DOI : 10.1175/2011MWR3510.1

F. Zhang, M. Zhang, and J. A. Hansen, Coupling ensemble Kalman filter with four-dimensional variational data assimilation, Advances in Atmospheric Sciences, vol.133, issue.9, pp.1-8, 2009.
DOI : 10.1007/s00376-009-0001-8