W. Thacker, The role of the Hessian matrix in fitting models to measurements, J. Geophys. Res, vol.94, issue.C5, pp.6177-6196, 1989.

I. Gejadze, F. Dimet, and V. Shutyaev, On analysis error covariances in variational data assimilation, SIAM J. Sci. Computing, vol.30, issue.4, pp.1847-1874, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00391893

Y. Sasaki, Some basic formalism in numerical variational analysis, Month. Wea. Rev, vol.98, issue.12, pp.875-883, 1970.

A. Jazwinski, Stochastic Processes and Filtering Theory, 1970.

S. Cotter, M. Dashti, J. Robinson, and A. Stuart, Bayesian inverse problems for functions and applications to fluid mechanics, Inverse Problems, vol.25, pp.1-43, 2009.

I. Gejadze and V. Shutyaev, An optimal control problem of initial data restoration, Computational Mathematics and Mathematical Physics, vol.39, issue.9, pp.1416-1425, 1999.

F. Dimet and V. Shutyaev, On deterministic error analysis in variational data assimilation, Nonlinear Processes in Geophysics, vol.12, pp.481-490, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00331085

T. Vuki?evi?, M. Steyscal, and M. Hecht, Properties of advection algorithms in the context of variational data assimilation, Q.J.R. Meteorol. Soc, vol.129, pp.1221-1231, 2001.

S. Jenkins, C. Budd, M. Freitag, and N. Smith, The effect of numerical model error on data assimilation, Comp. Appl. Math, vol.290, pp.567-588, 2015.

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

F. Dimet and O. Talagrand, Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects, Tellus A, vol.38, issue.2, pp.97-110, 1986.

L. Ning, F. Carli, A. Ebtehaj, E. Foufoula-georgiou, and T. Georgiou, Coping with model error in variational data assimilation using optimal mass transport, Water Resour. Res, vol.50, pp.5817-5830, 2014.

J. Derber, A variational continuous assimilation technique, Mon. Weather Rev, vol.117, pp.2437-2446, 1989.

Y. Trémolet, Model-error estimation in 4D-Var, Q.J.R. Meteorol. Soc, vol.133, issue.626, pp.1267-1280, 2007.

A. Carrassi and S. Vannitsem, Accounting for model error in variational data assimilation: a deterministic approach, Month. Wea. Rev, vol.138, pp.875-883, 2010.

D. Furbish, M. Y. Hussaini, F. Dimet, P. Ngnepieba, and Y. Wu, On discretization error and its control in variational data assimilation, Tellus, vol.60, pp.979-991, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00391879

A. K. Griffith and N. K. Nichols, Adjoint methods in data assimilation for estimating model error, Flow, Turbulence and Combustion, vol.65, issue.3/4, pp.469-488, 2000.

A. Griffith and N. Nichols, Accounting for model error in data assimilation using adjoint methods, Computational Differentiation: Techniques, Applications and Tools, pp.195-204, 1996.

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

S. Akella and I. Navon, Different approaches to model error formulation in 4D-Var: a study with high resolution advection schemes, Tellus, vol.61, pp.112-128, 2009.

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

A. Vidard, E. Blayo, F. Dimet, and A. Piacentini, 4D Variational Data Analysis with Imperfect Model, Flow, Turbulence and Combustion, vol.65, issue.3-4, pp.489-504, 2000.
URL : https://hal.archives-ouvertes.fr/inria-00325356

A. Vidard, F. Dimet, and A. Piacentini, Determination of optimal nudging coefficients, Tellus A, vol.55, pp.1-15, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00325360

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

Y. Trémolet, Accounting for an imperfect model in 4D-Var, Q.J.R. Meteorol. Soc, vol.132, issue.621, pp.2483-2504, 2006.

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, IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems, pp.377-382, 2006.

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

M. Fisher and H. Auvinen, Long Window 4D-Var, Proceedings of the ECMWF Seminar Series on Data assimilation for atmosphere and ocean, pp.189-202, 2011.

S. Patankar, Numerical Heat Transfer and Fluid Flow, 1980.

I. Gejadze, F. Dimet, and V. Shutyaev, On optimal solution error covariances in variational data assimilation problems, Journal of Computational Physics, vol.229, issue.6, pp.2159-2178, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00787292

R. Lehoucq, D. C. Sorensen, C. Yang, and . Users, Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM, 1998.

L. Hascoët and V. , TAPENADE 2.1 user's guide, INRIA Technical Report, issue.0300, pp.1-78, 2004.

W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical recipes in Fortran 77: the art of scientific computing, 1992.