References
- Anderson J. L . A non-Gaussian ensemble filter update for data assimilation. Mon. Weather Rev. 2010; 138: 4186–4198.
- Beal D. , Brasseur P. , Brankart J.-M. , Ourmieres Y. , Verron J . Characterization of mixing errors in a coupled physical biochemical model of the North Atlantic: implications for nonlinear estimation using Gaussian anamorphosis. Ocean Sci. 2010; 6: 247–262.
- Bertino L. , Evensen G. , Wackernagel H . Sequential data assimilation techniques in oceanography. Int. Stat. Rev. 2003; 71: 223–241.
- Bocquet M. , Pires C. , Wu L . Beyond Gaussian statistical modelling in geophysical data assimilation. Mon. Weather Rev. 2010; 138: 2997–3023.
- Brankart J.-M. , Testut C.-E. , Beal D. , Doron M. , Fontana C. , co-authors . Towards an improved description of ocean uncertainties: effect of local anamorphic transformations on spatial correlations. Ocean Sci. 2012; 8: 121–142.
- Burgers G. , van Leeuwen P. J. , Evensen G . Analysis scheme in the ensemble Kalman filter. Mon. Weather Rev. 1998; 126: 1719–1724.
- Casella G. , Berger R . Statistical Inference. 2002; 2nd ed, Thompson Learning, California, USA: Duxbury advanced series.
- Cohn S. E . An introduction to estimation theory. J. Meteorol. Soc. Jpn. 1997; 75: 257–288.
- Cover T. M. , Thomas A. J . Elements of Information Theory. 2006; 2nd ed, New York, USA: John Wiley.
- Doron M. , Brasseur P. , Brankart J.-M . Stochastic estimation of biochemical parameters of a 3D ocean coupled physical–biological model: twin experiments. J. Marine Syst. 2011; 87: 194–207.
- Evensen G . Data Assimilation: The Ensemble Kalman Filter. 2006; , Berlin: Springer.
- Genest C. , Rivest L.-P . On the multivariate probability integral transformation. Stat. Probab. Lett. 2001; 53: 391–399.
- Hunt B. R. , Kostelich E. J. , Szunyogh I . Efficient data assimilation for spatiotemporal chaos: a local ensemble transform Kalman filter. Phys. D. 2007; 230: 112–126.
- Ide K. , Courtier P. , Ghil M. , Lorenc A. C . Unified notation for data assimilation: operational, sequential and variational. J. Meteorol. Soc. Jpn. 1997; 75: 181–189.
- Jazwinski A . Stochastic Processes and Filtering Theory.
- Kalman R. E . A new approach to linear filtering and prediction problems. J. Fluids Eng. 1960; 82: 35–45.
- Kalman R. E. , Bucy R . New results in linear filtering and prediction problems. J. Bas. Eng. 1961; 83: 95–108.
- Lien G. Y. , Kalnay E. , Miyoshi T . Effective assimilation of global precipitation: simulation experiments. Tellus A. 2013; 65: 19915.
- Miller R. N. , Carter E. F. , Blue S. T . Data assimilation into nonlinear stochastic models. Tellus A. 1999; 51: 167–194.
- Miller R. N. , Ghil M. , Gauthiez F . Advanced data assimilation in strongly nonlinear dynamical systems. J. Atmos. Sci. 1994; 51: 1037–1056.
- Pires C. A. , Perdigao R . Non-Gaussianity and asymmetry of the winter monthly precipitation estimation from NAO. Mon. Weather Rev. 2007; 135: 430–448.
- Rosenblatt M . Remarks on a multivariate transformation. Ann. Math. Stat. 1952; 23(3): 470–472.
- Simon E. , Bertino L . Application of the Gaussian anamorphosis to assimilation in a 3-D coupled physical-ecosystem model of the North Atlantic with the EnKF: a twin experiment. Ocean Sci. 2009; 5: 495–510.
- Simon E. , Bertino L . Gaussian anamorphosis extension of the DEnKF for combined state parameter estimation: application to a 1D ocean ecosystem model. J. Marine Syst. 2012; 89: 1–18.
- Scholzel C. , Friedrichs P . Multivariate non-normally distributed random variables in climate research – introduction to the copula approach. Nonlin. Proc. Geophys. 2008; 15: 761–772.
- Tippett M. K. , Anderson J. L. , Bishop C. H. , Hamill T. M. , Whitaker J. S . Ensemble square-root filters. Mon. Weather Rev. 2003; 131: 1485–1490.
- Wackernagel H . Multivariate Geostatistics.
- Zhou H. , Gomez-Hernandez J. J. , Hendricks Franssen H.-J. , Li L . An approach to handling non-Gaussianity of parameters and state variables in ensemble Kalman filtering. Adv. Water Resour. 2011; 34: 844–864.