To what extent is your data assimilation scheme designed to find the posterior mean, the posterior mode or something else?

References

• Bennett A. F . Inverse modeling of the ocean and atmosphere. 2002; Cambridge University Press, Cambridge, United Kingdom. 256.
   Google Scholar
• Bishop C. H. , Hodyss D . Adaptive ensemble covariance localization in ensemble 4D-Var state estimation. Mon. Weather Rev. 2011; 139: 1241–1255.
   Web of Science ®Google Scholar
• Bocquet M. , Sakov P . An iterative ensemble Kalman smoother. Q. J. Roy. Meteorol. Soc. 2014; 140: 1521–1535.
   Web of Science ®Google Scholar
• Buehner M. , Houtekamer P. L. , Charette C. , Mitchell H. L. , He B . Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part I: description and single-observation experiments. Mon. Weather Rev. 2009; 138: 1550–1566.
   Web of Science ®Google Scholar
• Buehner M. , Morneau J. , Charette C . Four-dimensional ensemble-variational data assimilation for global deterministic weather prediction. Nonlin. Processes Geophys. 2013; 20: 669–682.
   Web of Science ®Google Scholar
• Clayton A. M. , Lorenc A. C. , Barker D. M . Operational implementation of a hybrid ensemble/4D-Var global data assimilation system at the Met Office. Q. J. Roy. Meteorol. Soc. 2013; 139: 1445–1461.
   Web of Science ®Google Scholar
• Courtier P . Dual formulation of four-dimensional variational assimilation. Q. J. Roy. Meteorol. Soc. 1997; 123: 2449–2461.
   Web of Science ®Google Scholar
• Courtier P. , Thépaut J.-N. , Hollingsworth A . A strategy for operational implementation of 4D-Var, using an incremental approach. Q. J. Roy. Meteorol. Soc. 1994; 120: 1367–1387.
   Web of Science ®Google Scholar
• El Akkraoui A. , Gauthier P. , Pellerin S. , Buis S . Intercomparison of the primal and dual formulations of variational data assimilation. Q. J. Roy. Meteorol. Soc. 2008; 134: 1015–1025.
   Web of Science ®Google Scholar
• Errico R. M. , Raeder K . An examination of the accuracy of the linearization of a mesoscale model with moist physics. Q. J. Roy. Meteorol. Soc. 1999; 125: 169–195.
   Web of Science ®Google Scholar
• Errico R. M. , Vukicevic T. , Reader K . Examination of the accuracy of a tangent linear model. Tellus A. 1993; 45: 462–477.
   Google Scholar
• Fairbairn D. , Pring S. R. , Lorenc A. C. , Roulstone I . A comparison of 4DVar with ensemble data assimilation methods. Q. J. Roy. Meteorol. Soc. 2014; 140: 281–294.
   Web of Science ®Google Scholar
• Gauthier P . Chaos and quadri-dimensional data assimilation: a study based on the Lorenz model. Tellus. 1992; 44A: 2–17.
   Google Scholar
• Jazwinski A. H . Stochastic Processes and Filtering Theory. 1970; Inc., Mineola, New York: Dover Publications. 376.
   Google Scholar
• Kleist D. T. , Ide K . An OSSE-based evaluation of hybrid variational–ensemble data assimilation for the NCEP GFS. Part II: 4DEnVar and hybrid variants. Mon. Weather Rev. 2015; 143: 452–470.
   Web of Science ®Google Scholar
• Klinker E. , Rabier F. , Kelly G. , Mahfouf J.-F . The ECMWF operational implementation of four dimensional variational data assimilation. Experimental results and diagnostics with operational configuration. Q. J. Roy. Meteorol. Soc. 2000; 126: 1191–1215.
   Web of Science ®Google Scholar
• Kuhl D. D. , Rosmond T. E. , Bishop C. H. , McLay J. , Baker N. L . Comparison of hybrid ensemble/4DVar and 4DVar within the NAVDAS-AR data assimilation framework. Mon. Weather Rev. 2013; 141: 2740–2758.
   Web of Science ®Google Scholar
• Le Dimet F.-X. , Talagrand O . Variational algorithms for analysis and assimilation of meteorological observations. Tellus A. 1986; 38: 97–110.
   Google Scholar
• Lewis J. M. , Lakshmivarahan S. , Dhall S. K . Dynamic data assimilation: a least squares approach. 2006; , Cambridge: Cambridge University Press. 654.
   Google Scholar
• Li Z. , Navon I. M . Optimality of variational data assimilation and its relationship with the Kalman filter and smoother. Q. J. Roy. Meteorol. Soc. 2001; 127: 661–683.
   Web of Science ®Google Scholar
• Lorenc A. C . Analysis methods for numerical weather prediction. Q. J. Roy. Meteorol. Soc. 1986; 112: 1177–1194.
   Web of Science ®Google Scholar
• Lorenc A. C . Development of an operational variational assimilation scheme. J. Meteorol. Soc. Jpn. 1997; 75: 339–346.
   Web of Science ®Google Scholar
• Lorenc A. C . Modelling of error covariances by 4D-Var data assimilation, Q. J. Roy. Meteorol. Soc. 2003a; 129: 3167–3182.
   Google Scholar
• Lorenc A. C . The potential of the ensemble Kalman filter for NWP – a comparison with 4D-Var. Q. J. Roy. Meteorol. Soc. 2003b; 129: 3183–3203.
   Web of Science ®Google Scholar
• Lorenc A. C. , Payne T . 4D-Var and the butterfly effect: statistical four-dimensional data assimilation for a wide range of scales. Q. J. Roy. Meteorol. Soc. 2007; 133: 607–614.
   Web of Science ®Google Scholar
• Lorenc A. C. , Bowler N. E. , Clayton A. M. , Pring S. R. , Fairbairn D . Comparison of hybrid-4DEnVar and Hybrid-4DVar data assimilation methods for global NWP. Mon. Weather Rev. 2015; 143: 212–229.
   Web of Science ®Google Scholar
• Mahfouf J.-F. , Rabier F . The ECMWF operational implementation of four dimensional variational data assimilation. Experimental results with improved physics. Q. J. Roy. Meteorol. Soc. 2000; 126: 1171–1190.
   Web of Science ®Google Scholar
• Navon I. M. , Zou X. , Derber J. , Sela J . Variational data assimilation with an adiabatic version of the NMC spectral model. Mon. Weather Rev. 1992; 120: 1433–1446.
   Web of Science ®Google Scholar
• Payne T. J . The linearization of maps in data assimilation. Tellus A. 2013; 65: 18840.
   Google Scholar
• Pedlosky J . Geophysical Fluid Dynamics. 1987; Springer, New York. 710.
   Google Scholar
• Rabier F. , Järvinen H. , Klinker E. , Mahfouf J.-F. , Simmons A . The ECMWF operational implementation of four-dimensional variational assimilation. I: experimental results with simplified physics. Q. J. Roy. Meteorol. Soc. 2000; 126: 1143–1170.
   Web of Science ®Google Scholar
• Rabier F . Overview of global data assimilation developments in numerical weather-prediction centres. Q. J. Roy. Meteorol. Soc. 2005; 131: 3215–3233.
   Web of Science ®Google Scholar
• Rawlins F. , Ballard S. P. , Bovis K. J. , Clayton A. M. , Li D. , co-authors . The Met Office global four-dimensional variational data assimilation scheme. Q. J. Roy. Meteorol. Soc. 2007; 133: 347–362.
   Web of Science ®Google Scholar
• Rosmond T. , Xu L . Development of NAVDAS-AR: non-linear formulation and outer loop tests. Tellus A. 2006; 58: 45–58.
   Google Scholar
• Sakov P. , Oliver D. S. , Bertino L . An iterative EnKF for strongly nonlinear systems. Mon. Weather Rev. 2012; 140: 1988–2004.
   Web of Science ®Google Scholar
• Talagrand O. , Courtier P . Variational assimilation of meteorological observations with the adjoint vorticity equation. I: theory. Q. J. Roy. Meteorol. Soc. 1987; 113: 1311–1328.
   Web of Science ®Google Scholar
• Tarantola A . Inverse problem theory and methods for model parameter estimation. 2005; , Philadelphia: Society for Industrial and Applied Mathematics. 342.
   Google Scholar
• Tremolet Y . Diagnostics of linear and incremental approximations in 4D-Var, Q. J. Roy. Meteorol. Soc. 2004; 130: 2233–2251.
   Google Scholar
• Wang X. , Lei T . GSI-based four-dimensional ensemble-variational (4DEnsVar) data assimilation: Formulation and single-resolution experiments with real data for NCEP global forecast system. Mon. Wea. Rev. 2014; 142: 3303–3325.
   Web of Science ®Google Scholar
• Zhang X. , Huang X.-Y. , Liu J. , Poterjoy J. , Weng Y. , co-authors . Development of an efficient regional four-dimensional variational data assimilation system for WRF. J. Atmos. Oceanic Technol. 2014; 31: 2777–2794.
   Web of Science ®Google Scholar