• Andersson E, Cardinali C, Fisher M, Hólm E, Isaksen L, Trémolet Y, Hollingsworth A. 2004. ‘Developments in ECMWF's 4D-Var system’. In: American Meteorol. Soc. Symposium on Forecasting the Weather and Climate of the Atmosphere and Ocean.
  • Bennett A, Chua B, Leslie L. 1996. Generalized inversion of a global numerical weather prediction model. Meteorol. Atmos. Phys. 60: 165178.
  • Courtier P. 1997. Dual formulation of four-dimensional variational assimilation. Q. J. R. Meteorol. Soc. 123: 24492461.
  • Courtier P, Thépaut J-N, Hollingsworth A. 1994. A strategy for operational implementation of 4D-Var, using an incremental approach. Q. J. R. Meteorol. Soc. 120: 13671387.
  • Courtier P, Andersson E, Heckley W, Pailleux J, Vasiljevic D, Hamrud M, Rabier F, Hollingsworth A, Fisher M. 1998. The ECMWF implementation of three dimensional variational assimilation (3D-Var). Part I: Formulation. Q. J. R. Meteorol. Soc. 124: 17831807.
  • Dee D. 1995a. On-line estimation of error covariance parameters for atmospheric data assimilation. Mon. Weather Rev. 123: 11281145.
  • Dee D. 1995b.. ‘Testing the perfect model assumption in variational data assimilation’. In: WMO Symposium on Assimilation of Observations in Meteorology and Oceanography: Tokyo.
  • Dee D, Da Silva A. 1998. Data assimilation in the presence of forecast bias. Q. J. R. Meteorol. Soc. 124: 269295.
  • Derber J. 1989. A variational continuous assimilation technique. Mon. Weather Rev. 117: 24372446.
  • Fisher M. 1998. ‘Minimization algorithms for variational data assimilation’. In: Seminar on Recent Developments in Numerical Methods for Atmospheric Modelling. ECMWF: 364385.
  • Fisher M. 2003. ‘Background error covariance modelling’. In: Workshop on Recent Developments in Data Assimilation for Atmosphere and Ocean, ECMWF: 4563.
  • Fisher M, Leutbecher M, Kelly G. 2005. On the equivalence between Kalman smoothing and weak-constraint four-dimensional variational data assimilation. Q. J. R. Meteorol. Soc. 131: 32353246.
  • Griffith A, Nichols N. 1998. ‘Adjoint methods for treating model error in data assimilation’. In: Numerical Methods for Fluid Dynamics, vol. VI. Institute for CFD: Oxford: 335344.
  • Jazwinski AH. 1970. Stochastic Processes and Filtering Theory. Academic Press.
  • Klinker E, Rabier F, Kelly G, Mahfouf J-F. 2000. The ECMWF operational implementation of four dimensional variational assimilation. Part III: Experimental results and diagnostics with operational configuration. Q. J. R. Meteorol. Soc. 126: 11911215.
  • Le Dimet F-X, Talagrand O. 1986. Variational algorithms for analysis and assimilation of meteorological observations: Theoretical aspects. Tellus 38A: 97110.
  • Mahfouf J-F, Rabier F. 2000. The ECMWF operational implementation of four dimensional variational assimilation. Part II: Experimental results with improved physics. Q. J. R. Meteorol. Soc. 126: 11711190.
  • McNally A. 2003. ‘The assimilation of stratospheric satellite data at ECMWF’. In: ECMWF/SPARC Workshop on Modelling and Assimilation for the Stratosphere and Tropopause: 103106.
  • Rabier F, Järvinen H, Klinker E, Mahfouf J-F, Simmons A. 2000. The ECMWF operational implementation of four dimensional variational assimilation. Part I: Experimental results with simplified physics. Q. J. R. Meteorol. Soc. 126: 11431170.
  • Rodgers C. 2000. Inverse Methods for Atmospheric Sounding. World Scientific.
  • Sasaki Y. 1970. Some basic formalisms in numerical variational analysis. Mon. Weather Rev. 98: 875883.
  • Talagrand O. 1998. ‘A posteriori evaluation and verification of analysis and assimilation algorithms’. In: Workshop on Diagnosis of Data Assimilation Systems, ECMWF: 1728.
  • Talagrand O, Bouttier F. 1999. ‘Internal diagnostics of data assimilation systems’. In: Workshop on Diagnosis of Models and Data Assimilation Systems, ECMWF: 407409.
  • Trémolet Y. 2006. Accounting for an imperfect model in 4D-Var. Q. J. R. Meteorol. Soc. 132: 24832504.
  • Vidard PA, Piacentini A, Le Dimet F-X. 2004. Variational data analysis with control of the forecast bias. Tellus 56: 177188.
  • Zupanski M. 1993. Regional four-dimensional variational data assimilation in a quasi-operational forecasting environment. Mon. Weather Rev. 121: 23962408.
  • Zupanski D. 1997. A general weak constraint applicable to operational 4D-Var data assimilation systems. Mon. Weather Rev. 125: 22742292.