N. Gordon, D. Salmond, and A. Smith, Novel approach to non-linear/non-Gaussian Bayesian state estimation, IEEE Processing-F, vol.140, issue.2

A. Cuzol and E. Mémin, A Stochastic Filtering Technique for Fluid Flow Velocity Fields Tracking, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.31, issue.7, pp.1278-1293, 2009.
DOI : 10.1109/TPAMI.2008.152

G. Evensen, Sequential data assimilation with a non linear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res, vol.99, issue.C510, pp.143-162, 1994.

F. Dimet 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

A. Gronskis, D. Heitz, and E. Mémin, Inflow and initial conditions for direct numerical simulation based on adjoint data assimilation, Journal of Computational Physics, vol.242, issue.6, pp.480-497, 2013.
DOI : 10.1016/j.jcp.2013.01.051
URL : https://hal.archives-ouvertes.fr/hal-00654290

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, 2000.
DOI : 10.1175/1520-0493(2000)128<2905:AHEKFV>2.0.CO;2

A. C. Lorenc, The potential of the ensemble Kalman filter for NWP???a comparison with 4D-Var, Quarterly Journal of the Royal Meteorological Society, vol.130, issue.595, pp.3183-3203, 2003.
DOI : 10.1256/qj.02.132

M. Buehner, Ensemble-derived stationary and flow-dependent background-error covariances: Evaluation in a quasi-operational NWP setting, Quarterly Journal of the Royal Meteorological Society, vol.130, issue.607, pp.1013-1043, 2005.
DOI : 10.1256/qj.04.15

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, vol.57, issue.4, pp.96-100, 2007.
DOI : 10.1175/MWR2946.1

A. M. Clayton, A. C. Lorenc, and D. M. Barker, Operational implementation of a hybrid ensemble/4D-Var global data assimilation system at the Met Office, Quarterly Journal of the Royal Meteorological Society, vol.140, issue.675, pp.1445-1461, 2012.
DOI : 10.1002/qj.2054

C. Liu, Q. Xiao, and B. Wang, An Ensemble-Based Four-Dimensional Variational Data Assimilation Scheme. Part I: Technical Formulation and Preliminary Test, Monthly Weather Review, vol.136, issue.9, pp.3363-3373, 2008.
DOI : 10.1175/2008MWR2312.1

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 I: Description and Single-Observation Experiments, Monthly Weather Review, vol.138, issue.5, pp.1550-1566, 2010.
DOI : 10.1175/2009MWR3157.1

Z. Li and M. Navon, Optimality of 4D-Var and its relationship with the Kalman filter and Kalman smoother, Quart. J. Roy. Meteor. Soc, pp.127-572, 2001.

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.519-1367, 1994.
DOI : 10.1002/qj.49712051912

A. T. Weaver, J. Vialard, and D. L. Anderson, Three- and Four-Dimensional Variational Assimilation with a General Circulation Model of the Tropical Pacific Ocean. Part I: Formulation, Internal Diagnostics, and Consistency Checks, Monthly Weather Review, vol.131, issue.7, pp.131-1360, 2003.
DOI : 10.1175/1520-0493(2003)131<1360:TAFVAW>2.0.CO;2

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

A. Akkraoui, Y. Trémolet, and R. Todling, Preconditioning of variational data assimilation and the use of a bi-conjugate gradient method, Quarterly Journal of the Royal Meteorological Society, vol.127, issue.672, pp.731-741, 2012.
DOI : 10.1002/qj.1997

G. Gaspari and S. E. Cohn, Construction of correlation functions in two and three dimensions, Quarterly Journal of the Royal Meteorological Society, vol.4, issue.2, pp.723-757, 1999.
DOI : 10.1002/qj.49712555417

G. Desroziers, J. Camino, and L. Berre, 4DEnVar: link with 4D state formulation of variational assimilation and different possible implementations, Quarterly Journal of the Royal Meteorological Society, vol.130, issue.684, pp.140-2097, 2014.
DOI : 10.1002/qj.2325

E. Ott, B. R. Hunt, I. Szunyogh, A. V. Zimin, M. C. Kostelich et al., A local ensemble Kalman filter for atmospheric data assimilation, pp.415-428, 2004.

C. Liu, Q. Xiao, and B. Wang, An Ensemble-Based Four-Dimensional Variational Data Assimilation Scheme. Part II: Observing System Simulation Experiments with Advanced Research WRF (ARW), Monthly Weather Review, vol.137, issue.5, pp.1687-1704, 2009.
DOI : 10.1175/2008MWR2699.1

M. Bocquet and P. Sakov, An iterative ensemble Kalman smoother, Quarterly Journal of the Royal Meteorological Society, vol.134, issue.682, pp.1521-1535, 2013.
DOI : 10.1002/qj.2236
URL : https://hal.archives-ouvertes.fr/hal-00918488

S. F. Bradford and B. F. Sanders, Finite-Volume Model for Shallow-Water Flooding of Arbitrary Topography, Journal of Hydraulic Engineering, vol.128, issue.3, pp.289-298, 2002.
DOI : 10.1061/(ASCE)0733-9429(2002)128:3(289)

L. Hascoët and V. , The Tapenade automatic differentiation tool, ACM Transactions on Mathematical Software, vol.39, issue.3, 2013.
DOI : 10.1145/2450153.2450158

D. P. Dee, Bias and data assimilation, Quarterly Journal of the Royal Meteorological Society, vol.125, issue.613, pp.3323-3343, 2005.
DOI : 10.1256/qj.05.137

B. Combès, A. Guibert, E. Mémin, and D. Heitz, Free-surface flows from Kinect: Feasibility and limits, in: FVR2011 -Forum on recent developments in Volume Reconstruction techniques applied to 3D fluid and solid mechanics, 2011.

B. Combes, D. Heitz, A. Guibert, and E. Mémin, A particle filter to reconstruct a free-surface flow from a depth camera, Fluid Dynamics ResearchMinor revision

J. L. Steward, I. M. Navon, M. Zupanski, and N. Karmitsa, Impact of non-smooth observation operators on variational and sequential data assimilation for a limited-area shallow-water equation model, Quarterly Journal of the Royal Meteorological Society, vol.134, issue.663, pp.323-339, 2011.
DOI : 10.1002/qj.935

J. L. Steward, I. M. Navon, M. Zupanski, and N. Karmitsa, Compressed file implementing code for the paper " Impact of nonsmooth observation operators on variational and sequential data assimilation for a limited-area shallow-water equation model, QJRMS, 2014.

E. Mémin, Fluid flow dynamics under location uncertainty, Geophysical & Astrophysical Fluid Dynamics, vol.45, issue.2, pp.119-146, 2014.
DOI : 10.1137/0726003