On model error in variational data assimilation

References

[1] S. Akella and I. M. Navon, Different approaches to model error formulation in 4D-Var: a study with high resolution advection schemes. Tellus61A(2009), 112–128.10.1111/j.1600-0870.2008.00362.xSearch in Google Scholar

[2] M. Fisher and P. Courtier, Estimating the covariance matrices of analysis and forecast error in variational data assimilation. ECMWF Research Department Techn. Memo. 220, 1995.Search in Google Scholar

[3] D. Furbish, M. Y. Hussaini, F.-X. Le Dimet, P. Ngnepieba, and Y. Wu, On discretization error and its control in variational data assimilation. Tellus60A(2008), 979–991.10.1111/j.1600-0870.2008.00358.xSearch in Google Scholar

[4] I. Gejadze, L.-X. Le Dimet, and V. Shutyaev, On analysis error covariances in variational data assimilation. SIAM J. Sci. Comput. 30(2008), No. 4, 1847–1874.10.1137/07068744XSearch in Google Scholar

[5] I. Gejadze, F.-X. Le Dimet, and V. Shutyaev, On optimal solution error covariances in variational data assimilation problems. J. Comput. Phys. 229(2010), 2159–2178.10.1016/j.jcp.2009.11.028Search in Google Scholar

[6] I. Gejadze, F.-X. Le Dimet, and V. Shutyaev, Computation of the optimal solution error covariance in variational data assimilation problems with nonlinear dynamics. J. Comput. Phys. 230(2011), 7923–7943.10.1016/j.jcp.2011.03.039Search in Google Scholar

[7] I. Gejadze and V. Shutyaev, An optimal control problem of initial data restoration. Comput. Math. Math. Phys. 39(1999), No. 9, 1416–1425.Search in Google Scholar

[8] I. Gejadze, V. Shutyaev, and F.-X. Le Dimet, Analysis error covariance versus posterior covariance in variational data assimilation. Q. J. R. Meteorol. Soc. 138(2012), 1–16.10.1002/qj.2070Search in Google Scholar

[9] A. K. Griffith and N. K. Nichols, Accounting for model error in data assimilation using adjoint methods. In: Computational Differentiation: Techniques, Applications and Tools(Eds. M. Berz, C. Bischof, G. Corliss, and A. Greiwank). SIAM, Philadelphia, 1996, pp. 195–204.Search in Google Scholar

[10] A. K. Griffith, M. J. Martin, and N. K. Nichols, Techniques for treating systematic model error in 3D and 4D data assimilation. In: Proc. of the Third WMO Int. Symposium on Assimilation of Observations in Meteorology and Oceanography, World Meteorological Organization, 2000, WWRP Report Series No. 2, WMO/TD - No. 986, pp. 9–12.Search in Google Scholar

[11] F.-X. Le Dimet and V. Shutyaev, On deterministic error analysis in variational data assimilation. Nonlinear Processes in Geophysics12(2005), 481–490.10.5194/npg-12-481-2005Search in Google Scholar

[12] F.-X. Le Dimet, V. P. Shutyaev, and I. Gejadze, On optimal solution error in variational data assimilation: theoretical aspects. Russ. J. Numer. Anal. Math. Modelling21(2006), No. 2, 139–152.10.1515/156939806776369492Search in Google Scholar

[13] F.-X. Le Dimet and O. Talagrand, Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus38A(1986), 97–110.10.1111/j.1600-0870.1986.tb00459.xSearch in Google Scholar

[14] J.-L. Lions, Contrôle optimal des systèmes gouvernés par des équations aux derives partielles. Dunod, Paris, 1968.Search in Google Scholar

[15] A. C. Lorenc, Analysis methods for numerical weather prediction, Q. J. R. Meteorol. Soc. 112(1986), 1177–1194.10.1002/qj.49711247414Search in Google Scholar

[16] G. I. Marchuk, V. I. Agoshkov, and V. P. Shutyaev, Adjoint Equations and Perturbation Algorithms in Nonlinear Problems. CRC Press Inc., New York, 1996.Search in Google Scholar

[17] I. M. Navon, Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography. Dynamics of Atmospheres and Oceans27(1997), 55–79.10.1016/S0377-0265(97)00032-8Search in Google Scholar

[18] Y. Sasaki, Some basic formalism in numerical variational analysis. Month. Wea. Rev. 98(1970), No. 12, pp.875–883.10.1175/1520-0493(1970)098<0875:SBFINV>2.3.CO;2Search in Google Scholar

[19] V. P. Shutyaev, F.-X. Le Dimet, and I. Yu. Gejadze, A posteriori error covariances in variational data assimilation. Russ. J. Numer. Anal. Math. Modelling24(2009), No. 2, 161–169.10.1515/RJNAMM.2009.011Search in Google Scholar

[20] A. M. Stuart, Inverse problems: a Bayesian perspective. Acta Numerica19(2010), 451–559.10.1017/S0962492910000061Search in Google Scholar

[21] A. Tarantola, Inverse Problems Theory: Methods for Data Fitting and Model Parameter Estimation. Elsevier, New York, 1987.Search in Google Scholar

[22] W. C. Thacker, The role of the Hessian matrix in fitting models to measurements. J. Geophys. Res. 94(1989), No. C5, 6177– 6196.10.1029/JC094iC05p06177Search in Google Scholar

[23] Y. Trémolet, Accounting for an imperfect model in 4D-Var. Q. J. R. Meteorol. Soc. 132(2007), No. 621, 2483–2504.10.1256/qj.05.224Search in Google Scholar

[24] P. A. Vidard, Vers une prise en compte de lèrreur modèles en assimilation de donnèes 4D-variationnelle. Application à unmodèle réaliste d’océan. Thèse de doctorat, Université Joseph Fourier(Grenoble). December 2001.Search in Google Scholar

[25] P. A. Vidard, E. Blayo, F.-X. Le Dimet, and A. Piacentini, 4D variational data analysis with imperfect model. Flow. Turb. Comb. 65(2000), 489–504.10.1023/A:1011452303647Search in Google Scholar

[26] P. A. Vidard, A. Piacentini, and F.-X. Le Dimet, Variational data analysis with control of the forecast bias. Tellus A56(2004), No. 3, 177–188.10.3402/tellusa.v56i3.14414Search in Google Scholar