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

M. Fisher and P. Courtier, Estimating the covariance matrices of analysis and forecast error in variational data assimilation, ECMWF Research Department Techn. Memo, vol.220, 1995.

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

I. Gejadze, L. Dimet, F. Shutyaev, and V. , On Analysis Error Covariances in Variational Data Assimilation, SIAM Journal on Scientific Computing, vol.30, issue.4, pp.1847-1874, 2008.
DOI : 10.1137/07068744X
URL : https://hal.archives-ouvertes.fr/inria-00391893

I. Gejadze, L. Dimet, F. Shutyaev, and V. , On optimal solution error covariances in variational data assimilation problems, Journal of Computational Physics, vol.229, issue.6, pp.2292159-2178, 2010.
DOI : 10.1016/j.jcp.2009.11.028
URL : https://hal.archives-ouvertes.fr/hal-00787292

I. Gejadze, L. Dimet, F. Shutyaev, and V. , Computation of the optimal solution error covariance in variational data assimilation problems with nonlinear dynamics, Journal of Computational Physics, pp.23079-7943, 2011.

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.

I. Gejadze, V. Shutyaev, L. Dimet, and F. , Analysis error covariance versus posterior covariance in variational data assimilation. Q, J.R. Meteorol. Soc, issue.138, pp.1-16, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00926878

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

A. K. Griffith, M. J. Martin, and N. K. Nichols, Techniques for treating systematic model error in 3D and 4D data assimilation, Proceedings of the Third WMO Int. Symposium on Assimilation of Observations in Meteorology and Oceanography, pp.9-12, 2000.

L. Dimet, F. Shutyaev, and V. , On deterministic error analysis in variational data assimilation, Nonlinear Processes in Geophysics, vol.12, issue.4, pp.481-490, 2005.
DOI : 10.5194/npg-12-481-2005
URL : https://hal.archives-ouvertes.fr/hal-00331085

L. Dimet, F. Shutyaev, V. P. Gejadze, and I. , On optimal solution error in variational data assimilation: theoretical aspects, Russian Journal of Numerical Analysis and Mathematical Modelling, vol.21, issue.2, pp.139-152, 2006.
DOI : 10.1515/156939806776369492
URL : https://hal.archives-ouvertes.fr/inria-00391910

L. Dimet, F. X. Talagrand, and O. , 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

J. L. Lions, Contrôle optimal des systèmes gouvernés par deséquationsdeséquations aux dérivées partielles . ? Paris: Dunod, 1968.

A. C. Lorenc and Q. J. Roy, Analysis methods for numerical weather prediction, Quarterly Journal of the Royal Meteorological Society, vol.108, issue.474, pp.1177-1194, 1986.
DOI : 10.1002/qj.49711247414

G. I. Marchuk, V. I. Agoshkov, and V. P. Shutyaev, Adjoint Equations and Perturbation Algorithms in Nonlinear Problems, 1996.

I. M. Navon, Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography, Dynamics of Atmospheres and Oceans, vol.27, issue.1-4, pp.2755-79, 1997.
DOI : 10.1016/S0377-0265(97)00032-8

Y. Sasaki, SOME BASIC FORMALISMS IN NUMERICAL VARIATIONAL ANALYSIS, Monthly Weather Review, vol.98, issue.12, pp.875-883, 1970.
DOI : 10.1175/1520-0493(1970)098<0875:SBFINV>2.3.CO;2

V. P. Shutyaev, L. Dimet, F. Gejadze, and I. Yu, A posteriori error covariances in variational data assimilation, Russian Journal of Numerical Analysis and Mathematical Modelling, vol.24, issue.2, pp.161-169, 2009.
DOI : 10.1515/RJNAMM.2009.011
URL : https://hal.archives-ouvertes.fr/inria-00391869

A. M. Stuart, Inverse problems: A Bayesian perspective, Acta Numerica, vol.19, issue.19, pp.451-559, 2010.
DOI : 10.1017/S0962492910000061

A. Tarantola, Inverse Problems Theory: Methods for Data Fitting and Model Parameter Estimation, 1987.

W. C. Thacker, The role of the Hessian matrix in fitting models to measurements, Journal of Geophysical Research, vol.93, issue.C5, pp.6177-6196, 1989.
DOI : 10.1029/JC094iC05p06177

P. A. Vidard, Vers une prise en compte de lerreur modèles en assimilation de données 4D- variationnelle. ApplicationàApplication`Applicationà un modèle réaliste d'océan, Thèse de doctorat, 2001.

P. A. Vidard, E. Blayo, L. Dimet, F. Piacentini, and A. , 4D variational data analysis with imperfect model, Flow. Turb. Comb, pp.65-489, 2000.
URL : https://hal.archives-ouvertes.fr/inria-00325356

P. A. Vidard, A. Piacentini, L. Dimet, and F. , Variational data analysis with control of the forecast bias, Tellus A, issue.3, pp.56177-188, 2004.
URL : https://hal.archives-ouvertes.fr/inria-00325592